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Investigation of the superconducting proximity effect (SPE) and magnetc dead layers (MDL) in thin film double layers

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Investigation of the superconducting proximity effect (SPE) and magnetc dead layers (MDL) in thin film double layers

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Content INVITATION OF THE SUPERCONDUCTING PROXIMITY EFFECT (SPE)
AND MAGNETIC DEAD LAYERS (MDL)
IN THIN FILM DOUBLE LAYERS

by

Go Tateishi

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PHYSICS)

May 2009

Copyright 2009 Go Tateishi
ii
Acknowledgements

This dissertation cannot have been completed without the help of many
individuals who have supported me during my study here at the University of
Southern California. Especially, I want to express my appreciations for the
following individuals.
First of all, I heartily thank my supervisor Dr. Gerd Bergmann for giving
me the opportunity to join his group, advising my research project, and providing
the financial support. I will forever appreciate his initiating me into the world of
highly skilled and professional research.
I also want to express my gratefulness to my co-workers in the laboratory:
Dr. Funing Song, Dr. Manjiang Zhang, Dr. Douglas Garrett, Liye Zhang and
Yaqi Tao. The skills I learned from Funing and Manjiang helped me get started
with the research and assistance from Liye and Yaqi helped me to solve a lot of
difficulties that I could not have handled by myself.
In addition, I want to give special thanks to Dr. Jia Grace Lu for providing
the lab facilities at UCI nano-fabrication lab and giving me much valuable advice.
I am also grateful to Dr. Daiwei Wang’s and Dr. Pai Chun Chang’s help in
preparing the chip samples and helping me to solve many technical problems in
the SET project.
I appreciate Dr. Bob Mueller’s help to setup and improve the lab equipment.
His broad knowledge in electronics and cryogenic technology enlarged my
research fields.
iii
I thank the faculty members Dr. Stephan Hass, Dr. Richard S. Thompson,
and Dr. Aiichiro Nakano for serving as my defense committee.
I thank Dr. Jichiro Urabe for advising and encouraging me.
I thank my best friend Mr. Brendan Callum for checking my written English.
Last but not least, I thank my parents, my brother, my grand parents, and my
uncle and aunt for their endless love, encouragement and support in these years.

iv
Table of Contents

Acknowledgements

List of Tables

List of Figures

Abstract

Chapter 1: Introduction
1.1 Discrepancies between experimental and theory in the
superconducting proximity effect
1.2 Magnetism of Ni thin film on different metallic substrate
1.3 Ni on Pb, magnetically dead or alive?

Chapter 2: Experimental procedure
2.1 Quartz substrate preparation
2.2 Evaporation source preparation
2.2.1 Boat evaporation source
2.2.2 Wire evaporation source
2.2.3 Alkali metal evaporation source
2.2.4 Tungsten coil evaporation source

2.3 Set up
2.4 Film production
2.4.1 Films for the Superconducting Proximity Effect (SPE)
2.4.2 Films for the Magnetic Dead Layers (MDL) by
Anomalous Hall Effect (AHE)
2.4.3 Films for the Magnetic Dead Layers (MDL) by Weak
Localization (WL)

2.5 Measurement
2.5.1 Superconducting transition temperature
2.5.2 Magneto and Hall resistance

ii

vi

vii

x

1
2

6
8

10
10
12
12
13
13
14
14
17
18
19

21

21
22
23

v
Chapter 3: The discrepancies of experiment and theory
in the Superconducting Proximity Effect (SPE)
3.1 Theoretical background
3.1.1 The thin film limit (the Cooper limit)
3.1.2 The transition temperature
3.1.3 The initial slope
3.1.4 The slope of inverse T
c
-reduction
3.1.5 The theoretical background of the numerical calculations
(1) The linear gap equation
(2) The gap equation for double layers

3.2 Comparison between experimental result and theory
3.2.1 The experimental results
3.2.2 Comparison between the experimental and theoretical
results
3.2.3 Conclusion

Chapter 4: The Magnetic Dead Layers (MDL) of Ni thin films
4.1 Motivation
4.2 Experimental results
4.2.1 Polyvalent substrate metal
4.2.2 Noble substrate metal
4.2.3 Alkali substrate metal

4.3 The MDL of the polyvalent substrate using the AHE

Chapter 5: The Dephasing and Pair-Breaking due to
the Magnetic Dead Ni Layers
5.1 Motivation
5.2 Experimental result
5.2.1 The MDL by the Anomalous Hall Effect (AHE)
5.2.2 The MDL by the Weak Localization (WL)

5.3 Comparison with the results from the RF oscillator method
5.4 Discussion
5.5 Conclusion

References

Appendix: The “Local Peak” in the magneto resistance curve of the
(Sb)/Pb/Ni sandwich film

24

24
24
26
28
30
31
31
36
38
38
40

42

43
43
44
44
53
57
60

63

63
64
64
66
71
73
78

79

82

vi
List of Tables

2.1 The purities of materials used with Ta or W boat

2.2 The purities of the ferromagnetic materials

2.3 The Property of Sb evaporation source

2.4 The substrate metals and their properties for evaporation

2.5 The substrate metals and their properties for evaporation

3.1 The experimental results and film information

4.1 The experimental results and information for the
(Sb)/polyvalent/Ni films

5.1 The MDL values in Ag/Pb/Ni sandwich film at 10 K

12

13

17

20

20

41

50

65

vii
List of Figures

2.1 The mask pattern for fabrication of films. The numbers from 1 to 6
indicate the electrodes

2.2 A sketch of the geometry where the evaporation sauces are
misaligned and a cross section of the films creating
the “rim effect.”

2.3 A cross section sketch for the superconducting transition
temperature measurement

2.4 A cross section sketch for the Hall resistance measurement

2.5 A cross section sketch for the Magneto resistance measurement

2.6 A sketch of the definition of the superconducting transition
Temperature

3.1 The normalized initial slope S
sn
for the Pb/Ag double layers as a
function of the Pb thickness

3.2 A sketch of the dynamic interpretation of the linear gap equation

3.3 T
c
versus d
Ag
for an Pb/Ag double layer

3.4 The inverse T
c
-reduction 1/(T
s
-T
c
) versus the Pb thickness d
Pb
for
double layers Ag/Pb

3.5 The inverse T
c
-reduction 1/(T
s
-T
c
) versus the Pb thickness d
Pb
for
double layers Mg/Pb

3.6 The inverse T
c
-reduction 1/(T
s
-T
c
) versus the Pb thickness d
Pb
for
double layers Zn/Pb

3.7 The inverse T
c
-reduction 1/(T
s
-T
c
) versus the Pb thickness d
Pb
for
double layers Sn/Pb

11

16

18

19

20

22

29

32

35

39

39

39

39

viii
4.1 The Hall curves of Ni on top of In (10.7 at.lay.) at 10K

4.2 The magnetic properties of the (Sb)/In/Ni film at 10K

4.3 A sketch of the total Hall resistance versus the magnetic field

4.4 The AHR R
yx
(0) of (Sb)/polyvalent/Ni film at 10K

4.5 The AHR curve versus Ni thickness with the temperature parameter;
5, 10, and 20 K, for the (Sb)/In/Ni sandwich film

4.6 The magnetic dead layers of thinner Pb substrate film, 1.3, 2.0, 5.0,
and 10.2 at.lay. at 10 KThe total Hall resistance curve of
(Sb)/Ag/Ni film at 10K

