University of Southern California Dissertations and Theses

The effects of crystal structure and composition on the magnetism of garnets & phyllosilicates

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The effects of crystal structure and composition on the magnetism of garnets & phyllosilicates

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Content THE EFFECTS OF CRYSTAL STRUCTURE AND COMPOSITION ON THE
MAGNETISM OF GARNETS & PHYLLOSILICATES
by
JoAnna Milam-Guerrero
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMISTRY)
December 2020
Copyright 2020 JoAnna Milam-Guerrero
for Victor & Maximilian
ii
Acknowledgments
I’ve been told that I can be terse. I disagree.
To everyone - thank you.
Much like raising a child, it [a PhD] takes a village.
iii
Contents
Page
Dedication ii
Acknowledgments iii
List of Tables vii
List of Figures viii
Abstract x
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Garnet Oxides as Type II Multiferroics . . . . . . . . . . . . 3
1.1.2 Magnetic Properties of Transition Metal Phyllosilicates for
Structural Understanding . . . . . . . . . . . . . . . . . . . 7
1.2 Crystal Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Garnet Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Phyllosilicates . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Basics of Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Magnetism in Garnets: A Historical Overview . . . . . . . . . . . . 14
1.4.1 Single Magnetic Site . . . . . . . . . . . . . . . . . . . . . . 14
1.4.2 Multiple Magnetic Sites . . . . . . . . . . . . . . . . . . . . 18
1.5 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Canting of the O
h
moments in response to diamagnetic cation
substitution in YIG 22
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Structure Determination . . . . . . . . . . . . . . . . . . . . 23
2.2.3 Physical Property Measurements . . . . . . . . . . . . . . . 23
2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 24
iv
2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . 32
3 Rare earth and diamagnetic cation substitution in YIG 35
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.2 Structure Determination . . . . . . . . . . . . . . . . . . . . 36
3.2.3 Physical Property Measurements . . . . . . . . . . . . . . . 37
3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . 42
4 Short-Range Magnetic Correlations within the T
d
Sublattice of
Garnets 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.2 Structure Determination . . . . . . . . . . . . . . . . . . . . 46
4.2.3 Physical Property Measurements . . . . . . . . . . . . . . . 46
4.2.4 RMC-SPINVERT . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . 57
4.5.1 RMC - SPINVERT . . . . . . . . . . . . . . . . . . . . . . . 57
4.5.2 Magnetic Structures . . . . . . . . . . . . . . . . . . . . . . 59
5 Magnetism & dielectric effects in a tetrahedrally coordinated gar-
net with Co
2+
67
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.2.2 Structure Determination . . . . . . . . . . . . . . . . . . . . 68
5.2.3 Physical Property Measurements . . . . . . . . . . . . . . . 69
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.5 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . 79
6 Transition metal phyllosilicate magnetism 83
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.2.1 Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
v
6.2.2 Structure Determination . . . . . . . . . . . . . . . . . . . . 86
6.2.3 Physical Property Measurements . . . . . . . . . . . . . . . 86
6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.5 Supplemental Information . . . . . . . . . . . . . . . . . . . . . . . 93
References 98
vi
List of Tables
Page
1.1 Table of common garnet cations per site . . . . . . . . . . . . . . . 10
2.1 CaY
2
ZrFe
4
O
12
Rietveld refinement results . . . . . . . . . . . . . . 27
2.2 CaY
2
ZrFe
4
O
12
vector components in Γ
9
. . . . . . . . . . . . . . . . 34
4.1 Ca
2
MZr
2
Fe
3
O
12
vector components in Γ
4
. . . . . . . . . . . . . . . 60
4.2 CaY
2
Zr
2
Fe
3
O
12
Rietveld refinement statistics . . . . . . . . . . . . 61
4.3 CaLa
2
Zr
2
Fe
3
O
12
Rietveld refinement statistics . . . . . . . . . . . . 62
5.1 Ca
3
Te
2
Co
2
ZnO
12
Rietveld refinement statistics . . . . . . . . . . . 71
5.2 Ca
3
Te
2
Co
2
ZnO
12
vector components in Γ
3
. . . . . . . . . . . . . . 79
5.3 Ca
3
Te
2
Co
2
ZnO
12
Curie-Weiss statistics . . . . . . . . . . . . . . . . 79
6.1 Curie-Weiss analysis results of transition metal clays . . . . . . . . 88
vii
List of Figures
Page
1.1 Multiferroic schematic . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Geometric magnetic frustration schematic . . . . . . . . . . . . . . 6
1.3 Garnet crystal structure . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Phyllosilicate crystal structure . . . . . . . . . . . . . . . . . . . . . 11
1.5 Types of magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.6 Garnet cubic sublattice network . . . . . . . . . . . . . . . . . . . . 15
1.7 Garnet intra- and inter-rod connectivity . . . . . . . . . . . . . . . 16
2.1 CaY
2
ZrFe
4
O
12
DCMS . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 CaY
2
ZrFe
4
O
12
heat capacity and Arrott plots . . . . . . . . . . . . 26
2.3 Neutron powder diffraction refinement of CaY
2
ZrFe
4
O
12
. . . . . . 28
2.4 CaY
2
ZrFe
4
O
12
magnetic structure . . . . . . . . . . . . . . . . . . . 29
2.5 CaY
2
ZrFe
4
O
12
ACMS . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.6 CaY
2
ZrFe
4
O
12
magnetic contribution difference plot . . . . . . . . . 33
3.1 CaTb
2
ZrFe
4
O
12
DCMS and M-H . . . . . . . . . . . . . . . . . . . 38
3.2 CaTb
2
ZrFe
4
O
12
neutron powder diffraction pattern . . . . . . . . . 39
3.3 CaTb
2
ZrFe
4
O
12
ACMS . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 CaTb
2
ZrFe
4
O
12
specific heat . . . . . . . . . . . . . . . . . . . . . . 41
3.5 Field-cooled CaTb
2
ZrFe
4
O
12
under heating and cooling . . . . . . . 43
3.6 CaTb
2
ZrFe
4
O
12
neutron diffraction pattern nuclear refinements . . 44
3.7 CaTb
2
ZrFe
4
O
12
neutron powder diffuse scattering . . . . . . . . . . 44
4.1 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
DCMS . . . . . . . . . . . . . 48
4.2 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
X-ray and neutron diffraction
pattern refinements . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 CaY
2
Zr
2
Fe
3
O
12
andCaLa
2
Zr
2
Fe
3
O
12
multipletemperatureneutron
diffraction data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 CaY
2
Zr
2
Fe
3
O
12
magnetic structure . . . . . . . . . . . . . . . . . . 52
4.5 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
specific heat . . . . . . . . . . 54
4.6 CaY
2
Zr
2
Fe
3
O
12
18 K RMC refinement . . . . . . . . . . . . . . . . 55
4.7 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
Rietveld refinements . . . . . 63
viii
4.8 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
M-H . . . . . . . . . . . . . . 64
4.9 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
ACMS . . . . . . . . . . . . . 64
4.10 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
diffuse scattering . . . . . . . 65
4.11 CaY
2
Zr
2
Fe
3
O
12
spin correlation plot . . . . . . . . . . . . . . . . . 65
4.12 CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
magnetic structures . . . . . 66
5.1 Ca
3
Te
2
Co
2
ZnO
12
X-ray and neutron powder diffraction refinements 70
5.2 Ca
3
Te
2
Co
2
ZnO
12
DCMS . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Ca
3
Te
2
Co
2
ZnO
12
neutron diffraction data . . . . . . . . . . . . . . 73
5.4 Ca
3
Te
2
Co
2
ZnO
12
magnetic structure illustrations . . . . . . . . . . 73
5.5 Ca
3
Te
2
Co
2
ZnO
12
magnetic vector illustrations . . . . . . . . . . . . 74
5.6 Ca
3
Te
2
Co
2
ZnO
12
specific heat . . . . . . . . . . . . . . . . . . . . . 76
5.7 Ca
3
Te
2
Co
2
ZnO
12
dielectric measurements . . . . . . . . . . . . . . 77
5.8 Ca
3
Te
2
Co
2
ZnO
12
multiple temperature refinements using Γ
3
. . . . 80
5.9 Ca
3
Te
2
Co
2
ZnO
12
magnetic specific heat and entropy . . . . . . . . 81
5.10 Ca
3
Te
2
Co
2
ZnO
12
ACMS . . . . . . . . . . . . . . . . . . . . . . . . 82
5.11 Ca
3
Te
2
Co
2
ZnO
12
Curie-Weiss Results . . . . . . . . . . . . . . . . . 82
6.1 Phyllosilicate powder XRD . . . . . . . . . . . . . . . . . . . . . . . 87
6.3 Ni
3
Si
2
O
5
(OH)
4
,Co
3
Si
2
O
5
(OH)
4
,Fe
2
Si
4
O
10
(OH)
2
Curie-Weissanal-
ysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2 Transition metal clays DCMS and M-H . . . . . . . . . . . . . . . . 94
6.4 Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
, and Fe
2
Si
4
O
10
(OH)
2
specific heat 95
6.5 1:1 and 2:1 phyllosilicate crystal structures . . . . . . . . . . . . . . 96
6.6 Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
, and Fe
2
Si
4
O
10
(OH)
2
ACMS . . . 97
ix
Abstract
This collection of works presents the knowledge we have gained relating crystal
structures to magnetic properties within the garnet and 1:1 phyllosilicate struc-
tures in the context of building a fundamental understanding of magnetism and
characterization. Chapters 2, 3, and 4 explore CaY
2
ZrFe
4
O
12
, CaTb
2
ZrFe
4
O
12
and Ca
2
MZr
2
Fe
3
O
12
(M = Y, La), respectively, as derivatives of Y
3
Fe
5
O
12
with
interrupted superexchange pathways.
Chapter 2 establishes the supposition that isolation of magnetism to a single
sublattice will result in antiferromagnetism, but multiple sublattice magnetism
results in ferrimagnetism.
1
Chapter 3 explores the effects of adding Tb
3+
onto
the cubic site creating the novel garnet CaTb
2
ZrFe
4
O
12
. This composition builds
upon the knowledge gained about the importance of the intrarod interaction path-
ways (A−B) with the added bonus of an f-electron containing cubic site that
provides additional magnetic exchange pathways and results in a unique mag-
netic susceptibility curve. To complete our understanding of the competitions
between the various sublattice exchange pathways, we present CaY
2
Zr
2
Fe
3
O
12
and
CaLa
2
Zr
2
Fe
3
O
12
in chapter 4 with magnetic cations isolated solely to the tetrahe-
dral sublattice.
x
Chapter 5 explores the fundamental magnetism of Ca
3
Te
2
Co
2
ZnO
12
while
chapter 6 explores the effects of morphology and composition changes in phyl-
losilicates.
ThemagneticstructureofCa
3
Te
2
Co
2
ZnO
12
wasdeterminedthroughtherefine-
ment of representational analysis against neutron powder diffraction data resulting
in a non-collinear magnetic structure that has a spiral spin motif around the rods
along the body diagonals of the unit cell. In the phyllosilicates, each transition
metal behaves as expected, based on element mass susceptibility and metal-oxide
literature precedence, within the edge-shared metal octahedral sheets using Curie-
Weiss analysis.
2
However, due to scrolling or stacking faults and thus magnetic
coupling between the metal sheets, the magnetic properties evolve into more com-
plex interactions such as metamagnetism or 2D magnetic ordering.
This study lays the groundwork for established information about the magnetic
exchange interactions and perhaps thus provides groundwork for design rules for
garnets and phyllosilicates as functional materials.
xi
Chapter 1
Introduction
This is a story about crystallography.
A story about relating crystal structures to magnetic properties through
painstaking crystallographic analysis with the expressed goal of designing for such
applications as data storage, catalysis, and energy storage.
There are multiple broad themes, like any good story, followed throughout
this document featuring the garnet crystal structure and the phyllosilicate layered
structure. Both structure-types can accommodate nearly any element from the
periodictablewhilemaintainingradicallydifferentcrystalpackingmotifs. Initially,
the garnets will be analyzed in the context of symmetry analysis. This will be
followed by a magnetic comparison of several transition metal phyllosilicates and
their respective morphologies.
The garnet portion starts like any other typical garnet story, with the high-
ordering temperature (T
c
= 565 K) ferrimagnet Y
3
Fe
5
O
12
(YIG).
3,4
By starting
with a high magnetic-ordering temperature sample, we had hoped that while mag-
netic ordering temperature (T
c
) suppression may occur, the T
c
would still be close
to room temperature making it a more practical material for everyday devices and
uses. But before we could selectively design a multiferroic garnet, we first had
to establish a knowledge base of the complex magnetic interactions in these intri-
cate oxides. This was accomplished by Abbey J. Neer (now Dr. Abbey J. Neer)
using several Co
2+
containing compositions and studying the structure-physical
property relationships by changing the diamagnetic backbone of Co
2+
-containing
garnets.
5,6
It is the aim of this thesis to continue expanding that knowledge base
1
through magnetic cation site tuning and magnetic crystallographic site isolation by
careful synthetic control, structural identification, and property characterizations
of garnets using CaM
2
ZrFe
4
O
12
(M = Y, Tb), Ca
2
MZr
2
Fe
3
O
12
(M = La, Y), and
Ca
3
Te
2
Co
2
ZnO
12
.
The investigation of the magnetic properties of phyllosilicates was born out
of curiosity and collaboration to better understand the nature, environment, and
oxidation state of the coordinated metals within structural layers. These materials
represent a large family of ecofriendly, Earth-abundant minerals for a multitude of
applicationsduetotheiruniquelamellarstructure.
7–11
Severaloftheseprettyclays,
in particular Ni
3
Si
2
O
5
(OH)
4
, was investigated by Erica S. Howard (now Dr. Erica
S. Howard) as a potential catalyst for oxidation and in doing so, the local structure
was throughly characterized (a daunting task given the so-called ‘approximate
crystallinity’ of the material).
11
In this thesis, we will correlate Dr. Howard’s well-
characterized clay crystal structure and morphology to the respective magnetic
properties of Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
, and Fe
2
Si
4
O
10
(OH)
2
.
This introductory chapter will outline the motivation and crystal chemistry of
both the garnet oxide and phyllosilicates to provide a broad view of the included
research within the context of the relative magnetic research goals. Furthermore,
a small amount of magnetism background will be discussed to provide the reader
with a basic understanding of magnetism and magnetic concepts.
2
1.1 Motivation
1.1.1 Garnet Oxides as Type II Multiferroics
Aferroicmaterialisdefinedasamaterialthatexperiencesaspontaneous,reversible
feature alignment that may be switched with the application of the coupled phe-
nomenon.
12–14
For example, a material is a ferroelectric when its electric dipoles
align and can be switched with the application of an external electric field. A fer-
romagnetic material is one where the electron spins may be aligned and switched
with the application of an external magnetic field. A multiferroic combines any
two or more ferroic orderings such as the relatively well-known piezoelectric where
the application of stress (electric field) induces an electric polarization (distortion).
Ferroicity and multiferroicity are depicted in Figure 1.1 with each corner occupied
Figure 1.1: The primary ferroic orders, ferroelectricity (P, inner-top yellow),
ferromagnetism (M, inner-right blue), and ferroelasticity (, inner-left red), with
their respective fields (electric (E), magnetic (H), and stress (σ)). Multiferroic
couplings between them are in secondary colored arrows.
by a ferroic ordering and the multiferroic interactions illustrated as orange, purple
and green arrows.
3
A useful coupling would be that of ferromagnets and ferroelectrics resulting
in a magnetoelectric, ideally within a single material. As one might imagine,
a magnetoelectric could be quite useful for such applications as sensors, filters,
and data memory storage where the (electric) magnetic field causes a (magnetic)
electric polarization and vice versa.
15–22
For example, current data storage relies on
a binary based system whereas using a multiferroic magnetoelectric material would
provide an additional two states of memory making a four-state logic system.
19,23
This increase of memory states results in increased computing capacity and gives
the best of both worlds with a fast low-power electrical write option and non-
destructive magnetic reading option.
23
Unfortunately, there exists very few materials that exhibit magnetoelectric
behavior within a single phase, with the most well-known compounds being
Bi
3
Fe
5
O
12
,
16
BiFeO
3
,
24
RMnO
3
where R = Gd, Tb, and Dy,
25
and CoCr
2
O
4
,
26
to
name a few. These compounds are referred to as Type I/II multiferroics.
As the name suggests, there are multiple types of magnetoelectrics:
27
• Type I (Proper) - Magnetism and ferroelectricity have independent sources
• TypeII(Improper)-Themagneticordercausesferroelectricitythroughsym-
metry breaking
• Type III - Domain walls (such as Néel walls) can destabilize neighboring
domains cause degenerate states to become more complex
• TypeIV-Bilayersandcompositesofdifferentferroelectricandferromagnetic
materials
The lack of single phase magnetoelectric diversity was brought up in Nicola
Spaldin’s (née Hill) Why Are There So Few Magnetoelectrics? which renewed
4
interest in both the fundamental studies and practical applications of magneto-
electrics.
28
The challenge arises as ferromagnetism requires unpaired electron spins while
ferroelectricity requires an insulating material (all paired electron spins). This
contraindication is appropriately called the d
0
vs d
n
problem. For example, the
off-centering, or displacement, that must occur in the unit cell of a ferroelectric is
only possible because there are no unpaired electrons to cause coulombic repulsion
between the electrons of the displaced cation and the surrounding anions. For
a ferromagnet, or a magnet in general, unpaired electrons are the source of the
magnetic moment. How these moments behave in an external magnetic field, as
wellashowtheyinteractwitheachother,determinesthepropertiesofthematerials
as discussed below in Section 1.3.
Ultimately, thefundamentalphysicsbehindferromagnetismandferroelectricity
hinder their coexistence within a single phase material due to competing demands;
however, there exists several methods to circumvent the issue of contraindica-
tion including mixing several materials (each with a different property, Type IV
listed above),
15,16
geometric frustration,
29–33
and non-centrosymmetric magnetic
ordering.
34–40
We aim to do this through research and understanding of magnetic
interaction exchange pathways within the garnet crystal structure, as started by
Dr. Neer, to design a single-phase magnetoelectric garnet.
We employ the garnet crystal structure as it has three unique cation sites in a
complex packing motif thereby allowing us to potentially induce geometric frustra-
tion and non-centrosymmetric magnetic ordering. Geometric frustration is most
easily visualized where three electron spins are located at the vertices of a triangle.
One spin is up, one spin is down, and the third electron spin becomes frustrated as
it is unable to find a unique ground state that can satisfy both neighboring spins
5
Figure 1.2: (a) An illustration of geometric frustration as a result of a triangular
framework. (b) A symmetric 1-D crystal structure with an inversion point at “X”