4.7 The total Hall resistance curve of (Sb)/Ag/Ni film at 10K

4.8 The AHR R
yx
(0) curve versus Ni coverage thickness with
temperature parameter

4.9 Magneto-resistance of (Sb)/Al/Ni film at 10 K

4.10 Magneto-resistance curve of (Sb)/Ag/Ni film at 10 K

4.11 The resistance of (Sb)K/Ni film at 10K

4.12 The AHC of (Sb)/K/Ni film at 10K

4.13 Magneto-resistance of (Sb)/K/Ni

4.14 The temperature dependence of the linear slope of the (Sb)/In/Ni
sandwich structure

5.1 The Anomalous Hall curve ΔR
yx
(0) versus magnetic field of
Ag/Pb/Ni film

5.2 The AHR R
yx
(0) of Ag/Pb/Ni film at 10K with the different
thickness of the Pb film

5.3 Magneto resistnace versus magnetic field.
The Ag/Pb/Ni sandwich film has 1.3 at.lay. of Pb thickness at 10K

5.4 The additional dephasing rate 1/τ
φ
due to the Ni coverage on top of
the P substrate versus Ni thickness at 10K
45

46

48

49

51

52

54

55

56

56

58

58

59

60

65

65

66

69

ix
5.5 The pair propagator of a Cooper pair in a superconductor

5.6 The particle-particle propagator in weak localization

(A.1) The magneto resistance; R
xx
(B)- R
xx
(0), of the (Sb)/Pb/Ni film
versus applied magnetic field B at 10 K

(A.2) The magneto resistance curve of Ag/Pb/Ni film at 10K
74

74

81

83
x
Abstract

When a thin superconducting film (S film) is condensed onto a thin normal
conducting film (N film), the first layers of the S film loose their
superconductivity. This phenomenon is generally called the “superconducting
proximity effect (SPE)”. As an investigation of SPE we focus on the transition
temperature of extremely thin NS double layers in the thin regime. Normal
metal is condensed on top of insulating Sb, then Pb is deposited on it in small
steps. The transition temperature is plotted in an inverse T
c
-reduction 1/Δ T
c

=1/( T
s
- T
c
) versus Pb thickness graph. To compare our experimental results
with the theoretical prediction, a numerical calculation of the SN double layer is
performed by our group using the linear gap equation. As a result, there are large
discrepancies between the experimental and theoretical results generally. The
results of the NS double layers can be divided into three groups in terms of their
discrepancies between experiment and theory.(1) Non-coupling ( T
c
= 0 K ): N=
Mg, Ag, Cu, Au. There are large deviations between experiment and theory by a
factor to the order of 2.5. (2) Weak coupling ( T
c
is low ( < 2.5 K )) : N=Cd, Zn,
Al. Deviation is present, but only by a factor of 1.5. (3) Intermediate coupling (
T
c
is around half of Pb’s ( ≈ 4.5 K)) : N=In, Sn. The experimental results agree
with the theory.
Next, we examine the detection of the magnetic dead layer (MDL) of Ni thin
films in terms of the anomalous Hall effect (AHE) with several non-magnetic
metal substrates. In our results, when Ni film is contact with a polyvalent metal
substrate film, the sandwich film has around 2 to 3.5 at.lay. of magnetic dead
xi
layers. However we have not observed the magnetic dead Ni layers with the
alkali and noble metal substrate film.
Finally, we revisit the Pb/Ni system to measure the magnetic scattering of
Ni with the method of Weak Localization (WL) to compare with the dephasing
rate due to the T
c
-reduction. In this series, we use only very thin Pb films
between 1.3 and 5 at.lay. deposited on top of the Ag substrate with about 37
at.lay. thickness, because we make the Ag substrate suppress the
superconductivity of the extremely thin Pb film with the SPE and avoid the
Azlamazov-Larkin fluctuations. After comparison, it becomes clear that the
dephasing rate from the T
c
-reduction method is much larger than that measured
by the weak localization (the factor is around 120). We consider not only “pair
breaking” but also “pair weakening”, and conclude that the reduction of the
superconducting transition temperature is not due to dephasing by magnetic
scattering but due to the resonance scattering of Cooper pairs by non-magnetic
d-states.
1
CHAPTER 1 : INTRODUCTION

When a thin superconducting film (S film) is condensed onto a thin normal conducting
film (N film), the first layers of the S film loose their superconductivity. This
phenomenon is generally called the “superconducting proximity effect (SPE)”. A similar
question arises, when a thin ferromagnetic film (F film) is condensed onto a thin normal
conducting film (N film). In the case the first layers of the F film loose their magnetism
and are denoted as “magnetic dead layers (MDL)”. In this thesis, investigations into the
above two phenomena are reported, specially the superconducting proximity effect of the
NS double layers (N=(s,p) metals, S=Pb) and the magnetic dead layers of the NF double
layers (N=non magnetic metals, F=Ni). The former is mentioned in chapter 3
“Discrepancies between experiment and theory in the superconducting proximity effect”,
the later is done in two chapters, in chapter 4 “Magnetism of Ni thin film on different
metallic substrates” and in chapter 5 “Ni on Pb, magnetically dead or alive?”,
respectively.

2
1.1 Discrepancies between experiment and theory in the superconducting proximity
effect

The superconducting proximity effect (SPE) was discovered by Meisser [29] who
investigated the properties of superconducting wires covered by normal conducting metal.
The intensive research of the SPE started in the 1960’s with the systematic experiments
of the Hilsch group in Geottingen. [22][23] Their research prompted a number of further
experimental investigations [3] [15] [17] [20] [32] and theories. [16][42] In recent years it
has been returned to with great interest; in particular, with SN multilayer or SF double
layer [1] [16][42] (S=superconductor, N=normal conductor, and F=ferromagnetic metal).
The double layer SN or the multilayer (SN)
n
are divided into two groups in terms of
component films. (1) a superconductor (S film) and a normal conductor (N film), (2) two
superconductor films, the film with the lower transition temperature (T
c
) is generally
denoted as N. In our project, we focus on the transition temperature of extremely thin NS
double layers in the thin regime. In these conditions, a minimum of experimental
parameters is required to perform a quantitative comparison with theory. Also, we use
only simple (s,p)metals for both N and S layers, because the superconducting properties
of an (s,p)metal can be reasonably well described by a single attractive electron-electron
interaction V
BSC
[2] and a single density of states.
The superconducting proximity effect is briefly described as following. According to
the BCS theory, with an isolated superconductor, an attractive interaction between a pair
of electrons causes the superconductivity. The pair, called a “Cooper pair”, consists of
two electrons with opposite momentums and spins near the Fermi surface. Next, when a
superconductor is in contact with a normal conductor, the Cooper pairs initially in the
3
superconductor penetrate the normal conductor. During their stay in the normal conductor,
the pair amplitude decays due to dephasing processes such as finite temperature (which is
also in the S), magnetic scattering, interaction with Fermi sea, and the electron-phonon
interaction. These processes cause a reduction of the transition temperature of the system.
At the transition temperature the creation and decay of the pair amplitude (pair
propagator) exactly balance each other. [7] A theoretical explanation about the SPE is
given in chapter 3 in detail.
Now consider a thin film which consists of SN double layers. When both thicknesses;
d
s
and d
n
, in a SN double layer are smaller than the Ginzburg-Landau coherence/thermal
coherence length, we can assume that the SN double layer is in the “thin film limit”. In
this case both of the gap functions Δ
s
and Δ
n
are essentially constant in each film. All
films performed in this series satisfy the “thin film limit’. DeGennes derived the T
c

equation of a SN double layer. [16]

( )






− Θ =
eff
D c
NV
1
exp 14 . 1 T
,
s
n n s s
s s
eff
) NV (
d N d N
d N
) NV (
+
=

The effective interaction parameter (NV)
eff
is averaged in space, and the weight of each
(NV) value in S and N film is proportional to the product of the density of states N times
thickness d with a vanishing BCS interaction, V
n
=0. In this series, normal metal is
condensed on top of insulating Sb then Pb is deposited on it in small steps. The transition
temperature is plotted in the inverse T
c
-reduction 1/Δ T
c
=1/(T
s
- T
c
) versus Pb thickness
graph. In the thin film limit, the normalized initial slope is given by
4
n
c
s
s
sn
d
T
T
d
S
Δ
Δ
=

Since Δd
n
= d
n
= const ≈ 3nm in this series,

s
n s sn c s c
d
d T S
1
T T
1
T
1








=
−
=
Δ

Since the inverse T
c
-reduction equation has a constant coefficient 1/S
sn
T
s
d
n
, when the Pb
thickness as not too small, it allows us to fit the measured T
c
with a straight line in the
1/ΔTc versus d
Pb
graph, and to determine its slope m = 1/S
sn
T
s
d
n
with a high degree of
accuracy.
To compare our experimental results with the theoretical prediction, a numerical
calculation of the SN double layer is performed by our group using the linear gap
equation. The superconducting phase transition in zero magnetic field is generally second
order. We use the following linear gap function derived by DeGennes and improved in
1964, [16]

) ( ) ( H d ) ( V ) (
D n
n
3
r' r' r r' r r Δ = Δ
∑
∫
Ω < ω
ω
,

Here, Δ(r) is the gap function at the position r. V(r) is the effective electron-electron
interaction at position r. ω
n
is the Matsubara frequency ( = (2n+1)πk
B
T/ħ ). Ω
D
is the
Debye frequency. The summation of
n
H
ω
is restricted in |ω
n
| < Ω
D
. The function
5
( ) ' r , r H
n
ω
is the product of the two Green functions ( ) ' r , r G
n
ω
and ( ) ' r , r G
*
n
ω
. This
equation can be rewritten with the based on a dynamic interpretation of the linear gap
equation with classical consideration.

( )
∫
∑
∫
∞ −
Ω < ω
ω −
Δ ρ
τ
= Δ
0
F
' t 2
T
3
) ( ) ( N ' t , ; 0 , ; v e
' dt
d ) ( V ) (
D n
n
r' r' r' r r' r r

The results of the NS double layers can be divided into three groups in terms of their
discrepancies between experiment and theory. (1) Non-coupling ( T
c
= 0 K ): N= Mg, Ag,
Cu, Au. There are large deviations between experiment and theory by a factor to the
order of 2.5. (2) Weak coupling ( T
c
is low ( < 2.5 K )) : N=Cd, Zn, Al. Deviation is
present, but only by a factor of 1.5 (from 1.25 with Cd to 1.7 with Al ). (3) Intermediate
coupling ( T
c
is around half of Pb’s ( ≈ 4.5 K)) : N=In, Sn. The experimental results agree
with the theory.

6
1.2 Magnetism of Ni thin film on different metallic substrate

The Magnetic Dead Layers (MDLs) of Ni film have been studied theoretically and
experimentally for more than three decades since they were first reported by Liebermann
et al. in 1970. [28] For theoretical investigation, the crystal structure of Cu and Ag is
mainly used as the substrate material for Ni films.

[18] [24] [38] [40][41] On the other
hand, for experimental study, several metals are adopted as substrate films. [8][26][27]
[30][31][33]-[36] In our project, we examine the magnetic properties of the Ni thin film
condensed on top of various kinds of non-magnetic metal films such as K, Ag, Mg, and
In. The MDL’s dependence on the substrate thickness and film temperature are
investigated with the Anomalous Hall Effect (AHE) and compared with other reports.
Consider a metal film containing atoms with magnetic moments, and assume that their
magnetization is perpendicular to the film. When we pass an electric current (x-direction)
through the film, the conduction electrons are scattered asymmetrically by the
magnetization of the atoms. The scattered electrons produce a transverse field which is
called “anomalous Hall field”, E
s
(y-direction). This field is proportional to the current
density j, and the magnetization (in z-component) M
z
; E
s
= R
s
M
z
j = ρ
s
j, [4][5]. Now, R
s

is the Anomalous Hall Constant (or extraordinary Hall constant) and ρ
s
is the Anomalous
Hall Resistivity. The anomalous Hall resistance is very large in amorphous ferromagnetic
metals. Since the atoms in an amorphous state have no periodic structure, practically all
the atoms scatter the conduction electrons asymmetrically.
In our measurement, since in the all magnetic field (up to 7 T) the low field condition
(ω
c
τ << 1; ω
c
is the cyclotron frequency, τ is the mean lifetime between two collisions) is
fulfilled, the non-magnetic/Ni sandwich film without magnetic moments only shows a
7
linear slope in the Hall resistance R
yx
(B) curve as a function of the applied magnetic field
B. When Ni atoms possess magnetic moments in or on the thin film, the atoms scatter the
conduction electrons asymmetrically and then we see the anomalous Hall resistance
(AHR) as a non-linear slope in the Hall resistance curves; R
yx
(B), with a negative sign
(normally).
When one extrapolates the Hall curve from the high magnetic field back to zero, one
can evaluate the anomalous Hall resistance at zero field, R
yx
(0). The magnitude of the
Anomalous Hall Resistance (AHR) at zero magnetic field, ΔR
yx
(0) is primarily
proportional to the magnetic moment in the z-component whose direction is
perpendicular to the film; ΔR
yx
(0) ∝ M
z
. [5]
We examine the detection of the MDL of Ni thin films in terms of the AHE with
several non-magnetic metal substrates. In our results, when the Ni film is contact with the
polyvalent metal substrate film, the sandwich film has around 2 to 3.5 at.lay. of magnetic
dead layers. However we have not observed the magnetic dead Ni layers with the alkali
and noble metal substrate films.

8
1.3 Ni on Pb, magnetically dead or alive?

Meservey et al. [31][33] investigated the proximity effect of the ferromagnetic metal
films with the spin-polarized tunneling method. They detected about 3 at.lay. of Magnetic
Dead Layers (MDLs) the Ni on Al substrate. Then Moodera and Meservey produced a
new sensor to improve the sensitivity with the RF oscillator method [8][34][35] and
measured Pb/Ni double layers with 9 nm (about 30 at.lay.) thickness of Pb substrate as
part of a 14MHz oscillator. When the Pb substrate changes its state from normal
conducting into superconducting, it increases the frequency of the oscillator by around 60
kHz. They observed the T
c
-reduction of the Pb film due to the Ni deposition on it. 0.4 nm
(about 1.8 at.lay.) of Ni coverage makes the transition temperature fall below 4.2 K. They
also observed a similar effect with Fe deposition whose thickness is only about 1/80 of Ni
thickness. From these experimental results they concluded that not only isolated Fe atoms
but also isolated Ni atoms deposited on the surface of Pb substrate at 4.2 K possess
magnetic moments. Furthermore, although magnetic moments were present on the Ni
atoms deposited on the Pb, the Hall-effect measurement did not detect them. [34]
However, they do not try to give a concrete value for this reduced moment of Ni atoms.
Therefore, we revisit the Pb/Ni system to measure the magnetic scattering of Ni with the
method of Weak Localization (WL); quantum interference. It is well known that the pair
breaking mechanism in superconductivity and the dephasing in weak localization are in
many aspects identical. In this series, we use only very thin Pb films between 1.3 and 5
at.lay. deposited on top of the Ag substrate with about 37 at.lay. thickness, because we
make the Ag substrate suppress the superconductivity of the extremely thin Pb film with
the SPE and avoid the Azlamazov-Larkin fluctuations. [21] We have two measurement
9
methods (1) the Anomalous Hall Effect (AHE) and (2) the Weak Localization (WL) in
this project.
With the AHE we observe MDLs with all of the Ag/Pb/Ni films. They are from 2.5 to
3.3 at.lay. From these results, we confirmed that Pb film covers the Ag substrate
completely and homogeneously, because if not, the MDL region would not show up. We
also measure the magneto resistance to investigate the dephasing of the conduction
electrons due to the Ni atoms deposited on top of the Pb film in Ag/Pb/Ni sandwich film.
S. Hikami, et al. derived the following quantum conductance correction by using the
Weak Localization theory in 1980. [37]