(labeled i). As the atoms are all the same type, the nuclear unit cell is from one
atom to another; however, the magnetic unit cell is seven atoms long and breaks
the spatial inversion. (c) An illustration of how the transverse-conical spin state
can be directed perpendicular to the spontaneous polarization vector thus giving
non-centrosymmetric magnetic ordering.
(Figure 1.2[a]). This frustration results in six degenerate ground states that when
seen in 3D space result in non-collinear orientations of the spins. Non-collinear
magnetic ordering may produce non-centrosymmetric magnetic ordering and thus
a polarization despite having a symmetric crystal structure (Figure 1.2[b]). For
example, in the cubic spinel CoCr
2
O
4
, the helical ordering breaks the spatial inver-
sion symmetry giving a non-centrosymmetric magnetic ordering.
38
This further
supports the path to a single-phase magnetoelectric using the garnet structure
through more exotic means.
In short, contraindication in a single phase material may be overcome by pecu-
liar magnetic structures that induce ferroelectricity. Thus, using the garnet crystal
structure, we try to compositionally tune each cation site and study superexchange
interactions. Fromthatknowledgebasewemaypotentiallytunethemagneticstate
towards a peculiar state with the possibility of multiferroic induction.
6
1.1.2 Magnetic Properties of Transition Metal Phyllosili-
cates for Structural Understanding
As briefly discussed above, phyllosilicates are a rich family of materials that can
accommodate much of the periodic table within a unique lamellar structure there-
fore making them a diverse playground for compositional tuning to specific appli-
cations.
To do this, there must exist a fundamental understanding of the structure-
propertyrelationships. AsanalyzedanddiscussedbyDr. Howard, characterization
of the phyllosilicate structure can be difficult due to its ‘approximate crystallinity’
that requires several techniques such as powder X-ray diffraction (PXRD, both in-
house and synchrotron), neutron pair distribution function (PDF), and X-ray pho-
toelectron spectroscopy (XPS).
11
To further supplement our knowledge and better
understand the bonding and oxidation state of the transition metal clays, magnetic
measurements were employed due to their high sensitivity to minute amounts of
magnetic material such as magnetic impurities. Through methods such as Curie-
Weiss analysis, we can calculate the relative ratios of each oxidation state of a
particular metal that is present in a given compound from the temperature-varied
magnetic susceptibility curve.
41
This is informative to the synthetic procedure as
we can determine the ideal conditions to maximize the stoichiometric Ni
2+
con-
centration in Ni
3
Si
2
O
5
(OH)
4
, for example.
What was originally studied for heterogeneous catalysis
11
can now potentially
be used for other applications as we have gained significant insight into its struc-
ture, magnetism, and capabilities.
7
1.2 Crystal Chemistry
1.2.1 Garnet Oxides
Garnets have the general formula R
3
B
2
A
3
O
12
where the R is the cubic site (12-
coordinate), B is the octahedral site (8-coordinate), and A is the tetrahedral site
(4-coordinate) as illustrated in Figure 1.3(b). All three cation sites experience
both corner and edge-sharing connectivity as the BO
6
octahedra are surrounded
by alternating corner sharing AO
4
tetrahedra and edge-sharing RO
8
that bridge
the neighboring octahedral together. This connectivity creates so-called ‘rods’
Figure 1.3: (a) Unit cell illustration of the garnet crystal structure with the
cubic site depicted as a hard sphere (dark green). (b) From left to right, the
unique garnet cation sites are: cubic (dark green, 8 coordinate), octahedral (sage, 6
coordinate), and tetrahedral (blue, 4 coordinate). (c) The octahedral site occupies
the center of the rod. (d) When looking along a rod, the octahedra are surrounded
by dodecahedra (cubic) and tetrahedra.
8
in the unit cell that were described by Andersson and O’Keefe in 1975.
42
Thus
garnets are rarely discussed in terms of close-packed systems of spheres but rather
as rods as illustrated in Figure 1.3(c). As the rods follow the body diagonals
of the cubic cell, there are four degenerate rods that create a basketweave-like
pattern. It is interesting to note that cubic subgroups of the garnet space group
Ia
¯
3d (#230) frequently exhibit some form of rod-packing, with examples including
Th
3
P
4
(I
¯
43d, #220),β-Mn (P 4
1
32, #213), and bixbyite (Ia
¯
3, #206).
43
It is these
rods that dominate many of the magnetic interactions and determine the physical
properties that garnets exhibit; those that will be the focus of this thesis.
Aswithanycrystalsystem, atomicdisorderplaysanimportantroleinelucidat-
ing the structure-property relationships and such disorder is common in garnets.
There exists no specific design rules for the garnet such as the ones that exist for
the perovskite, making composition design and tuning more challenging. Each site
can accommodate a large number of elements from the periodic table, with consid-
eration to cation size per polyhedral site, making the garnet quite compositionally
diverse. Using cation size as a guide, there are cations that have site specificity
that may be exploited, for example, to force otherwise site ambiguous cations onto
a specific site. For example, to isolate Co
2+
to a specific site one might consider
Te
6+
or Zr
4+
for the octahedral site or Zn
2+
for the tetrahedral site thus forcing
the cobalt to either the tetrahedral or octahedral site respectively. Table 1.1 out-
lines, in our experience within the garnet crystal structure, the site preferences for
common cations.
With multiple cation sites capable of accommodating both magnetic and non-
magnetic cations, the garnet crystal structure is a virtual playground to explore
complex magnetic interactions and how various changes in the pathways alter the
interactions between the electron spins.
9
Table1.1: Tableofionsfrequentlyfoundinthecubic, octahedral, andtetrahedral
sites of garnet with their respective number of d electrons.
Cation Valence R-Site C
b
B-Site O
h
A-Site T
d
Ga
3+
d
10
× ×
Zn
2+
d
10
×
Cu
2+
d
9
× ×
Ni
2+
d
8
× ×
Co
2+
d
7
× × ×
Fe
2+
d
6
× ×
Fe
3+
d
5
× ×
Mn
2+
d
5
× ×
Cr
3+
d
3
×
V
3+
d
2
×
Ti
3+
d
1
×
Al
3+
d
0
× ×
1.2.2 Phyllosilicates
Phyllosilicates are sheet materials with alternating silicate and metal oxide lay-
ers. The silicate layer consists of SiO
4
tetrahedra joined at three corners to make
six-membered rings and the metal oxide layer consists of edge-shared metal octa-
hedra that also form a hexagonal motif. When viewing along the c-axis, the two
hexagonal layers are slightly offset such that there exists a hexagonal hole at the
center of three joined octahedra and the SiO
4
ring, Figure 1.4(c). The two layers
are connected by a shared apical oxygen along the ab-axis. It should be noted
that the apical oxygen always points towards the metal layer which is also most
often coordinated with hydroxyls such as those seen sitting in the hexagonal hole
in Figure 1.4(d). Additionally, again due to the layered motif, these materials
have many exposed surfaces available for reactions such as those hydroxyl groups.
Despite the simplicity of these layered structures, phyllosilicates possess the ability
to contain a diverse array of elements and therefore may be compositionally tuned
to a specific application.
10
Figure1.4: Thephyllosilicatecrystalstructureiscomprisedofalternatingcorner-
shared SiO
4
tetrahedral rings(gray) (a) and edge-shared metal octahedra (teal)
(b). (c) Looking along the c-axis, the apical oxygen that joins the metal layer sits
directly under the Si atom and the hydroxyl nested within the hexagonal hole of
the silicate sheet can be seen in black. (d) The layers are held together by weak
hydrogen bonding by the surface hydroxyl groups (black).
Phyllosilicates have two major subcategories based on different layering pat-
terns: 1:1 and 2:1 phyllosilicates. 1:1 phyllosilicates have one tetrahedral layer for
every one octahedral layer whereas 2:1 phyllosilicates have two tetrahedral layers
for every one octahedral layer, with the 1:1 depicted in Figure 1.4(d).
Owing to low temperature synthesis, there exists a significant amount of mor-
phologicalcontrolavailablethroughsyntheticandcompositionalconditions. When
there exists size mismatches within this structure, specifically between the tetra-
hedral and octahedral layers, interlayer strain is introduced allowing the particles
to be anything from planar, rolled, helical, or nanotubular.
11
This variation of
11
morphology is accessible as the silicate tetrahedral layer is flexible and can accom-
modate strains by rocking, scrolling, or expanding.
11
Through precise synthetic and morphological control we can correlate magnetic
trends based on structure and particle shape. Exploring such complex interactions
may aid in guiding the design of functional phyllosilicates through better under-
standing of the structure and how various alterations to morphology change the
interactions between the electron spins.
1.3 Basics of Magnetism
Magnetism in a material originates from contributions from all the magnetic
moments of each atom within the material itself. In simplest terms, the magnetic
moments exist because unpaired electrons on atoms have orbital angular (L), spin
angular (S), and total angular momentum (J).
2
Each electron spin interacts with
its immediate environment (itself, nuclear, and non-magnetic atoms) as well as
with other unpaired electron spins. How these moments respond to an external
magnetic field, as well as how they interact with each other, determines the type
of magnetism a material contains.
2,44
For example (illustrated in Figure 1.5), a
material is paramagnetic if all the electron spins are randomly oriented, ferromag-
netic if aligned all in the same direction, antiferromagnetic if aligned antiparallel
(thus canceling out the overall moment), or ferrimagnetic if the spins are aligned
antiparallel but with different magnitudes (resulting in partial cancellation of the
overall moment).
To determine the type of magnetism in a sample, typically, temperature-
dependent DC magnetic susceptibility is taken. DC susceptibility is a useful, static
field technique where a small field is used to overcome any residual fields trapped
12
Figure1.5: Illustrationsofnon-collinearandcollinearspins. Unitcellsareshown,
where applicable, using black lines.
in the magnet, but kept small enough to avoid altering any low field magnetization
order. As the temperature decreases, the thermal energy is no longer sufficient to
disrupt the cooperative ordering of the spins, which leads the spins to ‘snap’ into
place forming an ordered structure. The temperature at which the spins align is
referred to as the ordering temperature (T
c
or T
N
) and depending on the type of
magnetism the material exhibits, there will be signature features in the magnetic
susceptibility curves at T
c
.
Most often, and certainly for the purposes of this document, magnetic atoms
interact via superexchange pathways rather than by direct exchange simply
because they are in an ionic solid, including oxides and fluorides.
2
A superex-
change pathway is an indirect exchange interaction between non-neighboring mag-
netic ions which is mediated by non-magnetic ions, in the case of garnet oxides by
diamagnetic oxygen ligands. Essentially, the direction of one spin influences the
spin on an oxygen which in turn influences a spin on another cation and so on.
13
These long range pathways, many of which are degenerate in energy, allow spins to
interact with each other quite strongly and have proven to result in exceptionally
complex magnetic properties.
1.4 Magnetism in Garnets: A Historical
Overview
Simultaneously in the mid-1950s, Bertaut and Geller independently recognized
that yttrium iron garnet (YIG, Y
3
Fe
5
O
12
) exhibited ferrimagnetic order with a
Curie temperature around 545 K.
3,4
This has been followed by extensive research
and numerous articles using YIG for tunable microwave devices,
45
phase shifters,
46
tunable filters,
47
circulators,
48
magnetoresistors,
46
and magneto optical imaging in
superconductors
49
to name just a few. This single material opened the door for
a vast amount of research into many different compositions of garnets and their
magnetic properties.
In the following, we highlight the various exchange pathways that exist within
the garnet structure, considering magnetic cations isolated on each sublattice as
well as the fully magnetic and site-mixed garnets.
1.4.1 Single Magnetic Site
Arguably one of the most well studied garnets is Gadolinium Gallium Garnet
(GGG), where the magnetic cations are isolated to the cubic site. GGG is a
good example of single site magnetism as Gd
3+
is a J = S (L = 0) system and
therefore can be treated as a classical Heisenberg model with antiferromagnetic
interactions.
50
As with FeSc
2
S
4
, GGG is a prime spin liquid candidate with no long
range ordering down to 25 mK and exhibits frustration-induced spin freezing below
14
125 mK.
30,51
This behavior can be directly attributed to its structural topology;
specifically, triangular prisms that form from the faces of the cubic site and align
such that a hyper-Kagomé lattice is created as seen in Figure 1.6 (a). GGG also
exhibits a rich phase diagram that results from long range dipolar interactions as
well as second and third nearest neighbor exchange interactions.
29,52–54
Many other rare-earth gallium garnets exhibit Néel temperatures below
1K.
52,55
Tb
3
Ga
5
O
12
is a particularly interesting system with Ising-like spins that
point, within local axes, in three orthogonal directions in the triangular sublat-
tice.
56
Ho
3
Ga
5
O
12
is another example of a garnet containing Ising moments and
was originally thought to be a good example of spin ice; however, the ground state
has been determined to be a complex mixture of long- and short-range clusters.
50
Garnets with transition metals on the cubic site have been typically reported
to order between 4 and 15 K due to strong intrasublattice interactions like those
found in Mn
3
Al
2
Ge
3
O
12
and Mn
3
Al
2
Si
3
O
12
.
57–59
Lau et al. compared the magnetic
properties of crystalline and glassy Mn
3
Al
2
Si
3
O
12
and found magnetic frustration
(a) (b)
Figure 1.6: The connectivity of the cubic sublattice results in geometric frustra-
tion systems. (a) An illustration of geometric frustration as a result of a triangular
lattice geometry created from the cubic sublattice along the rods (body diago-
nals). (b) Neighboring rods share a common edge-shared cubic site pictured in the
middle.
15
Figure 1.7: (a) Within a rod, the magnetic octahedral sublattice super-exchange
pathway is through the oxygens of the cubic site. (b) Between neighboring rods,
the tetrahedral’s oxygen then facilitates the exchange.
6
present in the glass whereas the crystalline sample showed no appreciable sup-
pression of its ordering temperature.
57
In this case, the presence of frustration in
the glass rather than the crystalline form was attributed to the greater degree of
structural disorder that interrupts the superexchange pathways in the material.
57
Incontrasttothecubicsite, theoctahedralpositionsitsatthecenteroftherods
described earlier and can therefore be categorized as occurring within a single rod,
Figure 1.7 (a), or between neighbors, Figure 1.7 (b). Dr. Neer reported the obser-
vation of quasi-one-dimensional magnetic order in the garnet CaY
2
Co
2
Ge
3
O
12
,
where the Co
2+
ions on the octahedral site adopt a highly anisotropic antiferro-
magnetic ground state with the moments fixed along the body diagonals of the unit
cell.
5
This alignment of the moments forms discrete antiferromagnetic chains that
undergo a magnetic-field driven quantum critical phase transition above fields of
6T. This motivated further interest in analogous materials with Co
2+
ions on the
octahedral site as a comparison where only the diamagnetic portions of the host
structure were varied, as seen in NaCa
2
Co
2
V
3
O
12
. Only a modest suppression of
16
the ordering temperature is seen in these phases, with a frustration index around
6, and is understood by considering that garnets consist of a network ofBO
6
octa-
hedra bound together at their corners by AO
4
tetrahedra and RO
8
dodecahedra
on the edges. Given the lack of direct connectivity between adjacent sites, more
complex superexchange pathways must mediate the magnetic interactions either
through the tetrahedral/cubic sites or along the edges of the polyhedra through
super-superexchange pathways that closely resemble those seen for theA–B inter-
actions in spinel [see Figures 1.7 (a) and (b)]. Yet, unlike spinels, an analogous
superexchange pathway also exists through the cubic site B–X–R–X–B so the
presence of so many competing exchange pathways likely causes the modest sup-
pression of the ordering temperature seen for the octahedral site.
Isolating magnetism to the tetrahedral site proves to be a difficult task as there
are few magnetic cations that have a strong preference for that site in garnets.
Instead, this site segregation is commonly achieved by targeting cations that prefer
to occupy the cubic or octahedral site such as Ca, Cr, Te, and Zr, and thereby
forcing the other ion to remain tetrahedral. Dodokin et al. studied “single lattice”
garnets (Na
3
Te
2
Fe
3
O
12
, Ca
3
SnSbFe
3
O
12
, NaCa
2
Sb
2
Fe
3
O
12
, and Ca
3
ZrSbFe
3
O
12
)
using Mossbauer spectroscopy to compare the intrasublattice exchange integrals
to those of YIG.
60
Below the T
N
, the spectra split by the magnetic hyperfine
interactionsleadingtospecificdistancesbetweenthespectrallinesthatindicatethe
Fe
3+
magnetic moments do not lie in the [111] direction like those of YIG.
60
It was
found that decreasing the lattice parameter in these systems generally increased
the ordering temperature, as would be expected for increasing the orbital overlap
with the diamagnetic oxygen ions. Additionally, Dodokin and coworkers
60
showed
that molecular-field theory aptly describes the temperature dependence of the
terahedral sublattice by demonstrating that the effective field (H
eff
(T)/H
eff
(0))
17
versus the effective temperature (T/T
N
) condensed to the same line regardless of
composition.
60
1.4.2 Multiple Magnetic Sites
YIG has been of great interest ever since it was first reported and has found
a multitude of applications such as optical absorption, ferrimagnetic resonance,
passive microwave devices, oscillators, and circulators to name a few.
4,49,61–63
The
presence of Fe
3+
(d
5
) on both the B and A-site incorporate an exceptionally high
number of unpaired spins into the lattice which interact so strongly that they order
at temperatures as high as 545K.
4
The easy axis of the moments is believed to be
along the four body diagonals,h111i with theB andA-site aligning antiparallel to
each other. Interestingly, the low temperature magnetic structure of YIG is well-
known to be incompatible with cubic crystal symmetry and requires a symmetry-
lowering distortion to the trigonal space group, R
¯
3.
64
Geller and coworkers first determined that isolating magnetic moments like
Fe
3+
to either the tetrahedral or octahedral sites creates an antiferromagnetic