−








π
=
Δ
T S
2
2
2
B
B
2
3
B
B
2
1
2
e
R
R
f f
η

From the theoretical fit with our experimental data, we evaluate the dephasing rate
1/τ
φ
due to the Ni deposition on top of Pb/Ag film. Also we calculate the dephasing rate
from the T
c
-reduction method performed by Moodera and Meservey [8][34][35]. After
comparison, it becomes clear that the dephasing rate from the T
c
-reduction method is
much larger than that measured by the weak localization (the factor is around 120). We
consider not only “pair breaking” but also “pair weakening”, and conclude that the
reduction of the superconducting transition temperature is not due to dephasing by
magnetic scattering but due to the resonance scattering of Cooper pairs by non-magnetic
d-states.

10
CHAPTER 2 : EXPERIMENTAL PROCEDURE

All films in this experiment are produced by quench condensation in ultrahigh vacuum
better than 10
-11
torr surrounding liquid helium. The fabrication and measurements of the
sample film’s thickness, Hall resistance, Magneto-resistance, and/or transition
temperature, are all done in the magnet cryostat in situ without destroying the high
vacuum and low temperature.

2.1 Quartz substrate preparation

The quartz plate that is used as the original substrate has a thermometer, a calibrated
100 Ω Allen Bradley carbon resistor, on the back. Since the thermometer is in thermal
equilibrium with the following films, it measures the correct temperature. The quartz
plate is cleaned by King Water; HNO
3
: HCl = 1:3, for inorganic and chromic acid for
organic dirt, respectively. Between each cleaning the substrate is rinsed by de-ionized
water; DI water. This cleaning process is repeated several times until the surface of the
plate is washed enough. It is dried naturally while avoiding dust in the air. After being
naturally dried, six gold electrodes are evaporated on the surface of the quartz substrate in
high vacuum around 10
-5
torr at room temperature. These are for contact between the
metal films that will be evaporated later in the experiment, and platinum electrodes that
are connected to a current source and a voltmeter for measurement. This substrate (with
gold electrodes on the surface) is set on the sample holder and covered by a copper mask
that has a following pattern for four point measurement in Fig 2.1.

11

Fig 2.1: The mask pattern for fabrication of films. The numbers from 1 to 6 indicate the
electrodes.

12
2.2 Evaporation source preparation

To produce the thin metal films, we adopted a method of thermal evaporation
involving the application of an AC current. The evaporation source holds up to three
materials, and there are four types of sources in terms of the property of each material.

2.2.1 Boat evaporation source

This source is for the low melting point metals; Mg, Cu, Ag, Au, Zn, Ga, In, Sn, Pb,
Sb, Bi. At first the Tantalum; Ta, or Tungsten; W, boat is annealed with electric current
20A for 1.5 min under high vacuum around 10
-5
torr at room temperature. Then the
material metal is melted on the annealed Ta or W boat and used as an evaporation source.
Usually Ta is used as a boat, but in the case of Au, W is adopted instead, because Ta
forms an alloy with Au. In the case of Mg and Zn, these metals are not adhesive to Ta
and the liquid balls on the boat, so they must be wrapped by Ta boats which have four
arms for wrapping. The purities of the metals are collected in TABLE 2.1. The current for
the evaporation is from 4.0 A for Mg to 21 A for Au.

TABLE 2.1 : The purities of materials used with Ta or W boat.

Metals Purity
Mg 99.95%
Cu, Ag, Au, Zn, Ga, Sn 99.999%
In, Pb, Bi 99.9995%
Sb 99.9999%

13
2.2.2 Wire evaporation source

This source is for the high melting point and sufficient vapor pressure ; Fe, Co, and Ni.
In these cases, 2.5 cm length and 1mm diameter wires are held directly by the Ni
electrodes of the evaporation source flange. The evaporation current is around 20 A. The
purities are collected in TABLE 2.2

TABLE 2.2 : The purities of the ferromagnetic materials.

Metals Purity
Fe 99.99%
Co 99.997%
Ni 99.999%

2.2.3 Alkali metal evaporation source

Alkali metals are evaporated by SAES Getters® evaporation dispenser. Around 10 A
of AC current is applied for the evaporation. The heat from such a high current causes a
chemical reaction in the dispenser, and emits the alkali metal atoms to the substrate. The
applied current must be well controlled and adjusted lower just after the start of the
evaporation because a large amount of the atoms will be released in a short time.

14
2.2.4 Tungsten coil evaporation source

The tungsten W, coil is used for Aluminum; Al, evaporation. Al easily forms an alloy
with both Ta and W. First, the W coil is annealed at 21 A of AC current under high
vacuum (around 10
-5
torr at room temperature). A large amount of the Al starts to
evaporate in a short time when it reaches critical temperature with around 20A of applied
AC current. Therefore, one should shorten the calibration time as much as possible after
the start of the evaporation.

2.3 Set up

The sample holder that holds the quartz substrate (covered by the mask and the
evaporation source that has three materials) is set in the cryostat with indium metal
sealing. To avoid the “rim effect”, particularly for the transition temperature
measurement, the line by the three centers of the each evaporation source has to be set
parallel in the x-direction to the film line made by the electrode #3 and #4. Fig 2.1 is a
sketch of the geometry for the misalignment of the evaporation source and a cross section
of its film. When the alignment between the evaporation source and the mask of the
quartz substrate is not correct, it causes a double transition curve called the “rim effect”
in the superconductor transition measurement. The double transition curve is caused by
two regions with different the transition temperatures. One is from the superconducting
lead only; T
c (Pb)
, the other is from the sandwich structure of the normal metal substrate
and superconducting lead; T
c (N+Pb)
. The assembled cryostat is pumped up over night until
the pressure reaches around 1.0 x 10
-5
torr at room temperature, and then reduced down to
15
about 10
-7
torr with liquid nitrogen at 77K. A leak check has to be performed before
disconnecting the cryostat from the pump stand and transferring it to the magnetic
cryostat. The pressure of the cryostat must be kept in the range of 10
-6
torr with the valve
between the cryostat and the pump stand closed. After confirmation of the pressure, the
cryostat is inserted into the magnetic cryostat which is precooled with liquid nitrogen and
liquid helium on the day before of the experiment with the thermal insulation at high
vacuum around 10
-6
torr. Then the cryostat is fully cooled down with liquid helium. The
vacuum and the temperature inside of the cryostat finally reach at around 10
-11
torr and
4.2 K, respectively. The evaporation of the metals and the measurements of thickness,
Hall resistance, Magneto-resistance, and transition temperature, are all done in the
magnet cryostat in situ without destroying the high vacuum and low temperature.
16

Fig 2.2 : A sketch of the geometry where the evaporation sauces are misaligned and a
cross section of the films creating the “rim effect.”
Quartz plate
mask
Pb
Normal metal
T
c (N+Pb)
T
c (Pb)

Normal
metal Pb
Pb
N
3
4
x
y
z
y
17
2.4 Film fabrication

The deposited film thickness is measured with a quartz oscillator from Technotrade
International® with an accuracy of about 15%. The film thickness is determined through
the frequency changes of the quartz oscillator. The resonant frequency of this oscillator is
initially around 5MHz and it decreases as metal is deposited on top. We monitor its
frequency change with a HP 5334B universal counter which connects to the oscillator
through an oscillating circuit and a sinuate output.
First of all for the initial film (film number zero) around 10 atomic layer thickness of
insulating amorphous antimony; Sb, is directly condensed on the quartz substrate to make
a fresh surface in every experiment. This Sb surface helps the following quench
condensed films become homogeneous, flat, and conducting. For example, a lead; Pb,
film will not make electrical contact below 30 atomic layer thickness without insulating
Sb film underneath, because Pb forms granular islands on the quartz plate surface [12];
however, a Pb film on an insulating Sb already conducts at between two and three atomic
layer thickness. This is the main reason we fabricate a Sb substrate film in each
experiment. After the Sb condensation, this substrate film is normally annealed at 40 K
for two minutes to remove any lattice defects.

TABLE 2.3 : The Property of Sb evaporation source.
Metal Source d(A) / at.lay. Hz / at.lay. I (Amp)
Sb Ta boat 3.11 10.89 5 ~ 7

18
2.4.1 Films for the Superconducting Proximity Effect (SPE)

Non-superconducting or lower T
c
than lead (T
c
(Pb) = 7.2K ) metal is condensed on
top of the Sb substrate (which has thickness of around 10 atomic layers) as the first film
in each experiment. The first film is annealed for two minutes at 38 K then covered by Pb
in several small thickness steps. After each Pb condensation, the films are also annealed
at 35 K every time. The materials used in this series and their evaporation data are
collected in TABLE 2.4 where the transition temperature of the superconducting
materials is for the quench condensed thin film.

Fig 2.3 : A cross section sketch for the superconducting transition temperature
measurement.

Pb ( 10 at.lay. )
Normal / lower Tc metal
Sb substrate
Quartz Plate
z
x
10 at.lay.
10 at.lay.
heater
Allen Bradley
Thermometer
19
2.4.2 Films for the Magnetic Dead Layers (MDL) by Anomalous Hall Effect
(AHE)

Non-magnetic metal is deposited on top of the Sb film as a substrate for the following
Ni films. The thickness of the non-magnetic film is unified at around 10 atomic layers for
all measurements in this series. After each condensation is completed, the film is
annealed at 35 K for two minutes for the same reasons mentioned before, except in the
case of the Bi
90
Pb
10
/Ni sandwich structure. In the Bi
90
Pb
10
case one has to reduce the
temperature down to 20K to avoid crystallization of the amorphous Bi
90
Pb
10
from the
over heating. The Non-magnetic film is covered in several steps of Ni. The materials used
in this series and their evaporation data are collected in TABLE 2.5.

Fig 2.4 : A cross section sketch for the Hall resistance measurement.

Ni ( 0.5at.lay. )
Non-magnetic metal
Sb substrate
Quatrz Plate
z
x
10 at.lay.
10 at.lay.
heater
Allen Bradley
Thermometer
20
TABLE 2.4 : The substrate metals and their properties for evaporation.
Metal Tc Source d(A) / at.lay. Hz / at.lay. I (Amp)
Pb 7.2 Ta boat 3.11 11.58 7 ~ 10
Cu 0 Ta boat 2.28 10.63 9 ~ 11
Au 0 W boat 2.57 25.85 12 ~ 16
Mg 0 Ta wrap 2.85 2.59 4 ~ 6
Cd 0.8 Ta boat 2.22 10.32 3 ~ 5
Zn 1.39 Ta wrap 2.48 9.22 4 ~ 6
Al 2.28 W coil 2.55 3.59 15 ~ 22
In 4.1 Ta boat 2.97 11.30 9 ~ 11
Sn 4.7 Ta boat 3.00 11.42 10 ~ 13

TABLE 2.5 : The substrate metals and their properties for evaporation.
Metal valence Source d(A) / at.lay. Hz / at.lay. I (Amp)
Ni 2 wire 2.22 10.31 23 ~ 27
K 1 dispenser 2.28 10.63 9 ~ 11
Ag 1 Ta boat 2.57 25.85 7 ~ 9
Mg 2 Ta wrap 2.85 2.59 4 ~ 6
Zn 2 Ta wrap 2.48 9.22 4 ~ 6
Al 3 W coil 2.55 3.59 15 ~ 22
In 3 Ta boat 2.97 11.30 9 ~ 11
Sn 4,3 Ta boat 3.00 11.42 10 ~ 13
Bi
90
Pb
10
3,5 Ta boat 3.28 16.78 5 ~ 7
Pb 2,4 Ta boat 3.11 18.51 7 ~ 10
Ga
90
Ag
10
3 Ta boat 2.68 8.89 9 ~ 12

Fig 2.5 : A cross section sketch for the Magneto resistance measurement.
Ni ( 0.5at.lay. )
Pb film
Ag substrate
Quatrz Plate
z
x
heater
Allen Bradley
1.3 – 5.0 at.lay.
37 at.lay.
Thermometer
21
2.4.3 Films for the Magnetic Dead Layers (MDL) by Weak Localization (WL)

For the initial film (film number zero) around 37 atomic layer thickness of silver; Ag,
is directly condensed on the quartz substrate in this series instead of Sb film. Pb atoms
are deposited on top of the Ag film as a substrate for the following Ni films. The different
thickness of Pb film is produced in each experiment 1.3, 2.0 and 5.0 at.lay. 1.3 at.lay.
thickness of the Pb substrate is the practical minimum due to the statistical distribution of
the condensed atoms necessary to a complete film. The Non-magnetic film is covered in
several steps of Ni. After each condensation is completed, the film is annealed at 35 K for
two minutes for the same reasons mentioned before. There are three reasons to choose a
Ag film as the first film instead of Sb: (1) When Pb is quench condensed, it is not
possible to condense a homogeneous film of a few atomic layers of Pb directly on a
quartz plate. It requires a homogeneous and sufficiently thick conducting metal substrate
underneath. (2) The Ag film suppresses the superconductivity of the extremely thin film
by the SPE. (3) Since Ni on top of the Ag film already shows the magnetism with only a
mono-layer thickness, the detection of the MDLs on Ni on a Ag/Pb sandwich film can
only be due to the Pb film in between the Ag and the Ni. Also it proves that there are no
holes in the Pb film.

2.5 Measurement

The temperature is measured by a 100 Ω Allen Bradley carbon resistor on the back of
the quartz plate. First, the carbon resistor is annealed at 275 degree Celsius for two hours
to remove thermal hysteresis. Then it is attached on the back of the quartz substrate with
22
Stycast which is a non-conductive epoxy resin and a good heat conducting glue for
cryogenic use. It is calibrated from a standard germanium resistor in the temperature
range of 2.5 K to 60 K.

2.5.1 Superconducting transition temperature

The resistance of the film is measured by using a four-point measurement. To find the
transition temperature; T
c
, we increase the temperature in small steps starting from the
initial liquid helium temperature; 4.2K. One can calculate the resistance of the film
pattern in Fig 2.1 by measuring the voltage between electrodes #5 and #6 during the
current flow of 0.05mA from #3 to #4. One has to apply such a small current to avoid
destroying the superconducting state. The transition temperature is defined by the
temperature at which the resistance is half of the normal conducting state. Each
temperature is set by a current from the heater on the back of the quartz plate.