coupling within either sublattice, but when spins were present on both the sign of
the coupling changed to become ferromagnetic within itself and antiferromagnetic
to the neighboring sites to result in a ferrimagnetic ground state.
1
More curiously,
they also noted that removal of magnetic cations from either the octahedral or
tetrahedral sublattice of Y
3
Fe
5
O
12
disrupts the ferrimagnetic order and causes a
canting of the moments in the opposite sublattice interactions due to changes in
the local molecular fields. Thus, the shared superexchange pathways that allow
the octahedral and tetrahedral sublattices to communicate with each other create
a highly correlated mechanism for establishing the ground state magnetic structure
that drives magnetic order well above room temperature.
18
Itis, thereforeinterestingtorecognizethatplacingspinsonallthreesitessimul-
taneously often results in more nuanced magnetic order. In particular, the Rare-
Earth Iron Garnets (or RIGs) where Y ions are substituted with magnetic rare-
earths like Tb, Gd, or Dy often show canted ferromagnetic order of the moments
on theR-site ions, which also prefer to align parallel to theB-site and anti-parallel
to theA-site.
4,65–68
These interactions result in a complex temperature-dependent
magnetization that exhibits a compensation point where the susceptibility drops
to zero as the collective order of the moments on theR-site and theB-site are able
to fully cancel out the moments of the tetrahedral ions. Cooling below the com-
pensation point results in a large jump in the magnetization as the large excess of
uncompensatedf spins on the rare earth ions begins to align in a canted ferromag-
netic fashion like the short-range umbrella structures seen by Louca and coworkers
in Tb
3
Fe
5
O
12
.
69
These complex magnetic structures are strongly reminiscent of the
spiral order seen in CoCr
2
O
4
and highlight the subtle compromises that must be
made to simultaneously satisfy so many competing interactions in the solid state.
1.5 Thesis Overview
This collection of works presents the knowledge we have gained relating crystal
structures to magnetic properties within the garnet and 1:1 phyllosilicate struc-
tures in the context of building a fundamental understanding of magnetism and
characterization. Chapters 2, 3, and 4 explore CaY
2
ZrFe
4
O
12
, CaTb
2
ZrFe
4
O
12
and Ca
2
MZr
2
Fe
3
O
12
(M = Y, La), respectively, as derivatives of Y
3
Fe
5
O
12
with
interrupted superexchange pathways. Chapter 5 and 6 explore the fundamental
magnetism of Ca
3
Te
2
Co
2
ZnO
12
and the effects of morphology and composition
changes in phyllosilicates, respectively.
19
Chapter 2 establishes the supposition that isolation of magnetism to a single
sublattice will result in antiferromagnetism, but multiple sublattice magnetism
results in ferrimagnetism.
1
This is seen in CaY
2
ZrFe
4
O
12
where the diamagneti-
cally diluted octahedral magnetic sublattice remains ordered while the magnetic
spins on the tetrahedral site experience temperature-dependent canting despite
having complete magnetic occupation.
Chapter 3 explores the effects of adding Tb
3+
onto the cubic site creating the
novel garnet CaTb
2
ZrFe
4
O
12
. This composition builds upon the knowledge gained
about the importance of the intrarod interaction pathways (A−B) with the added
bonus of an f-electron containing cubic site that provides additional magnetic
exchange pathways and results in a unique magnetic susceptibility curve.
To complete our understanding of the competitions between the various sub-
lattice exchange pathways, we present CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
in
chapter 4 with magnetic cations isolated solely to the tetrahedral sublattice. As
expected, and stated previously, the magnetic spins on the tetrahedral sublat-
tice became antiferromagnetic to each other due to a competition between the
nearest-neighboring tetrahedral sites. Furthermore, these two compositions offer
an interesting comparison for examining the effect of increasing cation size within
the diamagnetic backbone of the garnet crystal structure, and how such changes
affect the magnetic order.
The last garnet crystal system, Ca
3
Te
2
Co
2
ZnO
12
, is explored in chapter 5,
offering a comparison of single tetrahedral sublattice Co
2+
magnetism to those
explored in chapter 4 with single tetrahedral sublattice Fe
3+
magnetism, namely
CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
.
20
Finally, chapter 6 explores the magnetic properties of phyllosilicates to investi-
gate the effects of the changes in morphology and composition. This work demon-
strates that magnetism may aid in guiding the design of functional phyllosilicates
through better understanding of the structure.
21
Chapter 2
Canting of the O
h
moments in response to
diamagnetic cation substitution in YIG
2.1 Introduction
Using neutron powder diffraction and magnetic susceptibility measurements, this
chapter reports on the preparation and characterization of the temperature- and
field-dependent properties of CaY
2
ZrFe
4
O
12
a composition closely related to the
high temperature ferrimagnet Y
3
Fe
5
O
12
. By diluting the concentration of para-
magnetic ions on the octahedral sublattice of the garnet structure, temperature-
dependent canting of the magnetic moments is found. This reflects the importance
of the octahedral sublattice in mediating the magnetic interactions between the
tetrahedral sites and offers insight into the large number of competing magnetic
interactions in the garnet structure.
2.2 Experimental
2.2.1 Synthesis
Polycrystalline samples were synthesized by grinding stoichiometric ratios of
CaCO
3
, Y
2
O
3
, ZrO
2
, and Fe
2
O
3
and pressing into pellets before sintering in air.
All pellets were isolated from the cylindrical zirconia crucible using a layer of sacri-
ficial powder of the same composition as the pellet before heating to 900
◦
C for six
hours in air to decompose the carbonate precursors. After grinding and pressing
22
into pellets again, the samples were heated to 1200
◦
C for 24 hours until phase pure
by laboratory X-ray diffraction.
2.2.2 Structure Determination
Sample purity and potential site-mixing were evaluated using both X-ray and neu-
tron diffraction. Powder XRD was performed at room temperature using 11-BM
at Argonne National Laboratory with a wavelength of λ = 0.414551 Å. Neutron
diffraction data for CaY
2
ZrFe
4
O
12
was collected at the HB-2A high resolution neu-
tron powder diffractometer at High Flux Isotope Reactor at Oak Ridge National
Laboratory. A Ge(113) monochromator with a 90
◦
take-off angle and λ = 2.41 Å
were used. Data was collected over the range of 5.52
◦
-124
◦
in scattering angle (2θ)
with a step size of 0.05
◦
.
2.2.3 Physical Property Measurements
Temperature- and field-dependent DC magnetic susceptibility, AC magnetic sus-
ceptibility, and heat capacity were measured on a Quantum Design 14T Dyna-
cool Physical Property Measurement System. All magnetic measurements were
performed on bulk powder samples that were prevented from rotating under the
applied field using eicosane wax. Specific heat measurements were collected on
powdered samples that had been mixed with equal parts silver in order to increase
the thermal coupling to the sample stage. The contribution of the silver and ther-
mal grease were measured separately and subtracted.
70
23
Figure 2.1: (a) The temperature dependent DC magnetic susceptibility was
taken under 500 Oe from 2 to 400 K. CaY
2
ZrFe
4
O
12
has a room temperature
ferromagnetic-like ordering temperature followed by a broad feature. (b) Isother-
mal magnetizations along the broad susceptibility curve.
2.3 Results and Discussion
Sample purity was evaluated using X-ray and neutron powder diffraction by refin-
ing the structure against each data set separately, with the resulting parameters
of the Rietveld refinement listed in Table 2.1. The resulting fits to the room
temperature data confirmed the archetypal Ia
¯
3d space group (#230) expected for
garnet and showed that the Zr appears homogeneously distributed throughout the
octahedral sites.
Temperature-dependent DC magnetic susceptibility showed an ordering tem-
perature very near 300 K followed by a broad feature in Figure 3.1(a). A minimum
field of 500Oe was necessary to overcome any stray residual fields trapped in the
magnet when reporting zero field, but was maintained as small as possible to avoid
disturbing the ground state. As the temperature is decreased, the thermal energy
24
no longer disrupts the alignment of the moments, which leads to an increase in the
susceptibility as expected for any system containing unpaired spins.
It is commonly accepted that the coupling between the octahedral and tetra-
hedral Fe sites is antiferromagnetic,
1,71,72
in which case a maximum saturation
magnetization of 10 μ
B
per formula unit can be expected in the ordered state;
however, even at temperatures as low as 3K, the magnetization does not appear
to approach these values (see Figure 3.1[b]). Given the disordered nature of the
octahedral site, AC magnetic susceptibility measurements were performed at var-
ious frequencies to look for the presence of glassy magnetic domains (see Figure
2.5). For frequencies of 10, 100, and 1000 Hz, the AC moment (χ’) increases to
a plateau around 250 K, which persists until 40K. Considering the clear lack of
any frequency dependence to susceptibility, the magnetic moments appear to be
tightly locked into their ground state orientation and exhibit no coupling to the
oscillating field.
To more clearly elucidate the temperature where magnetic ordering begins,
isothermalmagnetizationtraceswerecollectedandplottedinthefashionofArrott,
as shown in the lower right inset of Figure 2.2.
73
In this way, the isotherms above
the ordering temperature exhibit a concave curvature whereas those below are
convex, with a linear response resulting at the Curie temperature, which indicates
that a high temperature magnetic phase transition occurs between 285 and 290K.
This magnetization data was then combined with specific heat measurements in
an attempt to quantify the fraction of spins that participate in this magnetic
transition.
As shown in Figure 2.2, the specific heat measurements show no sharp features
from2to375 K,whichwouldbeindicativeofalongrangeorderingofthemagnetic
moments. Rather, the lack of a clear ordering peak indicates that the system does
25
Figure 2.2: The specific heat from 2 to 200 K (main figure, blue) under 0 T
magnetic field has no distinguishable sharp feature that would be indicative of
a magnetic transition. The upper inset (maroon) is the specific heat from 225
to 375 K under 0 T which also does not show a sharp feature. All specific heat
measurementsarenormalizedperFe. ThelowerrightinsetshowsArrottplotsfrom
several isothermal M-H measurements as a way to further determine the ordering
temperature of CaY
2
ZrFe
4
O
12
.
not spontaneously order in a collective manner like what is seen in more traditional
magnetic materials, which would show so-called lambda anomalies in the specific
heat. Instead, the broadness likely results from short range correlations that create
a less coherently ordered magnetic structure through the entire material. This
supports the conclusion that the magnetic structure has canted spins that vary as
a function of temperature.
To better understand the nature of the ordered state in CaY
2
ZrFe
4
O
12
, powder
neutron diffraction was performed at Oak Ridge National Laboratory at 4, 50,
100, and 300 K to examine representative points along the susceptibility curve
(Figure3.1[a]). At room temperature, the neutron diffraction data is fit well using
26
Table 2.1: Results of the Rietveld refinement of CaY
2
ZrFe
4
O
12
against the pow-
der neutron diffraction data. Ca, Y, Zr, and Fe all sit at fixed, special positions
and are therefore not included.
Parameter 4 K 50 K 100 K 300 K
a 12.503(9) 12.515(6) 12.517(7) 12.534(1)
O position 0.028(3) 0.027(8) 0.028(1) 0.028(3)
0.055(2) 0.055(5) 0.054(7) 0.055(8)
0.650(9) 0.650(9) 0.650(4) 0.651(4 )
R
Bragg
2.42 3.67 5.22 2.20
O
h
Fe
#
μ 1.59 1.77 0.73 –
T
d
Fe
#
μ 1.84 2.12 1.92 –
O
h
Fe R
mag
13.30 20.10 21.20 –
T
d
Fe R
mag
5.60 9.43 11.20 –
the nuclear structure of the garnet. No additional peaks associated with scattering
from an ordered magnetic state were observed across this wide temperature range;
however, there is a clear temperature-dependence to the intensity of the magnetic
contribution to several of the nuclear peaks, indicating that the ordered state is
fully commensurate with a propagation vector, k = 0, as seen in Figure 2.3.
The method of representational analysis, as implemented in SARAh,
74
was
used to characterize the magnetic reflections at 27
◦
, 32
◦
, and 42
◦
, which indicated
a one 1D, one 2D and five 3D representations exist within the Little Group G
k
corresponding to a propagation vector k = 0. After evaluating each possible rep-
resentation, it was determined that CaY
2
ZrFe
4
O
12
was best described using the
ninth representation, Γ
9
, which consists of the basis vectors listed in Table 4.1.
The resulting topology of this representation produces a ferrimagnetic ordering
of the spins with the tetrahedral sublattice having a larger magnitude for the
magnetic moment, as seen in Figure 5.4.
Toconfirmtherobustqualityofthefit, thecoefficientswereresetmultipletimes
with different weights on each sublattice as well as varying coefficient signs. It
27
Figure 2.3: (a) Rietveld fitting of neutron powder diffraction powders at 100
K. The green squares, black line, and blue line represent the observed pattern,
fitting line, and difference line respectively. A secondary phase, indexed with green
vertical tick marks, was the Al sample can used in the neutron experiment. (b)
Consistent with the temperature dependent magnetic susceptibility, the magnetic
intensity on the first four lowest reflections first intensifies (from black to green in
the arrow) then decreases as the temperature decreases, with a maximum magnetic
contribution to reflections occurring at 100 K.
28
should be noted that the peak at 27
◦
is associated with the (112) and (211) planes,
which has primary contributions from the octahedral sublattice. In contrast, the
contribution to the peak at 32
◦
mostly results from the tetrahedral sublattice while
the peak at 42
◦
is a convolution of the two. Regardless of starting coefficient,
the refinement continually and consistently settled on the tetrahedral site having
a larger magnetic moment, which was easily monitored as specific planes have
contributions from a single sublattice. It should also be noted that swapping from
anantiferromagnettoaferromagneticcouplingbetweenthetwosublatticesshowed
Figure 2.4: (a) The refined magnetic structure at 50 K. (b) and (c) are the
octahedral and tetrahedral sublattices, respectively, separated to show the relative
canting within each sublattice.
29
very little difference in the quality of the fit, which is attributed to the very small
amount of magnetic scattering for the overall contributions. Nevertheless, there is
no reason to expect the coupling to change from the parent Y
3
Fe
5
O
12
, so the most
likely ground state is still ferrimagnetic, which is consistent with the isothermal
magnetization results in Figure 3.1(b). The intensity of magnetic contributions to
each plane, as a function of temperature, can be seen in Figure 2.3(b) and Figure
2.6 as difference lines. Interestingly, the degree of canting on the octahedral site is
temperature-dependent and increases with increasing temperature. This canting
can be attributed to the dilution of the strength of the octahedral molecular field
that thus weakens the interactions to the point that the sublattice cants with
varying amounts.It should be noted that the analysis of the neutron diffraction
assumes long-range periodicity and the magnetic structures presented are for a
fully ordered state despite the fact that a lambda anomaly is not observed. Given
that the peak width of the magnetic and nuclear reflection at all temperatures
measured, there is clearly some long-range coherence to the magnetic order but
there is also clear evident for some diffuse scattering that extends over a wide 2θ
range indicating even at 300 K.
The observed changes in magnitude and angle of the canting support the sup-
position that the molecular field of the tetrahedra help maintain the order of the
octahedraduetothestrongA–B superexchangeinteractions.
1
Thisistakenincon-
sideration that half of the magnetic octahedral cations have been removed, yet the
system retains long-range order throughout. The strength of the superexchange
pathways are especially germane within the context of the garnet rod-packing
structure as the tetrahedra surround the octahedra with a higher inter-rod con-
nectivity maintained throughout nonmagnetic cation substitution. As early as
30
1964, Geller and coworkers determined that the antiferromagnetic tetrahedral-
tetrahedral (A–A) coupling was stronger than the antiferromagnetic octahedral-
octahedral (B–B) interactions where the system went from an ideal ferrimagnet
(YIG) to a garnet with at a minimum, short-range antiferromagnetic interactions.
1
They further showed that the molecular field of the tetrahedral sublattice played
a critical role maintaining the order of the spins on the octahedral sites. This
observation was first hypothesized by Geller and coworkers while working with
a solid solution of Ca
3
Fe
2
Sn
3
O
12
- YIG, however neutron-diffraction experiments
were not performed at the time to understand the exact magnetic structure and
magnetic interactions in detail.
75
Given the relatively high ordering temperature
of these phases, the ability to induce magnetic canting through simple chemical
substitutions has the potential to open novel pathways for incorporating polar
functionalities into otherwise high-symmetry compounds.
2.4 Summary
The magnetic structure of CaY
2
ZrFe
4
O
12
was determined using neutron powder
diffraction and representational analysis. This phase provides a framework for a
room temperature ferrimagnetic system that exhibits non-trivial magnetic interac-
tions as the spins order followed by a temperature-dependent continuous alteration
of the canting in the long-ranged ordered structure. Disruption of the intrarod
superexchange interactions (A–B) appear to weaken the local molecular field of
the octahedral site and produce a localized canting of the octahedral moments
spins without perturbing the order of the tetrahedral sublattice.
31
2.5 Supplemental Information
Figure 2.5: Variable frequency AC magnetic susceptibility (ACMS) of
CaY
2
ZrFe
4
O
12
.
32
Figure 2.6: Room temperature and 4 K data were subtracted from 100 K data
(the data with the highest magnetic contribution) resulting in difference plots.
These difference plots illustrate the subtleties of which the data was fit with rep-
resentational analysis.
33
Table 2.2: Resulting vector components and total magnetization for each Fe ion within CaY
2
ZrFe
4
O
12
.
k = (0,0,0)
IR Fe position Atom BV components
Γ
9
O
h
1 (2, 0, 0) (0, 2, 0) (0, 0, 2) (0, 2, 0) (0, 0, 2) (2, 0, 0) (0, 0, 2) (2, 0, 0) (0, 2, 0)
2 (2, 0, 0) (0, -2, 0) (0, 0, -2) (0, 2, 0) (0, 0, 2) (-2, 0, 0) (0, 0, 2) (-2, 0, 0) (0, 2, 0)
3 (2, 0, 0) (0, -2, 0) (0, 0, 2) (0, 2, 0) (0, 0, -2) (-2, 0, 0) (0, 0, 2) (2, 0, 0) (0, -2, 0)
4 (2, 0, 0) (0, 2, 0) (0, 0, -2) (0, 2, 0) (0, 0, -2) (2, 0, 0) (0, 0, 2) (-2, 0, 0) (0, -2, 0)
5 (2, 0, 0) (0, 0, 2) (0, 2, 0) (0, 2, 0) (2, 0, 0) (0, 0, 2) (0, 0, 2) (0, 2, 0) (2, 0, 0)
6 (2, 0, 0) (0, 0, -2) (0, -2, 0) (0, 2, 0) (-2, 0, 0) (0, 0, 2) (0, 0, 2) (0, 2, 0) (-2, 0, 0)
7 (2, 0, 0) (0, 0, 2) (0, -2, 0) (0, 2, 0) (-2, 0, 0) (0, 0, -2) (0, 0, 2) (0, -2, 0) (2, 0, 0)
8 (2, 0, 0) (0, 0, -2) (0, 2, 0) (0, 2, 0) (2, 0, 0) (0, 0, -2) (0, 0, 2) (0, -2, 0) (-2, 0, 0)
Γ
9
T
d
1 (4, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 2, 0) (0, 0, 2) (0, 0, 0) (0, 0, 2) (0, -2, 0)
2 (4, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 2, 0) (0, 0, -2) (0, 0, 0) (0, 0, 2) (0, 2, 0)
3 (0, 0, 0) (2, 0, 0) (0, 2, 0) (0, 0, 0) (0, 2, 0) (-2, 0, 0) (0, 0, 4) (0, 0, 0) (0, 0, 0)
4 (0, 0, 0) (2, 0, 0) (0, -2, 0) (0, 0, 0) (0, 2, 0) (2, 0, 0) (0, 0, 4) (0, 0, 0) (0, 0, 0)
5 (0, 0, 0) (2, 0, 0) (0, 0, -2) (0, 4, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 2) (2, 0, 0)
6 (0, 0, 0) (2, 0, 0) (0, 0, 2) (0, 4, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 2) (-2, 0, 0)
7 (0, 0, 0) (2, 0, 0) (0, 0, 2) (0, 4, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 2) (-2, 0, 0)
8 (0, 0, 0) (2, 0, 0) (0, 0, -2) (0, 4, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 2) (2, 0, 0)
9 (4, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 2, 0) (0, 0, -2) (0, 0, 0) (0, 0, 2) (0, 2, 0)
10 (4, 0, 0) (0, 0, 0) (0, 0, 0) (0, 0, 0) (0, 2, 0) (0, 0, 2) (0, 0, 0) (0, 0, 2) (0, -2, 0)
11 (0, 0, 0) (2, 0, 0) (0, -2, 0) (0, 0, 0) (0, 2, 0) (2, 0, 0) (0, 0, 4) (0, 0, 0) (0, 0, 0)
12 (0, 0, 0) (2, 0, 0) (0, 2, 0) (0, 0, 0) (0, 2, 0) (-2, 0, 0) (0, 0, 4) (0, 0, 0) (0, 0, 0
34
Chapter 3
Rare earth and diamagnetic cation substitution
in YIG
3.1 Introduction
As was shown in the previous chapter, diamagnetic cation substitution on the gar-
net octahedral site resulted in temperature dependent spin canting in a long-range
ordered system, highlighting the importance of the octahedral interaction path-
ways. The superexchange intrarod interaction pathways (A–B) were interrupted
thus weakening the local molecular field of the octahedral site. Therefore, we have
established that the tetrahedral sublattice plays a critical role in maintaining the
order ofthe spins onthe octahedral sites. Essentially, theinterruption ofoctahedra
is manifested in the ordering of the tetrahedra as the tetrahedra require octahedral
pathways whereas the octahedra, although magnetically diluted, still have intact
exchange pathways.
To further explore the competing magnetic interactions in the garnet system,
the nonmagnetic Y
3+
was partially replaced with magnetic Tb
3+
on the cubic site
giving the novel CaTb
2
ZrFe
4
O
12
. Due to the connectivity of the garnet structure,
the cubic site is much like the tetrahedral site where it provides a superexchange
intrarod interaction pathway. This pathway, B–X–R–X–B, provides competing
exchange pathways that likely cause in CaTb
2
ZrFe
4
O
12
the slight suppression
of the ordering temperature seen for the octahedral site as compared to that of
CaY
2
ZrFe
4
O
12
. Furthermore, the introduction off-electron magnetism provides a
35
low-temperature compensation point that is a common characteristic of rare-earth
containing garnets; however, the incomplete occupation of several sites by mag-
netic cations produces a unique susceptibility curve with non-collinear magnetic
spins.
3.2 Experimental
3.2.1 Synthesis
Polycrystalline samples were synthesized by grinding stoichiometric ratios of
CaCO
3
, Tb
2
(C
2
O
4
)
3
·10 H
2
O, ZrO
2
, and Fe
2
O
3
and pressing into pellets before
sintering in air. Tb
2
(C
2
O
4
)
3
·10 H
2
O was synthesized by precipitating a solution of
Tb(NO
3
)
3
·6 H
2
O with an excess of oxalic acid, filtering, and drying the resulting
white powder at room temperature overnight. All pellets were isolated from the
cylindrical zirconia crucible using a layer of sacrificial powder of the same compo-
sition as the pellet before heating to 900
◦
C for six hours in air to decompose the
carbon containing precursors. Samples were subsequently heated to 1250
◦
C for 24
hours until phase pure as determined by laboratory X-ray powder diffraction.
3.2.2 Structure Determination
Sample purity and potential site-mixing were evaluated using both X-ray and neu-
tron powder diffraction. Powder XRD was performed at room temperature using
11-BM at Argonne National Laboratory with a wavelength of λ = 0.414551 Å.
Neutron diffraction data was measured at 3, 43, 50, 100, 180, 250, and 295K using
the BT-1 high resolution neutron powder diffractometer at the NIST Center for
Neutron Research. A Ge(311) monochromator with a 75
◦
take-off angle and λ =
36
2.077(5)Å were used. Data was collected over the range of 1.9
◦
-166.2
◦
in scattering
angle (2θ) with a step size of 0.05
◦
.
3.2.3 Physical Property Measurements
Temperature and field dependent DC magnetic susceptibility, AC magnetic sus-
ceptibility, and heat capacity were measured on a Quantum Design 14T Dynacool
Physical Property Measurement System. All magnetic measurements were per-
formed on bulk powder samples held in place using eicosane wax. Heat capacity
measurements were measured on powdered samples mixed with equal parts silver
in order to increase the thermal coupling to the sample stage. The silver and epoxy
contribution were measured separately and subtracted out.
70
3.3 Results and Discussion
The previously unreported garnet CaTb
2
ZrFe
4
O
12
has a unique, complex tem-
perature dependent susceptibility curve with multiple features as seen in Fig-
ure 3.1. The broad feature, with a maximum around 175 K, resembles that of
CaY
2
ZrFe
4
O
12
; however, it then drops to a compensation point, characteristic of
rare-earth iron garnets, at approximately 43 K.
2,70
A compensation point is a fea-
ture where the magnetic susceptibility drops to zero as the collective order of the
moments on one sublattice fully cancels out the moments of another sublattice or
sublattices.
2
Compensation points are most commonly characteristic of rare-earth
iron garnets where the low temperature magnetic contribution is from the tightly-
boundf-electrons.
2
In this case, CaTb
2
ZrFe
4
O
12
has Tb
3+
which has six unpaired
f-electrons. Cooling below the compensation point results in a jump in the mag-
netization as the excess of uncompensated f spins on the rare earth ions begin to
37
Figure3.1: (a)ThetemperaturedependentDCmagneticsusceptibilitywastaken
under 500 Oe from 2 to 400 K. (b) Isothermal magnetizations along the suscepti-
bility curve.
align in a canted fashion similar to those in the short-range umbrella structures
seen by Louca and coworkers in Tb
3
Fe
5
O
12
.
69
The offset between the zero field cooled (zfc) and field cooled (fc) compen-
sation points, best seen in the Figure 3.1(a) inset, indicates a first-order phase
transition, most likely to a lower symmetry tetragonal group similar to the mag-
netic structure of CaY
2
ZrFe
4
O
12
or CaY
2
Zr
2
Fe
3
O
12
. To confirm the existence of
a first-order transition, magnetic susceptibility was taken at 500 Oe under entirely
field-cooled conditions while heating and cooling, as seen in Figure 3.5(b). This
reproducible offset of the compensation point confirms the existence of a first-order
phase transition.
To better understand the nature of the ordered state, powder neutron diffrac-
tion was performed at NIST Center for Neutron Research on beamline BT-1 at
multiple temperatures to gather a sufficient understanding of this dynamic mag-
netic system. At room temperature, the neutron diffraction pattern fits well using
the nuclear structure of the garnet. As the temperature decreases, symmetry
38
Figure 3.2: (a) Neutron powder diffraction at room temperature and below
the ordering temperature showing the magnetic contribution to existing and new
peaks. (b) Neutron powder diffraction patterns taken from room temperature to
3 K, overlaid to show the magnetic peak shifts and growth.
allowed reflection peaks grow in intensity in addition to the appearance of new
peaks as seen in Figure 3.2(a). The existence of new, non-cubic-symmetry allowed
peaks indicates an incommensurate structure. The broadening and shifting of
peaks may be indicative of competing long and short range orderings. Evidence
of short range ordering can be seen at the peak at 36
◦
, where from 300 to 2 K,
significant diffuse scattering develops (Figure 3.7). Additionally, as seen in Figure
3.2(b) inset, the continually growing nuclear peaks shift to higher (2θ) with slight
broadening. Due to its complex nature, the CaTb
2
ZrFe
4
O
12
magnetic structure is
currently being studied using a combination of Irreducible Representation analysis
and Shubnikov symmetry.
76,77
The AC magnetic susceptibility of CaTb
2
ZrFe
4
O
12
results in a comparable
shape to the DC magnetic susceptibility with frequency independent curves. The
39
existence of frequency independent curves eliminates the possibility of glassiness
within the system although further interpretation of the complex χ” is underway.
Figure3.3: TheACmomentatmultiplefre-
quencies as a function of temperatures shows
a frequency-independent curve.
Interestingly, the specific heat of
CaTb
2
ZrFe
4
O
12
, as shown in Fig-
ure 3.4, is remarkably similar to
CaY
2
Zr
2
Fe
3
O
12
(Figure 2.2) with
no sharp features below 200 K. A
sharp, asymmetric lambda-like fea-
ture would traditionally be indica-
tive of a second order phase tran-
sition such as a magnetic order-
ing. We attribute the lack of
notable features to short range cor-
relations that create a less coher-
ently ordered magnetic structure
through the entire material, much like that of CaY
2
ZrFe
4
O
12
. It is notable that
the low temperature slope of the heat capacity has become more linear, making
this, in comparison to CaY
2
ZrFe
4
O
12
, a more ideally behaved ferrimagnet.
70
The
linearity of the slope and the existence of an exponential term in the magnon spe-
cific heat, due to the presence of a magnetic rare earth, makes the separation of
the various terms in the specific heat nontrivial. Thus far, making a non-magnetic
analogue has been unsuccessful. A non-magnetic compositional analogue would
make it possible to subtract out the lattice contributions to heat capacity, thus
isolating the magnetic contribution to entropy.
70
40
Figure 3.4: The specific heat and entropic change of CaTb
2
ZrFe
4
O
12
taken under
zero magnetic field.
3.4 Summary
This chapter represents a continuation of the efforts first discussed in the intro-
duction and chapter 2 where we reduce the magnetism on the octahedral site in
CaY
2
ZrFe
4
O
12
resulting in reduced symmetry and temperature dependent elec-
tron spin canting within the magnetic structure. Maintaining the octahedral and
tetrahedral composition, we then introduce magnetism on the cubic site to explore
the competing exchange pathways between the cubic and tetrahedral sites.
This material contains a complex magnetic structure with competing long
and short range orderings as well as a unique magnetization curve that resem-
bles that of CoCr
2
O
4
, a magnetoelectric where the ferroelectricity is induced by
its magnetic spiral ordering.
38
The complex magnetic structure determination of
CaTb
2
ZrFe
4
O
12
is currently being studied using Irreducible representational anal-
ysis and Shubnikov magnetic space groups applied to neutron powder diffraction
supported with low temperature X-ray powder diffraction. Above liquid nitrogen
41
temperatures, the Fe-containing sublattices provide the dominant magnetic con-
tribution due to their less-tightly boundd-electrons. However, as the temperature
decreases, the more tightly-bound cubicf-electron spins begin to contribute as evi-
denced by the compensation point. The combination of d- and f-electrons causes
long- and short-range interaction competitions indicated by the diffuse scattering
in Figure 3.7 as well as the subtle introduction of new peaks seen in Figure 3.6.
Ultimately, the materials in chapters 2, 3, and 4 provide a framework for a room
temperature ferrimagnetic systems that exhibit non-trivial magnetic interactions
as the spins order in temperature dependent continuous alterations of the canting
in the long-ranged ordered structure.
3.5 Supplemental Information
To confirm the existence and reproducibility of the first order phase transition
seen at the compensation point of 50 K, DC magnetic susceptibility was measured
at 500 Oe under entirely field-cooled conditions while both warming and cooling,
Figure 3.5(b). Within the inset of Figure 3.5(b), it can be seen that an offset, or
hysteresis, remains at the compensation point. A hysteresis like this is caused by
a latent heat of transformation such as those seen in a first-order phase transition.
Rietveld refinements of the nuclear contribution to the neutron powder diffraction
for significant temperatures along the susceptibility curve.
42
Figure 3.5: (a) DC magnetic susceptibility taken under standard zero field and
field-cooled (zfc/fc) conditions under 500 Oe. (b) DC magnetic susceptibility taken
under solely field-cooled (fc) conditions while warming and cooling under 500 Oe.
43
Figure 3.6: (a) Neutron powder diffraction Rietveld refinements at 3 and 50 K.
(b) Neutron powder diffraction Rietveld refinements at 180 and 295 K.
Figure 3.7: Significant diffuse scattering at low theta develops as the temperature
decreases.
44
Chapter 4
Short-Range Magnetic Correlations within the
T
d
Sublattice of Garnets
4.1 Introduction
We present a study on the nuclear and magnetic structures of two iron-based gar-
nets with magnetic cations isolated to the tetrahedral sites. CaY
2
Zr
2
Fe
3
O
12
and
CaLa
2
Zr
2
Fe
3
O
12
offer an interesting comparison for examining the effect of increas-
ing cation size within the diamagnetic backbone of the garnet crystal structure,
and how such changes affect the magnetic order. Despite both systems exhibiting
well-pronounced magnetic transitions at low temperatures, we also find evidence
for significant diffuse magnetic scattering due to a competition between nearest-
neighbor, next nearest-neighbor, and so on tetrahedral sites. This competition
results in an almost spiral-like magnetic structure on the tetrahedral sublattice
creating a mixture of temperature-dependent ferro- and antiferromagnetic interac-
tions above the long-range ordering temperature near 20K.
4.2 Experimental
4.2.1 Synthesis
Polycrystalline samples were synthesized by grinding stoichiometric ratios of
CaCO
3
, Y
2
O
3
, La
2
O
3
, ZrO
2
, and Fe
2
O
3
and pressing into pellets before sinter-
ing in air in multiple heating treatments. All pellets were heated on a layer of
45
sacrificial powder to isolate them from the zirconia crucible. Samples were first
heated to 900
◦
C for 6 hours in air to decompose the carbon containing starting
materials. Samples were subsequently heated at 1250
◦
C for 24 hours in air until
phase pure.
4.2.2 Structure Determination
Sample purity and potential site-mixing were evaluated using both X-ray and neu-
tron diffraction. Powder XRD was performed at room temperature using 11-BM
at Argonne National Laboratory at λ = 0.412797 Å.
Neutron diffraction data was collected at the HB-2A high resolution neutron
powder diffractometer at High Flux Isotope Reactor at Oak Ridge National Labo-
ratory. A Ge(113) monochromator with a 90
◦
take-off angle and λ = 2.41 Å were
used. Data was collected over the range of 5.5
◦
-124
◦
in scattering angle (2θ) with
a step size of 0.05
◦
.
4.2.3 Physical Property Measurements
Temperature– and field–dependent DC magnetic susceptibility, AC magnetic sus-
ceptibility, and heat capacity were measured on a Quantum Design 14T Dynacool
Physical Property Measurement System. All magnetic measurements were per-
formed on bulk powder samples held in place using eicosane wax. Heat capacity
measurements were measured on powdered samples mixed with equal parts silver
in order to increase the thermal coupling to the sample stage. The silver and epoxy
contribution were measured separately and subtracted out.
70
46
4.2.4 RMC-SPINVERT
Since the diffuse magnetic neutron scattering was strongest in the 18 K data of
the CaY
2
Zr
2
Fe
3
O
12
phase this was isolated by removal of the nuclear scattering
through subtraction of the 100 K data set. The data were then placed on an
absolute intensity scale (barn sr
−1
Fe
−1
) by normalisation to the calculated nuclear
Bragg profile from the 100 K data set. This subsequent diffuse magnetic scattering
was then fitted using the reverse Monte Carlo (RMC) program – SPINVERT,
78
using a supercell of 6× 6× 6 units of the crystal structure with a total volume of
442,284 Å
3
. Spins in these refinements were refined as three dimensional vectors,
as expected for tetrahedrald
5
Fe
3+
magnetic cations, with magnetic moments fixed
to 5.92 μ
B
and standard analytical magnetic form factors.
4.3 Results and Discussion
Both compositions exhibit signatures of antiferromagnetic order in the DC mag-
netic susceptibility curve, at 18 and 21 K for CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
respectively. These sharp peaks were followed by broader features around 7 K
(CaY
2
Zr
2
Fe
3
O
12
) and 10 K (CaLa
2
Zr
2
Fe
3
O
12
), as seen in the insets of Figure 4.1.
The presence of two magnetic ordering transitions is not uncommon for materials
containing multiple magnetic sublattices as in Mn
3
Cr
2
Ge
3
O
12
;
79
however, given
that Fe should be fully isolated to the tetrahedral sites care was taken to rule out
the presence of paramagnetic impurities and mixing between the sites.
As such, X-ray and neutron powder diffraction were collected at Argonne and
Oak Ridge National laboratory respectively.
47
Figure 4.1: Temperature dependent DC mag-
netic susceptibility under 500 Oe from 2 to 400
K. (a) CaY
2
Zr
2
Fe
3
O
12
orders at 18 K and (b)
CaLa
2
Zr
2
Fe
3
O
12
orders at 21 K.
Both data sets were care-
fully refined and showed no evi-
dence for any Fe on the octa-
hedral site as demonstrated in
Figure 4.2, with the relevant
parameters from the refinement
given in Tables 4.2 and 4.3.
Neutron powder diffraction
was performed at multiple tem-
peratures to monitor the poten-
tially dynamic magnetic order-
ing anticipated due to the pres-
ence of multiple features in
the DC magnetic susceptibility
curve.
As the temperature is
decreased, symmetry-allowed
magnetic reflections can be
seen in Figure 4.3(a) and
(b) for CaY
2
Zr
2
Fe
3
O
12
and
CaLa
2
Zr
2
Fe
3
O
12
respectively.
The higher angle magnetic
peaks appear below the respective ordering temperatures, 18 and 21 K, suddenly
as is typical for new magnetic peaks where the thermal energy is no longer suffi-
cient to disrupt the cooperative ordering of the spins and thus the spins ’snap’ into
place forming an ordered structure over a relatively small temperature range. This
48
Figure 4.2: Refined X-ray and neutron data of CaY
2
Zr
2
Fe
3
O
12
and
CaLa
2
Zr
2
Fe
3
O
12
in the left and right column respectively. (a) and (b) are Rietveld
refined fits of X-ray powder diffraction powders from 11-BM at 295 K. The red
circles, black line, and blue line represent the observed pattern, fitting line, and
difference line respectively. (c) and (d) are refined fits from the corresponding neu-
tron powder diffraction data at 1.5 K with the vanadium sample can (dark green)