Fig 2.6 : A sketch of the definition of the superconducting transition temperature.
R(ohm)
T (K) Tc
R (normal)
R/2
0
23
2.5.2 Magneto and Hall resistance

Both the magneto and Hall resistance are measured at the same time by the four-point
measurement in the magnetic field perpendicular to the film called z-direction in this
paper, with a range from -7 to +7 T. The film pattern is shown in Fig 2.1. The electric
current flows from electrode #3 to #4. The magneto resistance is calculated by the
voltage between electrodes #5 and #6, and the Hall resistance is determined by the
voltage between electrodes #2 and #5. A superconducting solenoid which is set in the
magnetic cryostat filled with liquid helium generates the thirty seven points of magnetic
fields; 0, 0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0,
7.0 T and corresponding negative values. The resistances of films are mainly measured at
10K. In addition, for determining the temperature dependence in the transition region
from the paramagnetic to the ferromagnetic state of Ni, the number of the measurement
temperatures is expanded to three; 5, 10, and 20K, from around two to five atomic layers
of Ni thickness. The measurement at 5K; however, is excluded when the T
c
for the
superconducting state of the substrate materials is close to or higher than 5K. Again, in
the Bi
90
Pb
10
/Ni case, measurement at 20 K is omitted to keep its state as amorphous. The
temperatures of 5 and 10 K can usually be reached by changing the current flow through
the film from electrode #3 to #4, without over loading to the film. However, when the
current necessary to reach the desired temperature exceeds the maximum value allowed
by the sample, one needs support from the heater on the back of the quartz plate to
achieve that higher temperature.

24
CHAPTER 3 : THE DISCREPANCIES BETWEEN
EXPERIMENTAL AND THEORY
IN THE SUPERCONDUCTING PROXIMITY EFFECT

When a thin superconducting film (S film) is condensed onto a thin normal conducting
film (N film), the first layers of the S film loose their superconductivity. This
phenomenon is generally called “superconducting proximity effect (SPE)”. In this
chapter, an investigation of the superconducting proximity effect of NS double layers
(N=(s,p) metals, S=Pb) is reported. When a double layer SN has two superconductor
films, the film with the lower transition temperature is denoted as N. In our project, as an
investigation of SPE we focus on the transition temperature of extremely thin NS double
layers in the thin regime.

3.1 Theoretical background for the SPE

3.1.1 The thin film limit (the Cooper limit)

Now consider a thin film which consists of SN double layers (S; superconducting, N;
normal conducting). The coherence length of the superconducting film is expressed in
two cases; pure limit; ξo, and dirty limit; ξo’

) T k 6 /( v 3 / 3 / v D ' : dirty
) T k 2 /( v v : pure
S B F o Ts F Ts o
S B F Ts F o
π = ξ = τ = τ = ξ
π = τ = ξ
λ η λ λ
η
(3.1.1-1)
25
Where v
F
is Fermi velocity, τ
Ts
= ħ / (2k
B
T
s
), D is diffusion constant, and ℓ is mean
free path. In the dirty case, the mean free path of the conduction electrons is much
smaller than the coherence length. Since all films fabricated in this experimental series
are in a disordered (polycrystalline) state, they are treated as the dirty case. With this
coherence length, the Ginzburg-Landau coherence length in the dirty limit is given as

c s
s
o GL
T T
T
'
2 −
ξ
π
= ξ (3.1.1-2)

When a thin superconducting film makes contact with a thin normal conducting film,
Cooper pairs in the S film penetrate the N film, creating a second coherence length
(referred to as the “thermal coherence length”) The thermal coherence lengths in the dirty
limit are collected in TABLE 3.1. When both thicknesses; d
s
and d
n
, in a SN double layer
are smaller than the Ginzburg-Landau coherence/thermal coherence length, we can
assume that the SN double layer is in the “thin film limit”. In this case both of the gap
functions Δ
s
and Δ
n
are essentially constant in each film. All films performed in this
series satisfy the “thin film limit’.

26
3.1.2 The transition temperature

Cooper applied the formula for the superconducting transition temperature to a SN
double layer from the BCS theory in 1961. [13]







− Θ =
eff
D c
V ) 0 ( N
1
exp 14 . 1 T (3.1.2-1)

Θ
D
: the Debye temperature, and N(0): the density of states per one spin at Fermi surface.
He changed the original BCS interaction V
BCS
to the effective BCS interaction V
eff
by
spatial average in the whole film.

n s
n n s s
eff
d d
d V d V
V
+
+
= (3.1.2-2)

DeGennes indicated the product of NV should be used in the T
c
equation instead of
the BCS interaction V
BCS
only. [16] The effective interaction parameter (NV)
eff
is
averaged in space and the weight of the each (NV) value in S and N film is proportional
to the product of the density of states N times thickness d.

n
n n s s
n n
s
n n s s
s s
eff
) NV (
d N d N
d N
) NV (
d N d N
d N
) NV (
+
+
+
= (3.1.2-3)

27
In addition when the N metal has a vanishing BSC interaction, V
n
=0, so that

s
n n s s
s s
eff
) NV (
d N d N
d N
) NV (
+
= (3.1.2-4)

Now T
s
is given by the following equation.

( )
∑
=
+
=
c
n
0 n
s
2
1
n
1
NV
1
(3.1.2-5)

Furthermore, the “weak coupling limit” (Θ
D
>>2πT
c
) is a special case of the “thin film
limit”. In this case, referred to also as the “Cooper limit”, the superconducting transition
temperature of the SN double layer is given by the BCS-Cooper equation.

( )






− Θ =
eff
D c
NV
1
exp 14 . 1 T (3.1.2-6)

28
3.1.3 The initial slope

From the Cooper-BCS T
c
equation in the Cooper limit, one can derive the initial slope
in T
c
versus the thickness of normal conducting metals graph.

( )








× =
=
s
n
s s
s
0 d
n
c
N
N
NV
1
d
T
dd
dT
n
(3.1.3-1)

When a normalized initial slope S
sn
is defined as following, it is independent from the
superconducting film thickness d
s
until the thickness becomes a large value.

( )








= ≡
=
s
n
s
0 d
n
c
s
s
sn
N
N
NV
1
dd
dT
T
d
S
n
(3.1.3-2)

S
sn
is proportional to the ratio of the density of the states N
n
/N
s
and to the reciprocal of
the BCS interaction parameter (NV)
s
. From above theory the transition temperature T
c

and the normalized initial slope S
sn
are independent from the mean free path or the
coherence/thermal coherence length of both S and N films in the thin film limit including
the Cooper limit. At the first step of the experimental investigation for the normalized
initial slope S
sn
Pb is condensed on top of the insulating Sb substrate, and then Ag is
deposited on it in small steps. This experiment was performed by Dr. Zhang Manjiang
with several combinations of Pb and Ag thickness. [43] The experimental results of the
normalized initial slope are plotted in Fig 3.1. We can see that the experimental results
essentially agree with the theoretical prediction that the normalized initial slope S
sn
is
29
independent from the thickness of S film. The concrete value is S
sn
= S
PbAg
= 0.66 ± 0.5.
However the evaluating process for the initial slope is not efficient. First, the slope is
calculated by curve fitting, see Fig 3.1. Second, one needs several experiments for each
normal metal, as measurements must be conducted at varying thicknesses of the S film.
Therefore, we formulated a new method to evaluate the initial slope of the SN double
layers, as mentioned in the next section.