used in the experiment. Nuclear reflections are highlighted in yellow on the first
row while the magnetic reflections are the second row.
contrasts with the peak at 15
◦
, for both samples, where a growing diffuse scattering
peak shifts to lower theta until the sharp appearance of the magnetically ordered
Bragg peak. This diffuse peak continues to grow with decreasing temperature as
well as shifting to slightly lower theta as illustrated in Figure 4.3 and Figure 4.10.
49
Figure 4.3: Symmetry-allowed magnetic peaks appear at (a) 18 K for
CaY
2
Zr
2
Fe
3
O
12
and (b) 21 K for CaLa
2
Zr
2
Fe
3
O
12
. Both compositions have a
dynamic diffuse scattering peak at the (101) reflection (15
◦
) before the systems
order.
At room temperature, and above the ordering temperature, the neutron data
is fit well using the nuclear structure of the garnet, cubic Ia
¯
3d. Below the order-
ing temperature, additional peaks appear at 15
◦
, 47
◦
, 67
◦
, and 84
◦
with magnetic
50
contribution to several of the nuclear peaks at 26
◦
, 35
◦
, and 41
◦
. Representational
analysis was used to fit the neutron data at 1.5 K with the following associated
magnetic reflections at: 15
◦
, 26
◦
, 35
◦
, 41
◦
, 47
◦
, 67
◦
, and 84
◦
. All of the observed
magnetic reflections were indexed using the propagation vector k = 0, but within
the space group R
¯
3c (#167). The space group symmetry was lowered based on
literature and historical precedence where iron garnets have been more accurately
modeled using trigonal space groups.
64,80,81
For example, it has been observed that
the magnetic structure of YIG is not accurately described with cubic crystal sym-
metry, but with space group R
¯
3 for better agreement with bulk magnetometry.
64
R
¯
3c was chosen while exploring the possible subgroups and subgroup pathways to
R
¯
3 using Bilbao Crystallographic Server.
82,83
Symmetry analysis of the magnetic structure was performed using SARAh,
74
which returned five one-dimensional and one two-dimensional representations
within the Little Group G
k
. Both compositions were fit using the fourth rep-
resentation, Γ
4
, as seen fit in Figure 4.2 and illustrated in Figure 4.4. This rep-
resentation consists of the basis vectors, listed in Table 4.1, with a non-collinear
topology that resembles a spiral that winds around and along the rods as seen in
Figure 4.4.
The overall Fe spin magnitude, 3.40 and 3.85 μ
B
at 1.5 K for CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
respectively, is in part supported by the isothermal M-H
measurements, (Figure 4.8), where at sufficiently low temperatures the magnetic
moments per Fe retain paramagnetic attributes with values up to 2.59 and 2.79μ
B
for CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
respectively at 14 T. The lack of complete
spin saturation at 14 T is indicative that the system continues to have incoherent
51
Figure 4.4: The refined magnetic structure of CaY
2
Zr
2
Fe
3
O
12
at 1.5 K. Both
compositions are refined using the same representation where CaLa
2
Zr
2
Fe
3
O
12
can
be visualized in Figure 4.12. (a) Looking along the c-axis, the tetrahedral site
surrounding the rods can be seen as a star-like motif. (b) Looking along thea and
b-axes, top and bottom respectively, the degree of canting can be visualized.
spin distributions or non-collinear distributions thus resulting in a lower-than-
expected overall spin magnitude. The Fe spin moments and experimental M-H
moments are listed and seen in Tables 4.2 and 4.3 and Figure 4.8, respectively.
The overall magnetic moments, for all low temperatures, are larger in the lan-
thanum containing composition, which we attribute to higher covalent character
of the lanthanum cation versus that of the yttrium cation. In an 8-coordinate
environment, lanthanum (III) and yttrium (III) have ionic radii of 1.160 Å and
1.019 Å respectively. The smaller radius of yttrium is sufficient, even at only
one third occupancy of the cubic site, to cause the unit cell to decrease from
12.819(1) Å to 12.710(5) Å (at 295 K from synchroton X-ray powder diffraction)
as well as increasing the octahedral metal-oxygen bond (Zr–O) from 2.085(2) Å to
2.107(2) Å increase the tetrahedral metal-oxygen bond (Fe–O) from 1.881(4)) Å
52
to 1.912(6) Å, and decrease the average cubic metal-oxygen bond from 2.519(0) Å
to 2.484(4) Å. Thus, CaY
2
Zr
2
Fe
3
O
12
contains longer tetrahedral and octahedral
metal-oxygen bonds indicating higher covalency for the lanthanum cation over that
of the yttrium cation.
Typically, due to the crystal structure of the garnet, it is the octahedral sites
that have the largest impact on the superexchange pathways within the mate-
rial; however, in this instance, the cubic site plays a more central role as a cou-
pling pathway. This is best exemplified when comparing the magnetic structures
of each composition at different temperatures. CaLa
2
Zr
2
Fe
3
O
12
experiences a
larger degree of temperature dependent canting while the magnetic structures of
CaY
2
Zr
2
Fe
3
O
12
do not appear to have a significant change in spatial orientation,
as seen in Figure 4.12. So, while the unit cell of CaLa
2
Zr
2
Fe
3
O
12
may be larger,
its shorter octahedral and tetrahedral metal-oxygen bond lengths provide stronger
superexchange pathways, which makes the ordering temperature slightly higher
than that of CaY
2
Zr
2
Fe
3
O
12
. Conversely, since the average cubic metal-oxygen
bond of CaLa
2
Zr
2
Fe
3
O
12
is larger, the magnetic structure undergoes increased
canting changes as a function of temperature. These subtle changes to the radii
directly effect the orbital overlap with the oxygen ligands, and thereby the degree
of covalency, that the material experiences along the diamagnetic backbone and
has an impact on the magnetic ordering temperature.
To further understand the DC magnetization curve of these materials, specific
heat measurements were performed from 2 to 200 K. As shown in Figure 4.5, both
specific heat measurements exhibit a sharp asymmetric lambda-like anomaly at the
respective magnetic ordering temperatures. This type of feature is traditionally
indicative of a second order phase transition, and in this case most likely corre-
sponds to a long-range collective magnetic order transition. The presence of a
53
Figure 4.5: The specific heat of CaY
2
Zr
2
Fe
3
O
12
(top, maroon) and
CaLa
2
Zr
2
Fe
3
O
12
(bottom, blue) have one distinct feature at their respective order-
ing temperatures, thus agreeing well with the magnetic susceptibility.
single feature further supports the conclusion that the spins eventually order in a
collective manner; however, the broad feature DC magnetization is not reflected
in the specific heat measurements, which suggests its origin may be related to
short-range correlations between the spins.
ACmagneticsusceptibilitymeasurementswereusedtoexplorethepossibilityof
short-range ordering or glassy features at various AC frequencies, shown in Figure
4.9. Two maxima occur at the same temperatures as those in the DCMS and as
they are frequency independent, indicate no glassiness within these systems. We
tentatively attribute the broad feature in the DCMS and the diffuse scattering in
the neutron powder diffraction to coexisting local, short-range ordering.
To obtain a greater understanding of the short range magnetic correlation in
these materials in their paramagnetic phase, data was obtained by fitting diffuse
54
magnetic scattering data in CaY
2
Zr
2
Fe
3
O
12
at 18 K, where the magnetic diffuse
scattering was strongest. Consistent results were obtained across a large number
of refinements with a typical fit of χ
2
of 13.5 as seen in Figure 4.6. The nearest-
neighbor correlation is ferromagnetic and all other significant magnetic correla-
tions, that are between atoms separated by less than 10 Å, are antiferromagnetic
as seen in Figure 4.11. There are a number of weak ferromagnetic correlations
between atoms separated by 5-12 Å distances, but these all appear to be associ-
ated with cations connected to each other through a sequence of nearest neighbor
distances and are therefore likely a result of the ferromagnetic nearest neighbor
correlations.
Figure 4.6: RMC fit, using Heisenberg-
like spins, to the diffuse magnetic scatter-
ing of CaY
2
Zr
2
Fe
3
O
12
measured at 18 K.
Data is shown in black, fit in red, and the
difference in green.
Comparison of the correlations
obtained from the paramagnetic phase
and the ordered antiferromagnetic
structure provides a likely explana-
tion for the canting of the T
d
sites
and the role this plays in reducing
the magnetic frustration in this struc-
ture. Examination of any one Fe in the
magnetic structure shows that these
atoms are all aligned ferromagnetically
with their surrounding nearest neigh-
bor cations; this is consistent with the
ferromagnetic correlations in the corre-
lated paramagnetic phase.
After completely removing the magnetic cations from the octahedral site, it
comes as no surprise that the ordering temperature would drop from the 570K
55
seen in YIG to the low temperatures found for Ca
2
MZr
2
Fe
3
O
12
, but it is somewhat
unexpected that the tetrahedral sublattice would order as high as the 20K given
the lack of short superexchange pathways to couple the spins. Yet, extensive work
on ferrimagnets like YIG have clearly shown the antiferromagnetic tetrahedral–
tetrahedral (A−A) coupling is stronger than the antiferromagnetic octahedral–
octahedral (B−B) interactions.
1
So, while the strongest magnetic interactions
are still present, due to the garnet rod packing and lack of direct connectivity of
the tetrahedra the local symmetry of the tetrahedral sublattice is lowered. The
strength of theA−A coupling was exploited as the cubic sublattice was modified
to a more covalent cation and the metal-oxygen bonds decrease enabling greater
super exchange pathways for the magnetic cations and thus increased the ordering
temperature.
4.4 Summary
The magnetic structures of CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
have been deter-
mined through the refinement using irreducible representations against powder
neutron diffraction data, which reveals the co-existence of both long- and short-
range magnetic order. Both compositions order in a non-collinear fashion at 18 K
and 21 K for CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
respectively. The slight shift
in the ordering temperatures, as well as the difference in the magnitude of the
Fe spins, is attributed to the changing character of the orbital overlaps between
Y and La. It is this difference that highlights the rod connectivity of the garnet
crystal structure, in this case the cubic sublattice, and the impact of even slight
compositional tuning on magnetic properties.
56
4.5 Supplemental Information
Powder XRD was performed at room temperature using 11-BM at Argonne
National Laboratory at λ = 0.412797 Å. Neutron powder diffraction data for
both compositions was collected using the HB-2A high resolution neutron pow-
der diffractometer at HFIR at Oak Ridge National Laboratory equipped with a
Ge(113) monochromator with a 90
◦
take-off angle and λ = 2.41 Å. Data was col-
lected over the range of 5.5
◦
-124
◦
in scattering angle (2θ) with a step size of 0.05
◦
.
The Rietveld refinement results and statistics are listed in Table 4.2 and Table 4.3
for CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
respectively. Both compositions were fit
using Γ
4
, as seen in Table 4.1.
The growing diffuse scattering peak for both compositions is highlighted. Most
notably, the system, according to Figure 4.10, is not fully ordered until below
the ordering temperature asserted based on magnetic property measurements.
The transition temperature from the heat capacity is also slightly below that
determined from the magnetic property measurements but in excellent agreement
with the neutron diffraction data making the precise temperature at which order
emerges slightly lower than stated in the manuscript.
4.5.1 RMC - SPINVERT
Stereographic projections of the refined spin orientations, both from individual
refinements andaveraged out over all refinements, wereexamined and did not show
anyindicationofapreferredorientation. Toconfirm,theserefinementswerecarried
out in which the spins were, artificially, constrained to be oriented along the [100],
[110] and [111] directions. No significant deterioration in the fits was observed,
which suggests that the data obtained is insensitive to spin orientation. Thus while
57
the results obtained are consistent with the random orientation of spins expected
for tetrahedral Fe
3+
d
5
cations, which typically have very low magnetocrystalline
anisotropy, this may be partly due to the very modest quality of the data available.
If, as is typically the case in metal oxides, the separation between Fe atoms is
sufficient that magnetic interactions must be facilitated by superexchange. Exam-
ination of the crystal structure reveals that this must occur via five atom superex-
change bridges. For the nearest neighbors and closest three Fe – Fe neighbors with
antiferromagnetic interactions coupling is possible through a combination of Fe –
O – Zr – O – Fe and Fe – O – Ca/Y – O – Fe pathways, although the latter should
presumably be more significant due to the greater radial extension of the Zr 4d
orbitals. It should also be noted at this point that the Fe cations separated by
≈7.4 Å lack any direct links through the zirconium octahedra, which may explain
its weaker antiferromagnetic correlations. The complex nature of these superex-
change pathways makes it difficult to understand why the nearest neighbors and
other significant correlations have opposite signs.
Comparison of the correlations obtained from the paramagnetic phase and
the ordered antiferromagnetic structure provides a likely explanation for the non-
collinear spins in the order structure and the role this plays in reducing the mag-
netic frustration in this structure. Comparing the distances for which there are
likely superexchange pathways in terms of increasing distance we will start with
the nearest neighbors. Here examination of the Fe sites in the ordered structure
shows that the spins for all sites have angles of less than 90
◦
with at least three of
the neighboring spins and the average of all of these angles with their four neigh-
bors are less than 90
◦
. In contrast, for the spins of the Fe atoms separated by
≈5.9 Å from each other in the ordered structure neighboring spins all have greater
than a 90
◦
angle from each other but are typically far from the 180
◦
expected
58
of purely antiferromagnetic correlations. For the Fe–Fe atoms separated by≈6.4
Å, where the refined antiferromagnetic correlations are the strongest, there are
only very small canting angles that prevent spins from being antiferromagnetically
coupled to each other. Finally, for Fe cations separated by≈7.4 Å which have
the weakest of the significant antiferromagnetic correlations in the paramagnetic
phase, the spins on each Fe site have an angle of less than 90
◦
with at least three of
their four neighbors and the average of all of these angles with their four neighbors
are less than 90
◦
. Thus it appears that for the three Fe–Fe distances for which
significant correlations are observed in the paramagnetic phase it appears that, on
average, the ordered phase satisfies the sign of the correlation expected from the
paramagnetic phase. For Fe cations, for which significant magnetic correlations
can be identified as arising from a superexchange pathway, this pattern breaks
down only for Fe–Fe distances of≈7.4 Å but this is consistent with their weaker
antiferromagnetic correlations in the paramagnetic phase, likely a result of the
lack of Fe-O-Zr-O-Fe superexchange pathways. This suggests the highly canted
structure plays a key role in satisfying the magnetic correlations expected from
the paramagnetic phase.
4.5.2 Magnetic Structures
The magnetic structures of CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
have been deter-
mined through the refinement using irreducible representations against powder
neutron diffraction data, which reveals the co-existence of both long- and short-
range magnetic order. Both compositions order in a non-collinear fashion at 18 K
and 21 K for CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
respectively.
59
Table 4.1: Resulting vector components and total magnetization for each Fe ion within Ca
2
MZr
2
Fe
3
O
12
.
k = (0,0,0)
IR Fe position Atom BV components
Γ
4
T
d
1 (1, 0, 0) (0, 1, 0) (0, 0, 1)
2 (0, 1, 0) (-1, -1, 0) (0, 0, 1)
3 (-1, -1, 0) (1, 0, 0) (0, 0, 1)
4 (0, -1, 0) (-1, 0, 0) (0, 0, 1)
5 (-1, 0, 0) (1, 1, 0) (0, 0, 1)
6 (1, 1, 0) (0, -1, 0) (0, 0, 1)
7 (-1, 0, 0) (0, -1, 0) (0, 0, -1)
8 (0, -1, 0) (1, 1, 0) (0, 0, -1)
9 (1, 1, 0) (-1, 0, 0) (0, 0, -1)
10 (0, 1, 0) (1, 0, 0) (0, 0, -1)
11 (1, 0, 0) (-1, -1, 0) (0, 0, -1)
12 (-1, -1, 0) (0, 1, 0) (0, 0, -1)
60
Table 4.2: Results of the Rietveld refinement of CaY
2
Zr
2
Fe
3
O
12
against the powder neutron diffraction data. Ca, Y,
and Zr all sit upon special positions and are therefore not included. It should be noted that the high temperature refine-
ments are nuclear refinements within Ia
¯
3d while the lowest temperature measurements (with magnetic contributions)
are refined within R
¯
3c therefore a c-lattice parameter is included as well as additional general positions.
CaY
2
Zr
2
Fe
3
O
12
Parameter 1.5 K 12 K 100 K
a (Å) 17.882(8) 17.884(9) 12.699(7)
c (Å) 10.985(1) 10.984(4) –
Fe1 position 0.166(6), 0.708(3), 0.083(3) 0.166(6), 0.708(3), 0.083(3) –
O1 position 0.087(5), 0.095(5), 0.130(0) 0.087(5), 0.095(5), 0.130(0) 0.028(4), 0.055(5), 0.652(9)
O2 position 0.117(2), 0.265(2), 0.174(2) 0.117(2), 0.265(2), 0.174(2) –
O3 position 0.613(2), 0.708(0), 0.284(3) 0.613(2), 0.708(0), 0.284(3) –
O3 position 0.510(5), 0.612(9), 0.085(0) 0.510(5), 0.612(9), 0.085(0) –
T
d
Fe Coeff (C1, C2, C3) 0.333(7), 3.426(3), -0.934(2) 0.190(9), 1.615(3), -0.549(1) –
T
d
Fe μ 3.40 1.62 –
R
Mag/Bragg
26.1 / 6.30 27.5 / 6.51 – / 7.8
61
Table 4.3: Results of the Rietveld refinement of CaLa
2
Zr
2
Fe
3
O
12
against the neutron powder diffraction data. Ca,
La, and Zr all sit at fixed, special positions and are therefore not included. It should be noted that the high tem-
perature refinements are nuclear refinements within Ia
¯
3d while the lowest temperature measurements (with magnetic
contributions) are refined within R
¯
3c therefore ac-lattice parameter is included as well as additional general positions.
Parameter 1.5 K 15 K 295 K
a (Å) 18.057(9) 18.126(0) 12.846(9)
c (Å) 11.092(3) 11.083(2) –
Fe1 position 0.166(6), 0.708(3), 0.083(3) 0.166(6), 0.708(3), 0.083(3) –
O1 position 0.085(0), 0.095(5), 0.118(2) 0.079(2), 0.087(9), 0.133(4) 0.029(7), 0.053(2), 0.651(5)
O2 position 0.121(8), 0.262(9), 0.169(8) 0.123(6), 0.260(9), 0.181(6) –
O3 position 0.615(6), 0.709(0), 0.281(1) 0.619(9), 0.706(4), 0.286(0) –
O4 position 0.508(3), 0.610(9), 0.082(3) 0.505(8), 0.608(9), 0.093(2) –
T
d
Fe Coeff (C1, C2, C3) 0.301(0), 3.990(0), 0.179(1) -0.093(0), 2.346(0), -0.542(0) –
T
d
Fe μ 3.85 2.45 –
R
Mag/Bragg
7.9 / 9.8 11.6 / 9.1 – / 11.1
62
Figure 4.7: Rietveld refinements of CaY
2
Zr
2
Fe
3
O
12
neutron powder diffraction at (a) 1.5 K, (b) 12 K, (c) 100 K and
CaLa
2
Zr
2
Fe
3
O
12
neutron powder diffraction at (d) 1.5 K, (e) 15 K, and (f) 295 K.
63
Figure 4.8: Isothermal M–H measurements of (a) CaY
2
Zr
2
Fe
3
O
12
and (b)
CaLa
2
Zr
2
Fe
3
O
12
. Temperatures were chosen both above and below each respec-
tive ordering temperature. At sufficiently low temperatures, the hysteresis curves
open at low fields (2000 Oe). Consistent with refinement results, CaLa
2
Zr
2
Fe
3
O
12
resulted in slightly overall higher magnetic moments due to higher covalency and
exchange interactions.
Figure 4.9: AC magnetic susceptibility curves for (a) CaY
2
Zr
2
Fe
3
O
12
and (b)
CaLa
2
Zr
2
Fe
3
O
12
exhibit similar shapes to those of the DC magnetic susceptibility
(DCMS) curves where there exists two maxima. These maxima occur at the same
temperatures as those in the DCMS and have no frequency dependence.
64
Figure 4.10: The diffuse scattering peak at 15
◦
can be seen growing and shifting
to lower theta as the temperature decreases for both (a) CaY
2
Zr
2
Fe
3
O
12
and (b)
CaLa
2
Zr
2
Fe
3
O
12
.
Figure 4.11: Spin correlation < S
0
.S
r
> versus r from RMC fits to the diffuse
magnetic scattering of CaY
2
Zr
2
Fe
3
O
12
, averaged over 300 refinements. Errors in
the values are smaller than the circular markers.
65
Figure 4.12: Illustrations of the magnetic structures of CaY
2
Zr
2
Fe
3
O
12
and
CaLa
2
Zr
2
Fe
3
O
12
respectively.
66
Chapter 5
Magnetism & dielectric effects in a tetrahedrally
coordinated garnet with Co
2+
5.1 Introduction
To continue studying magnetism isolated to a single sublattice within the gar-
net structure, Ca
3
Te
2
Co
2
ZnO
12
was synthesized. This bright, cobalt blue garnet
was first studied in 1968 by Kasper et al. and, to the best of our knowledge,
has not been further characterized with physical property measurements such as
magnetism or capacitance.
84
The introduction of cobalt within the garnet structure affords the chance to
observe how single-ion anisotropy isolated to a single cation sublattice affects
its magnetic properties. This system and its magnetic exchange pathways
can be compared to other Co-containing garnets, such as CaY
2
Co
2
Ge
3
O
12
and
NaCa
2
Co
2
V
3
O
12
studied by Neer et al., where the effects of sublattice magnetic
occupation by Co
2+
on the octahedral site with a changing diamagnetic back-
bone were compared.
5,85
Furthermore, this chapter also compares the nuclear and
magnetic structures of Ca
3
Te
2
Co
2
ZnO
12
to observe the effects of isolated mag-
netism type (Fe
3+
versus Co
2+
) on the tetrahedral site with CaY
2
Zr
2
Fe
3
O
12
and
CaLa
2
Zr
2
Fe
3
O
12
, from previous chapters.
Unsurprisingly, the switch of iron to cobalt results in a switch from next
nearest neighbor (NNN) antiferromagnetic interactions to ferromagnetic interac-
tions. Furthermore, while the magnetic structure of Ca
3
Te
2
Co
2
ZnO
12
resembles
67
CaY
2
Zr
2
Fe
3
O
12
or CaLa
2
Zr
2
Fe
3
O
12
, there exists antiferromagnetic character in
the ordering that is a function of a highly anisotropic system typically seen when
Co
2+
is present.
5.2 Experimental
5.2.1 Synthesis
Polycrystalline samples were synthesized by grinding stoichiometric ratios of
CaCO
3
, Co(C
2
O
4
)·2H
2
O, ZnO, and Te(OH)
6
and pressing into pellets. A molar
excess of 2.15 Te(OH)
6
was used due to the volatility of tellurium. Co(C
2
O
4
)·2H
2
O
was prepared in house using Co(NO
3
)
3
· 6H
2
O in excess oxalic acid, filtered, and
dried overnight under vacuum giving a fine, light pink powder. All pellets were
heated on top of and buried under a layer of sacrificial powder to isolate them from
the zirconia crucible. The crucible was also covered to further prevent volatiliza-
tion. Samples were heated to 1040
◦
C for 1 hour in air to completion.
5.2.2 Structure Determination
Sample purity and potential site-mixing were evaluated using both X-ray and neu-
tron diffraction. Powder XRD was performed at room temperature using 11-BM
at Argonne National Laboratory at λ = 0.412797 Å.
Neutron diffraction was measured at 1.5, 4, 6, 10, 20, and 300K using the BT-
1 high resolution neutron powder diffractometer at the NIST Center for Neutron
Research. A Ge(311) monochromator with a 75
◦
take-off angle andλ = 2.077(2)Å
were used. Data was collected over the range of 1.9
◦
- 166.3
◦
in scattering angle
(2θ) with a step size of 0.05
◦
.
68
For physical characterization a final densification was performed using spark
plasma sintering (SPS). The pellet was cold pressed at 3 kN in a Carver press prior
to SPS. It was then evacuated for 15 minutes, or until the pressure reached <1
hPa, pressed from 3 kN to 8 kN, and heated to 850
◦
C isothermally for 3 minutes
resulting in 93% densification. The pressure was quickly removed, from 8 kN to 3
kN over 30 seconds, and then allowed to cool for seven minutes until the internal
instrument thermocouple reads approximately 30
◦
C.
5.2.3 Physical Property Measurements
Temperature– and field–dependent DC magnetic susceptibility, AC magnetic sus-
ceptibility, and heat capacity were measured on a Quantum Design 14T Dynacool
Physical Property Measurement System. All magnetic measurements were per-
formed on bulk powder samples held in place using eicosane wax. Heat capacity
measurements were measured on powdered samples mixed with equal parts silver
in order to increase the thermal coupling to the sample stage. The silver and epoxy
contribution were measured separately and subtracted out.
70
UsingSPSdensifiedpellets, magnetocapacitancemeasurementswereperformed
by first painting the pellets with Ag-epoxy (brand) and fixing an epoxy-coated
copper wire to each side creating a plate capacitor. The edges of the pellet were
sanded to ensure no short circuits and then each electrode side was connected to
a shielded stainless steel co-axial cable within a custom built measurement probe.
The capacitance was measured on a high precision capacitance bridge Andeen-
Hagerling 2700A at multiple frequencies within a Quantum Design 14T Dynacool
Physical Property Measurement System (PPMS) for control of the magnetic field
and temperature.
69
5.3 Results and Discussion
Sample and crystallographic site purity was evaluated using Rietveld refinement
and confirmed against both X-ray and neutron powder diffraction as pictured in
Figure 5.1 with the resulting refinement parameters listed in Table 5.1. The result-
Figure5.1: RietveldrefinementsofsynchrotronX-ray(a)andneutron(b)powder
diffraction with corresponding goodness of fit values. Refer to Figure 5.8 for details
of the refinement fits.
ing fits to the room temperature data confirmed the conventional Ia
¯
3d (# 230)
space group expected for a garnet. The crystallographic site purity was analyzed
to confirm that the magnetic cobalt remains isolated on the tetrahedral site thus
providing an adequate comparison to other cobalt-containing single magnetic site
compositions.
The temperature dependent DC magnetic susceptibility (DCMS) curve indi-
cates a ferromagnetic ground state at approximately 13.6 K. A minimum field of
500 Oe was necessary to overcome any residual stray fields trapped within the
instrumentation and magnet while being as small as possible so as to not disrupt
the magnetic ground state. Using the Curie-Weiss equation, the high temperature
70
Table 5.1: Results of the Rietveld refinement of Ca
3
Te
2
Co
2
ZnO
12
against the
neutron powder diffraction data. Ca, Te, Co, and Zn all sit at fixed, special
positionsandarethereforenotincludedforthecubicrefinement. Itshouldbenoted
that the high temperature refinements are nuclear refinements within Ia
¯
3d while
the lowest temperature measurements (with magnetic contributions) are refined
within R
¯
3c therefore ac-lattice parameter is included as well as additional general
positions.
Parameter 1.5 K 300 K
a (Å) 17.788(2) 12.602(7)
c (Å) 10.912(6) –
Ca1 position 0.125(6), 0.000(0), 0.250(0) –
Ca2 position 0.622(7), 0.263(5), 0.191(6) –
Zn1/Co1 position 0.166(6), 0.708(3), 0.083(3) –
O1 position 0.076(8), 0.082(3), 0.120(7) 0.025(9), 0.049(4), 0.642(4)
O2 position 0.120(7), 0.263(5), 0.191(6) –
O3 position 0.611(4), 0.707(5), 0.291(5) –
O3 position 0.511(8), 0.599(9), 0.078(5) –
T
d
Co Coeff (C1, C2, C3) 1.946(4), 1.210(9), 0.256(9) –
R
mag
11.8 –
R
Bragg
5.83 3.55
Figure 5.2: (a) Temperature dependent zero-field cooled/field cooled magnetic
(zfc,fc) susceptibility data for Ca
3
Te
2
Co
2
ZnO
12
taken under 500 Oe. (b) Isother-
mal magnetization measurement taken at 2 K.
71
region (200-300 K) of the DCMS was fit and results in a Θ
CW
of – 53 K and an
effective paramagnetic moment of 6.40 μ
B
per formula unit (4.52 μ
B
per Co).
This moment per Co
2+
is within 87% agreement of the expected value of Co
2+
in a high-spin, tetrahedrally coordinated environment (d
7
, S=3/2, L=3) and well
within the known experimental range for such an environment when the orbital
angular momentum is unquenched and decoupled from the spin. The negative
sign of Θ
CW
indicates a predominately antiferromagnetic exchange interaction
between the spins. This is attributed to the antiferromagnetic character present
to the presence of the highly anisotropic Co
2+
, despite an overall ferromagnetic
system.
To further understand the discrepancies between the DCMS curve and Curie-
Weissanalysis, theneutronpowderdiffractiondatawasrefinedatmultipletemper-
atures along the DCMS curve. As the temperature decreases, magnetic reflections
appear, as can be seen in Figure 5.3, at 19
◦
, 23
◦
, 48
◦
, 56
◦
, and 59
◦
. These magnetic
reflections were indexed using the propagation vector k = 0 and representational
analysis was used to fit the neutron data within the space group R
¯
3c (# 167).
Initially, attempts were made to model the data within space group Ia
¯
3d, how-
ever, the refinement would not converge into an acceptable or physically logical
ground state. Consequently, the symmetry was lowered to trigonal space groups
which have been successfully used to model garnet magnetic structures in the past.
Prime examples of this include YIG or CaY
2
Zr
2
Fe
3
O
12
studied by our group (as
seen in chapter 4).
64,80,81
Symmetry analysis of the magnetic structure was performed using SARAh,
74
which returned five one-dimensional and one two-dimensional representations
within the Little GroupG
k
. After careful analysis, Ca
3
Te
2
Co
2
ZnO
12
was fit using
the third representation, Γ
3
, as seen fit in Figure 5.1 and illustrated in Figure 5.4.
72
Figure 5.3: The ordering temperature of Ca
3
Te
2
Co
2
ZnO
12
can be seen to be
between 10 and 20 K, consistent with DCMS, as new magnetic peaks appear at 10
K in the measured data. Nuclear and magnetic reflections are shown as pink and
blue tick marks, respectively.
Figure 5.4: From left to right, the magnetic structure of Ca
3
Te
2
Co
2
ZnO
12
is
illustrated within the unit cell, along the a-axis, and along the c-axis respectively.
This representation consists of the basis vectors, listed in Table 4.1, with a non-
collinear topology that resembles a spiral that winds around and along the rods as
seen in Figure 5.5(b) and (c).
Interestingly, upon direct comparison of the magnetic structures of
CaY
2
Zr
2
Fe
3
O
12
and CaLa
2
Zr
2
Fe
3
O
12
, it can be seen that each coupled interac-
tion switches from antiferromagnetic to ferromagnetic and vice versa. This is best
73
Figure 5.5: (a) An illustration of a rod in the Ca
3
Te
2
Co
2
ZnO
12
garnet with cubic
and tetrahedral polyhedra and a hard sphere octahedral site. (b) Tetrahedra are
edge - sharing with dodecahedra between different rods and corner - sharing with
dodecahedra along the same rod. Cobalt to cobalt distances are shown. (c) For
Ca
3
Te
2
Co
2
ZnO
12
, lookingalongarod, eachsetoftetrahedraarecolorcoordinated.
(d) In CaY
2
Zr
2
Fe
3
O
12
, the two sets of tetrahedra are ferromagnetic to each other.
(e) Notable cobalt to cobalt distances are highlighted.
seen in Figure 5.5(c), where the three tetrahedra sharing an octahedra face (at
a distance of 5.9 Å) are a set spinning one direction while the other set on the
opposite octahedral face are spinning the opposite direction. In Figure 5.5(e), the
tetrahedral–tetrahedral distances are labeled as well as color coded with each set
on an octahedral face. The two smaller distances, 3.9 Å and 5.9 Å, are antiferro-
magnetic interactions that, for the shortest M – O – O – M distance, travel along
the octahedral site. The two larger distances, 6.3 Å and 7.1 Å, are ferromagnetic
and, again considering the shortest M – O – O – M the most likely superexchange
pathway, travel along the cubic site.
74
As there now exists several contradictory analyses as whether this system if fer-
romagnetic or antiferromagnetic, this chapter proposes the following: that Curie-
Weiss analysis results in predominantly antiferromagnetism based on the NN inter-
actions while the DCMS curve results in a ferromagnetic material based on bulk
effect. Upon close inspection of the magnetic vectors, as seen in Figure 5.4(mid-
dle), it can be seen that they lie primarily within thea−b plane with a very slight
canting along thec-axis. The slight canting along thec-axis, for every vector, is in
one direction resulting in a minor uncompensated moment along one axis. This is
in stark contrast to the tetrahedral Fe garnets from chapter 4 where the magnetic
vectors canceled out along all three axes. Thus, while Ca
3
Te
2
Co
2
ZnO
12
is globally
antiferromagnetic, there does exist an uncompensated moment along one axis that
is mostly easily seen in the bulk DCMS measurements.
Specific heat measurements were performed on both Ca
3
Te
2
Co
2
ZnO
12
and its
structural, non-magnetic analogue, Ca
3
Te
2
Zn
3
O
12
. As shown in Figure 5.6(a) and
(b), in the absence of a magnetic field, a sharp lambda anomaly is seen around
13.5 K which agrees with the onset of the ferromagnetic ordering in the DCMS
curve. Figure5.6(a)showstherawspecificheatdataofbothCa
3
Te
2
Co
2
ZnO
12
and
Ca
3
Te
2
Zn
3
O
12
. Ca
3
Te
2
Zn
3
O
12
data is adjusted by 7.5% to account for differences
in the atoms compositional mass, according to Liang et al.
86
Upon adjustment,
Ca
3
Te
2
Zn
3
O
12
data is subtracted from Ca
3
Te
2
Co
2
ZnO
12
thus accounting for the
phonon contributions to specific heat as seen in Figure 5.6(b).
AC magnetic susceptibility (ACMS) measurements were used to confirm the
absenceofshort-rangeorglassyfeaturesatvariousACfrequencies, showninFigure
5.10. One maximum occurs at the same temperature as that of both the DCMS
and the specific heat measurements with no frequency dependence thus indicating
no glassiness within this composition.
75
Figure 5.6: (a) The total heat capacity C
P
measured below 70 K in the absence
of an external magnetic field. The gray curve shows the specific heat of the non-
magnetic analogue Ca
3
Te
2
Zn
3
O
12
that was slightly rescaled by 7.5% to match the
measured curve of Ca
3
Te
2
Co
2
ZnO
12
. (b) The spin specific heat C
mag
obtained
after subtraction of the phonon contribution.
To compare magnetism on unique crystallographic sites, this composi-
tion is analyzed against NaCa
2
Co
2
V
3
O
12
and CaY
2
Co
2
Ge
3
O
12
, which have
a fully magnetically occupied octahedral site previously studied by Neer et
al.
5,85
CaY
2
Co
2
Ge
3
O
12
adopts Ising-like, antiparallel chains of spins along the
body diagonals while NaCa
2
Co
2
V
3
O
12
contains a more two-dimensional system
with ferromagnetic layers that are coupled antiferromagnetically.
85
The switch
from an almost one-dimensional system (CaY
2
Co
2
Ge
3
O
12
) to two-dimensions
(NaCa
2
Co
2
V
3
O
12
) is a result of the changes in the local environment of the cobalt
octahedra.
85
In other words, the diamagnetic backbone, specifically the tetra-
hedral germanium or vanadium, provide a substantial enough change in orbital
overlap that the octahedra become less distorted along the length of the rods in
76
NaCa
2
Co
2
V
3
O
12
.
85
Thus it is the less distorted octahedra (NaCa
2
Co
2
V
3
O
12
) that
give a more two-dimensional magnetic structure.
Interestingly, Ca
3
Te
2
Co
2
ZnO
12
has both strongly distorted octahedra and
tetrahedra, leading us to perhaps naively expect a more collinear magnetic struc-
ture. However, this is not the case and thus sheds further light on the importance
of the tetrahedral and cubic sites in the garnet structure. It would be a notewor-
thy exercise to compare Ca
3
Te
2
Co
2
ZnO
12
to another garnet composition with only
Co
2+
on the tetrahedral site. It is also important to recall that the tetrahedral site
is only two-thirds filled with a magnetic cation, and may therefore have interrupted
magnetic interactions causing the more non-collinear magnetic structure.
Lastly, temperature dependent dielectric measurements were performed on a
93% dense pellet first upon cooling then upon warming at multiple frequencies as
seen in Figure 5.7(a) and (b) respectively. As the temperature decreases, several
Figure 5.7: Temperature dependent dielectric measurements taken at 1, 2, 5, 10,
and 20 kHz alternating current as the temperature decreases (a) and subsequently
increases (b).
features evolve at approximately 267 K and 32 K in the capacitance and corre-
sponding loss. These features shift as a function of frequency as expected, and are
77
attributed to the time dependence to the electric field as well as a latency within
the material itself (e.g. grain boundaries, etc.). Interestingly, the feature at 32 K
has a hysteresis between the cooling and warming measurements indicating a first
order structural transition. As seen in Figure 5.1(b), there are additional nuclear
(non-magnetic) peaks at 1.5 K supporting this supposition. Further exploration
using low-temperature synchrotron X-ray powder diffraction would complete this
structural characterization.
The high temperature features around 267 K are, in our experience, common
peaks for these garnet oxides; however, the introduction of a local maxima at 300
K in the warming curve is a curiosity without an explanation currently. More than
likely, Ca
3
Te
2
Co
2
ZnO
12
is exhibiting magnetostriction upon undergoing first-order
transitions from R
¯
3c to Ia
¯
3d.
5.4 Summary
The magnetic structure of Ca
3
Te
2
Co
2
ZnO
12
was determined through the refine-
ment of representational analysis against neutron powder diffraction data resulting
in a non-collinear magnetic structure that has a spiral spin motif around the rods
along the body diagonals of the unit cell. There exists competing ferromagnetic
and antiferromagnetic interactions within Ca
3
Te
2
Co
2
ZnO
12
with an uncompen-
sated moment along one axis resulting in a bulk ferromagnet.
Specific heat and dielectric measurements confirm the magnetic phase transi-
tion as well as correctly refining the unit cell in a lower symmetry such as R
¯
3c.
Further magnetodielectric characterization would prove interesting for this spiral-
spin structure as seemingly both the nuclear and magnetic structure have broken
the quintessential cubic garnet symmetry.
78
5.5 Supplemental Information
Table 5.2: Resulting vector components and total magnetization per Co ion
within Ca
3
Te
2
Co
2
ZnO
12
.
k = (0,0,0)
IR Atom BV components
Γ
3
1 (1, 0, 0) (0, 1, 0) (0, 0, 1)
2 (0, 1, 0) (-1, -1, 0) (0, 0, 1)
3 (-1, -1, 0) (1, 0, 0) (0, 0, 1)
4 (0, -1, 0) (-1, 0, 0) (0, 0, 1)
5 (-1, 0, 0) (1, 1, 0) (0, 0, 1)
6 (1, 1, 0) (0, -1, 0) (0, 0, 1)
7 (1, 0, 0) (0, 1, 0) (0, 0, 1)
8 (0, 1, 0) (-1, -1, 0) (0, 0, 1)
9 (-1, -1, 0) (1, 0, 0) (0, 0, 1)
10 (0, -1, 0) (-1, 0, 0) (0, 0, 1)
11 (-1, 0, 0) (1, 1, 0) (0, 0, 1)
12 (1, 1, 0) (0, -1, 0) (0, 0, 1)
Table 5.3: Curie-Weiss analysis results of Ca