Fig 3.1 : The normalized initial slope S
sn
for the Pb/Ag double layers as function of the
Pb thickness. S
sn
= S
PbAg
= 0.66 ± 0.5.
30
3.1.4 The slope of inverse T
c
-reduction

In this series, normal metal is condensed on top of the insulating Sb then Pb is deposited
on it in small steps. The thicknesses of the normal metals are collected in TABLE 3.1.
The transition temperature is plotted in the inverse T
c
-reduction 1/Δ T
c
=1/( T
s
- T
c
)
versus Pb thickness graph. In the thin film limit, the normalized initial slope is given by

n
c
s
s
sn
d
T
T
d
S
Δ
Δ
=
Because Δd
n
= d
n
= const ≈ 3nm in this series,

s
n s sn c s c
d
d T S
1
T T
1
T
1








=
−
=
Δ

Since the inverse T
c
-reduction equation has a constant coefficient 1/S
sn
T
s
d
n
, when the Pb
thickness is not too small, it allows us to fit the measured T
c
with a straight line in the
1/ΔTc versus d
Pb
graph, and to determine its slope m = 1/S
sn
T
s
d
n
with a high degree of
accuracy. The normalized initial slope of the AgPb double layer is S
sn
= S
PbAb
=0.66. This
is in agreement with the results in Fig 3.1 which shows that S
sn
= S
PbAb
=0.66±0.5.
Therefore to compare the experimental results and numerical calculations for the
following SPE experiment, we have adopted this new method for determining the slope
of T
c
.

n s sn
d T S
1
m≡
31
3.1.5 The Theoretical background of the numerical calculations

(1) The Linear gap equation

To compare our experimental results with the theoretical prediction, a numerical
calculation of the SN double layer is performed by our group using the linear gap
equation. The superconducting phase transition in zero magnetic field is generally second
order. The gap function; Δ(r), is the order parameter of the phase transition and is
determined self-consistently. When the temperature of a superconductor is close to the
transition temperature T
c
, the gap function is small and only its linear term contributes to
physical phenomena. Gorkov formulated this linear gap equation first in 1959 [19], and
DeGennes and improved in 1964 [16] as

) ( ) ( H d ) ( V ) (
D n
n
3
r' r' r r' r r Δ = Δ
∑
∫
Ω < ω
ω
,
(3.1.5.1-1)
) ( G ) ( TG k ) ( H
*
n B
n n
r' r r' r r' r
, , ,
ω ω ω
= (3.1.5.1-2)

Here, Δ(r) is the gap function at the position r. V(r) is the effective electron-electron
interaction at position r. ω
n
is the Matsubara frequency ( = (2n+1)πk
B
T/ħ ). Ω
D
is the
Debye frequency. The summation of
n
H
ω
is restricted in |ω
n
| < Ω
D
. The function
( ) ' r , r H
n
ω
is the product of the two Green functions ( ) ' r , r G
n
ω
and ( ) ' r , r G
*
n
ω
and
represents the amplitude of a Cooper pair traveling from r’ to r, because a Green function
( ) ' r , r G
n
ω
expresses the amplitude of an electron which is traveling from r’ at past time
t’( < 0 ) to r at the presence t (=0). Furthermore, these Green functions; ( ) ' r , r G
n
ω

32
and ( ) ' r , r G
*
n
ω
, are complex conjugates of each other. Therefore we can also say that the
product ( ) ' r , r G
n
ω
( ) ' r , r G
*
n
ω
is proportional to the probability of a single electron
traveling from r’ to r. If we accept the product ( ) ' r , r G
n
ω
( ) ' r , r G
*
n
ω
to be the propagator
of a single electron, we have an equivalent problem to a Cooper pair, and its solution is
also the solution of the gap equation. The following explanation is based on a dynamic
interpretation of the linear gap equation with classical consideration. [6]

Fig 3.2 : A sketch of the dynamic interpretation of the linear gap equation.

The right side of equation (3.1.5.1-1); d
3
r’ ( ) ' r , r H
n
ω
Δ(r’) excluding Σ
ω
, shows the
number of electrons in the volume element d
3
r’ at position r at the time t=0 (present).
This is caused by the propagating electrons from an arbitrary position r’ where virtually
one injects [N(r’)Δ(r’)/τ
T
]d
3
r’dt’ electrons constantly in the volume element d
3
r’ per
( r’,t’)
( r, t = 0)
ρ(v
F
;r,0;r’,t’)
v
F

probability
density
( ) ( )
dt' d
Δ N
3
T
r'
r' r'
τ

number of electrons
in the volume element d
3
r’
per time interval dt’

exp(-2|ω
n
||t|)

decay
d
3
r’H
ωn
(r,r’)Δ(r’)
at the position r
all arriving electrons
number of
propagation
to find the
at the time 0
at the position r
( )
( ) ( )
∫
∞ −
−






τ
Δ
ρ
0
3
T
F
t' ω 2
dt d
N
' t , ; 0 , ; v e
n
r'
r' r'
r' r

inject
in the volume element d
3
r’

33
time interval dt’. During the propagation some of the electrons (Cooper pairs) are
dephased as exp(-2|ω
n
||Δt’|) under the finite temperature where Δt’ is the time passed
after the departure from r’. The Matsubara component (frequency) ω
n
is a characteristic
time of the pair amplitude decaying. In the superconductivity all Matsubara components
which are less than the Debye frequency contribute to physical phenomena. In addition
the minimum Matsubara frequency ( n = 0 ) yields the decay rate 2ω
o
= 2πk
B
T/ħ. It
decays as exp(-|t’|/τ
T
) where τ
T
≡ ħ/(2πk
B
T) is called the “thermal coherence time”.
When one virtually injects electrons at the position r’ during the time interval
(t’,t’+dt’) in the past with the constant injection rate per volume ; N(r’)Δ(r’)/τ
T
, there are
[N(r’)Δ(r’)/τ
T
]d
3
r’dt’ electrons in the volume element d
3
r’ (see Fig 3.2). Now, N(r’) is
the BCS density of states and Δ(r’) is the energy gap (both at the position r’). These
electrons travel from r’ to an arbitrary position r with their Fermi velocity, decaying as
exp(-2|ω
n
||t’|). In addition we introduce the propagation density ρ(v
F
;r,0;r’,t’) of an
electron. It shows the probability density to find an electron at the presence ( t = 0 ) and
position r, when the electron leaves the position r’ at time t’( < 0 ) and propagates with
Fermi velocity v
F
for all directions. Therefore the number of arriving electrons at the
position r in the volume element d
3
r’ from the position r’ is given by the integration over
the time t’ from negative infinity to present and written as

( )
( ) ( )
∫
∞
ω −
τ
Δ
ρ
0
-
3
T
F
' t 2
dt' d
N
' t , ; 0 , ; v e
n
r'
r' r'
r' r (3.1.5.1-3)

From a comparison with d
3
r’ ( ) ' r , r H
n
ω
Δ(r’) which is mentioned earlier and given by the
right side of equation (3.1.5.1-1) but excluding Σ
ω
. We can express ( ) ' r , r H
n
ω
as
34
( ) ( ) ( ) ( )
∫
∞
ω
τ
ω − ρ =
0
-
T
n F
dt'
' t 2 exp ' t , ; 0 , ; v N , H
n
r' r r' r' r (3.1.5.1-4)

Also we sum (3.1.5.1-3) over all frequencies |ω
n
| < Ω
D
, and perform the integral ∫ d
3
r’
over the whole volume of the system, then multiply the result with the BCS interaction
V(r) at the position r. The result has to recover the gap function Δ(r) for every position r.
Therefore we can rewrite the linear gap equation (3.1.5.1-1) as

( )
∫
∑
∫
∞ −
Ω < ω
ω −
Δ ρ
τ
= Δ
0
F
' t 2
T
3
) ( ) ( N ' t , ; 0 , ; v e
' dt
d ) ( V ) (
D n
n
r' r' r' r r' r r (3.1.5.1-5)

It is obvious that we can consider the propagation in space and the decay in time
individually. The temperature at which the gap function is recovered self-consistently is
the transition temperature of the system. [7]
In the numerical calculation of this linear gap equation, many parameters ( thickness,
mean free path, transparency at the interface, and so on) can be set and made flexible.
The experimental results are plotted in Fig 3.3 in order to compare them with the
numerical calculations. The numbers of the right side of each curve give the reduced
transmission rate T ≤ 1. The transition curve changes with transmission rate T, but the
initial slope doesn’t. This deviation of the initial slope between the experimental and
numerical results will be discussed later.
35

Fig 3.3 : T
c
versus d
Ag
for PbAg double layer. The large full circles are the
experimental results. The numbers below T give the reduction of transmission
through the interface.