3
Te
2
Co
2
ZnO
12
at both 500 Oe and
1 T.
Parameter 500 Oe 1 T
S 3/2
L 3
Θ
CW
-53 K -51 K
High Spin-Only μ
eff
(L = 0) 3.87
High spin μ
eff
from coupling (L +S) 5.20
μ
eff
per F.U. (μ
B
) 6.40 6.36
μ
eff
per metal cation (μ
B
) 4.52 4.49
Θ
CW
R
2
0.9994 0.9999
79
Figure 5.8: The neutron diffraction data for Ca
3
Te
2
Co
2
ZnO
12
was refined at
each collected temperature using Γ
3
at 1.5 K (a), 4 K (b), 6 K (c), and 10 K (d).
Neutron powder diffraction data at 300 K (e) nuclear structure was refined using
Ia
¯
3d.
80
Figure 5.9: Ca
3
Te
2
Co
2
ZnO
12
magnetic specific heat divided by temperature
(top) and entropy (bottom). The saturation value ofS at high temperature is 3.51
J mol
−1
f.u.
K
−1
. The dashed line indicates the expected total entropy Rln2, which
is the maximum entropy derived from the Helmholtz free energy expressions.
2
Interestingly, the saturation value is 2/3 the value of the total entropy expected
which correlates nicely to the tetrahedral sublattice being only 2/3 occupied by
magnetic cations.
81
Figure 5.10: AC magnetic susceptibility at several frequencies shows a sharp
peak at the magnetic ordering temperature corresponding in the DCMS.
Figure 5.11: Curie-Weiss analysis was performed at both (a) 500 Oe and (b) 1
T.
82
Chapter 6
Transition metal phyllosilicate magnetism
6.1 Introduction
Studies on phyllosilicates are typically focused on the correlation between region
(or origin) and physical properties. Being studied from a geological perspective,
thus maintaining sample location virginity, makes structure-property relationship
assignments more difficult as the geological samples are not typically one composi-
tion. That being said, phyllosilicates offer an enormous compositional playground
for a variety of applications, such as catalysis,
7,10,87,88
magnetism,
8,89,90
and energy
storage.
9,91
This chapter begins by creating a baseline and starting studies with
more simplified transition metal phyllosilicates that contain only one magnetic
transition metal.
Through careful synthetic control, it is possible to synthesize pure Ni, Fe, and
Co phyllosilicates. Structurally, phyllosilicates are layered materials with a corner
sharing, pseudohexagonal network of Si tetrahedra alternating with edge-sharing
metal octahedra, as seen in Figure 1.4. The Si-O tetrahedra join the metal layers
at their apical oxygen, and the layers are held together by relatively weak hydrogen
bonding by the surface hydroxyl groups. These materials are labelled as 1:1 or 2:1
as the ratio of Si:Metal layers is varied as seen in Figure 6.5. The possibility of
different layer patterns creates slight differences in spacing that is best identified
in X-ray powder diffraction (XRPD), specifically along the (00l). Most interest-
ingly, with a design baseline, phyllosilicates have multiple cation sites allowing
83
for compositional tuning using a multitude of the periodic table such as compo-
sitions like (Mg, Ni)
3
Si
2
O
5
(OH)
4
and (Na,Ca)
0.33
(Al,Mg)
2
(Si
4
O
10
)(OH)
2
.
9,92
The
edge shared octahedra layered with corner-shared Si rings as well as the material
morphology, offers a unique topology for magnetic studies with the possibility of
magnetic frustration or complex multidimensional magnetism.
Ni
3
Si
2
O
5
(OH)
4
nanoscrolls were first synthesized in 1954 by Roy et al.
93
and
have since been synthetically and structurally well characterized.
94,95
Krasilin et
al. studied the magnetic properties of Ni
3
Si
2
O
5
(OH)
4
concluding that the fer-
romagnetic interlayer coupling was mediated through the interlayer bonds in the
nanotubes and that organo-modified clays only have full spin alignment after the
high-field spin-flop transition.
95
Both Fe
2
Si
4
O
10
(OH)
2
and Ni
3
Si
2
O
5
(OH)
4
phyllosilicates exhibit more tradi-
tional ferromagnetic behavior with the added caveat that site mixing is more likely
tooccurintheFe-containingsamplesasFetendstohavelesscationsitepreference.
Multisiteoccupationofthemagneticcationcouldleadtoafrustratedordisordered
system depending on the cation distribution. Unsurprisingly, the relative cation
size is linearly reflected in the unit cell size and interlayer spacing.
Herein, this chapter presents magnetic – structure property relationships and
comparisons of the 1:1 clays Ni
3
Si
2
O
5
(OH)
4
and Co
3
Si
2
O
5
(OH)
4
as well as the
2:1 Fe
2
Si
4
O
10
(OH)
2
. This study lays the groundwork for established information
about the magnetic exchange interactions and perhaps thus provides groundwork
for design rules for these functional materials.
84
6.2 Experimental
6.2.1 Synthesis
Ni
3
Si
2
O
5
(OH)
4
Synthesis Scroll-like samples of Ni
3
Si
2
O
5
(OH)
4
were syn-
thesized using a two step hydrothermal process. Stoichiometric amounts of H
2
SiO
3
andNi(NO
3
)
2
·6H
2
Owereaddedto15mLdistilledwaterandstirreduntildissolved.
Upon dissolution, the solution was gelled by the addition of NaOH and allowed
to sit for 72 hours. The gel was then transferred to a Teflon lined stainless steel
Parr autoclave and heated to 200
◦
C for 50 hours. The resulting teal powder was
vacuum filtered, washed with water, and dried in vacuo.
Co
3
Si
2
O
5
(OH)
4
Synthesis Scroll-like samples of Co
3
Si
2
O
5
(OH)
4
were syn-
thesized using a single-step hydrothermal process. Stoichiometric amounts of
Na
2
SiO
3
·5H
2
O and CoCl
2
·6H
2
O were dissolved together in de-ionized water.
Upon dissolution, the solution was gelled by the addition of NaOH and excess
polyvinylpyrrolidone (PVP). The gel was then transferred to a Teflon lined stain-
less steel Parr autoclave and heated to 200
◦
C for three days. The resulting pink
powder was vacuum filtered, washed with ethanol, and dried in vacuo.
Fe
2
Si
4
O
10
(OH)
2
Synthesis Platelet-like samples of Fe
2
Si
4
O
10
(OH)
2
were
synthesized using a two step hydrothermal process. Stoichiometric amounts of
Na
2
SiO
3
·5H
2
O and Fe
2
(SO
4
)
3
·H
2
O were dissolved together in de-ionized water at
concentrationsof0.133Mand0.067M,respectively. Upondissolution, thesolution
was adjusted to pH = 12 using NaOH pellets and allowed to gel for four days to
promote coordination complex formation. The gel was then transferred to a Teflon
linedstainlesssteelParrautoclaveandheatedto150
◦
Cforfourdays. Theresulting
orange powder was vacuum filtered, washed with water, and dried in vacuo.
85
6.2.2 Structure Determination
Sample purity was evaluated using both in-house and synchrotron X-ray powder
diffraction on a Bruker D8 diffractometer with a Co source (λ
1
= 1.7889 Å, λ
2
=
1.7928 Å), equipped with a motorized anti-air scatter screen and Lynxeye detector
as well as using 11-BM at Argonne National Laboratory at λ = 0.457861 Å,
respectively.
6.2.3 Physical Property Measurements
Temperature and field dependent DC magnetic susceptibility, AC magnetic sus-
ceptibility, and heat capacity were measured on a Quantum Design 14T Dynacool
Physical Property Measurement System. All magnetic measurements were per-
formed on bulk powder samples held in place using eicosane wax.
Heat capacity measurements were measured on sample powder ground with
equal parts silver in order to increase the thermal coupling to the sample stage.
The silver and epoxy contribution were measured separately and subtracted out.
70
6.3 Results and Discussion
As phyllosilicate materials have a tendency to be less crystalline, the X-ray diffrac-
tion patterns typically consist of broad, asymmetric peaks that make structural
determination more difficult, but can make identification of impurities much easier
as those products would have a noticeably different peak shape distribution (e.g.
highly Lorentzian versus the broad clay peaks). The corresponding XRD patterns
match well with such samples as the 1:1 magnesium serpentine mineral, Lizardite
(Mg
3
Si
2
O
5
(OH)
4
,ICSD75933)andthe2:1Pryophyllite(Al
2
Si
4
O
10
(OH)
2
,AMCSD
86
0000285), which are the same crystal structures, without evidence of impuri-
ties. The X-ray powder diffraction shows the long range order of the as-prepared
Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
, and Fe
2
Si
4
O
10
(OH)
2
as seen in Figure 6.1. Any
Figure 6.1: Powder X-ray diffraction patterns of Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
and Fe
2
Si
4
O
10
(OH)
2
using in-house and synchrotron sources. Miller indices are
based on the reported trigonal structure (P 31m) indicated with orange tick marks.
missing peaks from the reflection list can be attributed to small particle size, tur-
bostratic disorder and strain, or selective broadening of the basal layers resulting
in coherence about the stacking axis.
11
Both Ni
3
Si
2
O
5
(OH)
4
and Co
3
Si
2
O
5
(OH)
4
87
Table 6.1: Curie-Weiss analysis results of transition metal clays
Parameter Ni
3
Si
2
O
5
(OH)
4
Co
3
Si
2
O
5
(OH)
4
Fe
2
Si
4
O
10
(OH)
2
d-electrons d
8
d
7
d
5
# unpaired d-electrons 2 3 5
S 1 3/2 5/2
L 3 3 0
T
C
or T
N
(K) 20 12 6
Θ
CW
52 K -41 K 83 K
High Spin-Only μ
eff
(L = 0) 2.83 3.87 5.92
High Spin μ
eff
(L +S) 4.47 5.20 5.92
μ
eff
per F.U. (μ
B
) 5.21 9.54 7.77
μ
eff
per metal cation (μ
B
) 3.00 5.51 5.49
Θ
CW
R
2
0.9999 0.9998 0.9988
are well-fit using a 1:1 structure model as illustrated in Figure 1.4 and refined
by Dr. Howard et al.
11
Fe
2
Si
4
O
10
(OH)
2
, however, does not easily align to a 1:1
structure, as seen in Figure 6.1(bottom), and thus far, has been shown to be more
suitably modeled (by Dr. Eric McClure) as a 2:1 phyllosilicate structure.
Temperature-dependent DC magnetic susceptibility (DCMS) showed order-
ing temperatures of approximately 20, 12, and 6 K for Ni
3
Si
2
O
5
(OH)
4
,
Co
3
Si
2
O
5
(OH)
4
, andFe
2
Si
4
O
10
(OH)
2
respectively, asseeninFigure6.2(a-c). Each
DCMS experiment was run under a field of 500 Oe to overcome any residual fields
remaining within the magnet, but small enough so as not to disturb the mag-
netic ground state of the material. Each sample susceptibility was fit in the high-
temperature region (200-300 K) to the Curie-Weiss equation yielding the results
listed in Table 6.1.
For Ni
3
Si
2
O
5
(OH)
4
the moment of 3.00 μ
B
is in an acceptable agree-
ment range with the expected value of spin-only 2.83 μ
B
, for Ni
2+
– d
8
in a high-spin octahedral coordination environment with some
orbital contribution, where L + S is an expected 4.47 μ
B
. This is
especially congruent when considering the presence of Ni
3+
impurities.
88
Figure 6.3: Curie-Weiss anal-
ysis of (a) Ni
3
Si
2
O
5
(OH)
4
,
(b) Co
3
Si
2
O
5
(OH)
4
, and (c)
Fe
2
Si
4
O
10
(OH)
2
.
The presence of Ni
3+
was confirmed using Ni
2p lines in X-ray photoelectron spectroscopy
(XPS), performed by Dr. Howard et al.,
albeit deconvolution of the exact ratio of
oxidation states present was inconclusive.
11
The Curie-Weiss results are in close agree-
ment with the magnetization results (Figure
6.2[d]) that show an ideally saturated value
of 2μ
B
per Ni
2+
as expected. The suscepti-
bility curve shape indicates a ferromagnetic
material and this is supported by the posi-
tive Θ
CW
seen in Figure 6.3(a).
Interestingly, the open magnetization
curve shows meta-magnetic features up to
1 T that do not appear in Co
3
Si
2
O
5
(OH)
4
or Fe
2
Si
4
O
10
(OH)
2
. At this time, it
is hypothesized that this field-dependent
magnetic transition is a function of the
scrolling morphology of Ni
3
Si
2
O
5
(OH)
4
. To
explore this, a zinc substituted phase, such
as Ni
2.6
Zn
0.4
Si
2
O
5
(OH)
4
, could be used
in anticipation that the presence of zinc
removes the scrolling giving a platelet mor-
phologythusremovingthemeta-magnetism.
Previous work by Krasilin et al. concluded
89
that Ni
3
Si
2
O
5
(OH)
4
behaved similarly toα-
Ni(OH)
2
, that has Ni layers bonded to pseudohexagonal SiO
4
tetrahedra networks,
which is described as having 2D magnetic ordering. The authors observed a meta-
magnetic hysteresis and attributed this to the ferromagnetic – antiferromagnetic
interfaces of the nanostructures similarly seen inα-Ni(OH)
2
.
95
Arguably the most
interesting observation is that Ni
3
Si
2
O
5
(OH)
4
has a Θ
CW
higher than α-Ni(OH)
2
(Θ
CW
= 35 K).α-Ni(OH)
2
has a 2D ferromagnetic ordering followed by a 3D anti-
ferromagnetic ordering, which may be significantly stronger in Ni
3
Si
2
O
5
(OH)
4
as
a result of the scroll-type morphology.
An effective moment per Co
2+
of 5.51 μ
B
is in excellent agreement for a high-
spin, octahedral cobalt cation with an unquenched orbital moment that is decou-
pled from the spin (in other words, L+S). It is not uncommon for cobalt to
experimentally exhibit an unquenched moment, as seen in an unrelated structure
within this thesis (chapter 5) in the tetrahedrally coordinated Co
2+
garnet. Sur-
prisingly, the magnetization of Co
3
Si
2
O
5
(OH)
4
saturates at only 2 μ
B
as opposed
totheexpected3μ
B
perCo
2+
. Curie-Weissanalysisindicatesanantiferromagnetic
system with a negative Θ
CW
(Figure 6.3[b]); however, the DCMS curve resembles
that of a ferromagnet. Taking the DCMS curve, CW analysis, and magnetization
curve together, this chapter offers the supposition that this system is similar to
Ca
3
Te
2
Co
2
ZnO
12
where there exists bulk ferromagnetism and dominant antiferro-
magnetic interactions. This conclusion is drawn based on the single-ion anisotropy
of cobalt coupled with the scrolling morphology where the overlapping magnetic
cobalt layers are interacting in such a way that there is a minor uncompensated
moment along a specific axis.
Lastly, Fe
2
Si
4
O
10
(OH)
2
presents with a Curie-Weiss value of 5.49 μ
B
in excel-
lent agreement for a d
5
, high-spin system. The susceptibility curve has a more
90
broad shape, resembling a glassy material, with a ferromagnetic transition feature
at 6 K. As seen in Figure 6.3(c), the field-cooled data peels up and away from
the Curie-Weiss line at approximately 160 K indicating strong short range anti-
ferromagnetic coupling. Furthermore, a Θ
CW
of 80 K is a relatively high value for
Θ
CW
that, taken with both the broad DCMS curve and existence of short range
antiferromagnetic coupling, is a result of competing short- and long-range compet-
ing interactions giving a moderately glassy material. The presence of glassiness is
understandable as platelet morphology is more susceptible to stacking faults and
can therefore more easily lose coherence.
Specific heat measurements were performed on all three transition metal clays
and their structural, non-magnetic analogue, Mg
3
Si
2
O
5
(OH)
4
. As shown in Fig-
ure 6.4(a), in the absence of a magnetic field, Ni
3
Si
2
O
5
(OH)
4
has a sharp lambda
anomaly that agrees with the onset of the ferromagnetic ordering in the DCMS
curve. Co
3
Si
2
O
5
(OH)
4
has a broad feature that agrees with the onset of the
magnetic ordering; however, the lack of distinct maximum is indicative of a more
complex phase transition such as that belonging to a 2D magnetic material. Sur-
prisingly, Fe
2
Si
4
O
10
(OH)
2
contains no discernible feature which further supports
the supposition that Fe
2
Si
4
O
10
(OH)
2
is a glassy, 2:1 material.
For further understanding of the complex magnetic interactions seen in these
materials, alternating current magnetic susceptibility (ACMS) was run at multiple
frequencies as seen in Figure 6.6. Each composition has a maximum in the AC
moment (6.6 top, respectively) that corresponds well with the DCMS transition
temperature. Ni
3
Si
2
O
5
(OH)
4
has very little frequency dependency with a shift of
only 0.4 K from 10 Hz to 10,000 Hz confirming a lack of glassiness. The same can
be said of Co
3
Si
2
O
5
(OH)
4
, which has little to no frequency dependent shifting in
91
theACmomentmaxima. TheACmomentmaximaforFe
2
Si
4
O
10
(OH)
2
noticeably
shift as a function of frequency, a classic indicator of glassiness in a material.
Interestingly, the AC phase for the non-glassy Ni
3
Si
2
O
5
(OH)
4
and
Co
3
Si
2
O
5
(OH)
4
has multiple features. A peak in the AC phase (χ
00
) represents
a transition temperature; therefore, there are multiple subtle transitions occurring
within the Ni and Co material. The existence of two peaks within Co
3
Si
2
O
5
(OH)
4
could tentatively be attributed to the presence of 2D magnetic ordering or com-
peting interactions between the in-plane antiferromagnetic coupling and the out of
plane interactions that result in a minor uncompensated moment. Further charac-
terization, such as magneto-specific heat or possibly thin-film magnetic measure-
ments, would shed light on this material. The unique shape of the Ni
3
Si
2
O
5
(OH)
4
AC phase is currently being studied.
Ground state calculations would prove useful for all three compositions, specif-
ically when trying to determine if the predominant magnetic interactions are in-
or out-of-plane in regards to the phyllosilicate sheets that have scrolling overlap.
6.4 Summary
Pure Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
, and Fe
2
Si
4
O
10
(OH)
2
were synthesized and
characterized showing a direct dependence of magnetic properties on the mate-
rials morphology. Each transition metal behaves as expected, based on element
mass susceptibility and metal-oxide literature precedence, within the edge-shared
metal octahedral sheets using Curie-Weiss analysis.
2
However, due to scrolling or
stacking faults and thus magnetic coupling between the metal sheets, the mag-
netic properties evolve into more complex interactions such as metamagnetism or
2D magnetic ordering.
92
Ni
3
Si
2
O
5
(OH)
4
scrolls resemble structure, morphology, and a metamagnetic
transitionsimilartothatofα-Ni(OH)
2
whichisknowntohavebotha2Dferromag-
netic ordering followed by a 3D antiferromagnetic ordering. Co
3
Si
2
O
5
(OH)
4
scrolls
present a contradictory story with both ferromagnetic and antiferromagnetic fea-
tures in multiple measurements similar to Ca
3
Te
2
Co
2
ZnO
12
that this chapter con-
cludes is a function of the single-ion anisotropy of cobalt. Lastly, Fe
2
Si
4
O
10
(OH)
2
,
a material with five unpaired d-electrons, exhibits the lowest magnetic suscepti-
bility due to metal layer separation and loss of coherence from stacking faults,
thus further highlighting the importance of phyllosilicate crystal structure and
morphology.
Phyllosilicates have both the compositional and structural capabilities to be
tuned for specific desired functionalities. This chapter demonstrates that even
simple clays, depending on morphology, have the capacity for more unique mag-
netic properties.
6.5 Supplemental Information
93
Figure 6.2: DC magnetic susceptibilities were taken under 500 Oe. (a) Ni
3
Si
2
O
5
(OH)
4
(b) Co
3
Si
2
O
5
(OH)
4
(c)
Fe
2
Si
4
O
10
(OH)
2
Magnetizations were taken above and below each respective phyllosilicates magnetic ordering temper-
ature. (d) Ni
3
Si
2
O
5
(OH)
4
(e) Co
3
Si
2
O
5
(OH)
4
(f) Fe
2
Si
4
O
10
(OH)
2
94
Figure 6.4: (a) The total heat capacity C
P
measured below 200 K in the absence
of an external magnetic field. The gray and black curve shows the specific heat
of the non-magnetic analogue Mg
3
Si
2
O
5
(OH)
4
. (b) The spin specific heat C
mag
obtained after subtraction of the phonon contribution.
95
Figure 6.5: Phyllosilicate structures showing a 1:1 and 2:1 structural comparison. Figure credit to Dr. Erica S.
Howard.
11
96
Figure 6.6: AC magnetic susceptibility data taken at 10, 100, 1000, 10,000 Hz
for Ni
3
Si
2
O
5
(OH)
4
, Co
3
Si
2
O
5
(OH)
4
, and Fe
2
Si
4
O
10
(OH)
2
respectively.
97
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Abstract (if available)

Abstract This collection of works presents the knowledge we have gained relating crystal structures to magnetic properties within the garnet and 1:1 phyllosilicate structures in the context of building a fundamental understanding of magnetism and characterization. Chapters 2, 3, and 4 explore CaY₂ZrFe₄O₁₂, CaTb₂ZrFe₄O₁₂ and Ca₂MZr₂Fe₃O₁₂ (M = Y, La), respectively, as derivatives of Y₃Fe₅O₁₂ with interrupted superexchange pathways. ❧ Chapter 2 establishes the supposition that isolation of magnetism to a single sublattice will result in antiferromagnetism, but multiple sublattice magnetism results in ferrimagnetism. Chapter 3 explores the effects of adding Tb³⁺ onto the cubic site creating the novel garnet CaTb₂ZrFe₄O₁₂. This composition builds upon the knowledge gained about the importance of the intrarod interaction pathways (A − B) with the added bonus of an f-electron containing cubic site that provides additional magnetic exchange pathways and results in a unique magnetic susceptibility curve. To complete our understanding of the competitions between the various sublattice exchange pathways, we present CaY₂Zr₂Fe₃O₁₂ and CaLa₂Zr₂Fe₃O₁₂ in chapter 4 with magnetic cations isolated solely to the tetrahedral sublattice. ❧ Chapter 5 explores the fundamental magnetism of Ca₃Te₂Co₂ZnO₁₂ while chapter 6 explores the effects of morphology and composition changes in phyllosilicates. ❧ The magnetic structure of Ca₃Te₂Co₂ZnO₁₂was determined through the refinement of representational analysis against neutron powder diffraction data resulting in a non-collinear magnetic structure that has a spiral spin motif around the rods along the body diagonals of the unit cell. In the phyllosilicates, each transition metal behaves as expected, based on element mass susceptibility and metal-oxide literature precedence, within the edge-shared metal octahedral sheets using Curie-Weiss analysis. However, due to scrolling or stacking faults and thus magnetic coupling between the metal sheets, the magnetic properties evolve into more complex interactions such as metamagnetism or 2D magnetic ordering. ❧ This study lays the groundwork for established information about the magnetic exchange interactions and perhaps thus provides groundwork for design rules for garnets and phyllosilicates as functional materials.

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University of Southern California Dissertations and Theses

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Creator Milam-Guerrero, JoAnna Lee (author)

Core Title The effects of crystal structure and composition on the magnetism of garnets & phyllosilicates

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Chemistry

Publication Date 12/08/2020

Defense Date 09/15/2020

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag clay magnetism,crystallography,garnets,isolated garnet magnetism,magnetic structures,magnetism,OAI-PMH Harvest,phyllosilicates

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Melot, Brent (committee chair), Narayan, Sri (committee member), Ravichandran, Jayakanth (committee member)

Creator Email jo.a.milam@gmail.com,milamgue@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-411365

Unique identifier UC11667171

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Legacy Identifier etd-MilamGuerr-9187.pdf

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Document Type Dissertation

Rights Milam-Guerrero, JoAnna Lee

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

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