36
(2) The gap equation for double layers

Now we evaluate the linear gap equation into a SN double layer of two thin films S
and N, which are both superconducting. [44] We are going to evaluate the linear gap
equation in the thin film limit. The thickness of the films is d
s
and d
n
. If we set an area to
be A in x-y plane of the film, the volume element is Adz’ which is located between z’
and z’+dz’. In the N film, the number of electrons which start during the time (t’, t’+dt’)
( t’< 0 ) from this sheet is N
n
Δ
n
(z’)Adz’dt’/τ
T
. When both films satisfy the thin film limit,
the electrons; N
n
Δ
n
(z’)Adz’dt’/τ
T
, distribute evenly over both films after a very short time.
The equilibrium distribution in each film is proportional to the density of states.
Therefore, the density of the electrons in each film is constant.

N→S : ( )
T n n
n n s s
s
T
3
F
/ ' dt ' dz ) ' z ( N
d N d N
N
/ ' dt d ) ( ) ( N ' t , ; 0 , ; v τ Δ
+
= τ Δ ρ r' r' r' r' r
(3.1.5.2-1)

N →N : ( )
T n n
n n s s
n
T
3
F
/ ' dt ' dz ) ' z ( N
d N d N
N
/ ' dt d ) ( ) ( N ' t , ; 0 , ; v τ Δ
+
= τ Δ ρ r' r' r' r' r
(3.1.5.2-2)

37
When the time it takes to achieve equilibrium distribution is much shorter than the
thermal coherence time τ
T
,, the densities are essentially constant for the whole dt’
integration. In this case, the result of the time integration gives 1/2|ω
n
|. Therefore, the
linear gap equation in the S film becomes following. ( S → S and N → S )













Δ + Δ
+ ω τ
= Δ
∫ ∫
∑
−
Ω < ω
n
s
D n
d
0
n n
0
d
s s
n n s s
s
n T
s s
' dz ) ' z ( N ' dz ) ' z ( N
d N d N
N
2
1 1
V ) z (
(3.1.5.2-3)

This equation makes the left side a constant value for Δ
s
(z) which is given by the average
of Δ
s
(z’) and Δ
n
(z’). Therefore consistency can only be achieved when both Δ
s
and Δ
n
are
constant. This gives the solution for the thin film limit.

( )






Δ + Δ
+ ω τ
= Δ
∑
Ω < ω
n n n s s s
n n s s
s
n T
s s
N d N d
d N d N
N
2
1 1
V
s n
(3.1.5.2-4)

( )






Δ + Δ
+ ω τ
= Δ
∑
Ω < ω
n n n s s s
n n s s
n
n T
n n
N d N d
d N d N
N
2
1 1
V
n n
(3.1.5.2-5)

These are the two gap equations which DeGennes derived for the thin film limit. We
extended this equation for the case where two metals have different Debye temperatures.
[16]

38
3.2 Comparison between experimental result and theory

3.2.1 The experimental results

The experimental results for Ag/Pb, Mg/Pb, Zn/Pb, and Sn/Pb are plotted in Figs 3.4 -
3.7. In this series, a thin normal conducting metal film; N, is condensed on top of the Sb
substrate and then covered by Pb in several small thickness steps. The full circles are
experimental results, and the full upward triangles are numerical calculations. The mean
free path in the thin Pb film is around 3 nm, and then the corresponding coherence length
in the dirty limit; ξ
Pb
’
, is around 13 nm. As shown in the figures, when the NS double
layer film has Pb thickness; d
Pb
, which is less than the pair coherence length; ξ
Pb
’
= 13 nm,
it makes the inverse T
c
-reduction; 1/ΔT
c
, a linear function of Pb thickness; d
Pb
. We found
two remarkable points; first, both the experimental results and the theoretical results
show the fitted curve as a straight line. ( In addition, the lines fitted by the experimental
and theoretical data intersected at the same point on the y axis in the all cases.) Second,
there are large discrepancies between the experimental and theoretical results in the
Ag/Pb, Mg/Pb, and Zn/Pb cases. Sn/Pb is the only case where there is agreement between
experiment and theory. The open downward triangles are theoretical results whose
density of states of Pb; N
s
, is increased artificially to fit with the experimental results. The
adjusted density of states is larger than the free electron density of states. This is caused
by strong electron-phonon mass enhancement. All of the experimental results and film
information are collected in TABLE 3.1 with N films arranged according to their T
c

where some N films are superconducting metal with a T
c
below the T
c
of Pb. To
39
investigate the discrepancies between the experimental results and the theoretical
calculations, the ratio of the slopes m
theo
/m
exp
of each film is calculated, see TABLE 3.1.

Fig 3.4 : the inverse T
c
-reduction 1/Δ T
c

=1/( T
s
- T
c
) versus Pb thickness for double
layers of Ag/Pb

Fig 3.5 : the inverse T
c
-reduction 1/Δ T
c

=1/( T
s
- T
c
) versus Pb thickness for double
layers of Mg/Pb

Fig 3.6 : the inverse T
c
-reduction 1/Δ T
c

=1/( T
s
- T
c
) versus Pb thickness for double
layers of Zn/Pb
Fig 3.7 : the inverse T
c
-reduction 1/Δ T
c

=1/( T
s
- T
c
) versus Pb thickness for double
layers of Sn/Pb

40
3.2.2 Comparison between the experimental and theoretical results

The experimental results do not agree with the theoretical prediction derived by the
linear gap equation, especially in the normal conductor N film case. From the TABLE 3.1
it is obvious that the discrepancies have no relation to the film thickness of the N film and
thermal coherence length. However, in terms of the coupling strength of N films, the
result is divided into three groups; (1) non-coupling T
c
= 0 K : N= Mg, Ag, Cu, Au, (2)
weak coupling T
c
is low ( < 2.5 K) : N=Cd, Zn, Al, and (3) intermediate coupling T
c
is
around half of Pb’s ( ≈ 4.5 K) : N=In, Sn. This discrepancy decreases as the T
c
of the N
film increases. In group (1), the discrepancy between the experiment and the theory is
very large ( by a factor to the order of 2.5.). As mentioned before, to fit the theoretical
results to the experimental data the density of states of Pb; N
s
, has to be increased
artificially. The factor of this discrepancy is very large, around 2.2 in the Ag case, and 4.0
in the Mg case. This is due to the strong electron-phonon mass enhancement.

41
TABLE 3.1 : The experimental results and film information. The columns give the
experimental code, normal conductor materials, the transition temperature of the normal
conductor materials, thickness of the normal conducting film, the coherence length in the
dirty limit, the experimental normalized initial slope, the ratio of the density of states with
the electron-phonon enhancement factor, and the ratio of the inverse T
c
reduction slope
between experimental and theoretical slope; m
exp
/ m
theo
. The density of states included
the electron-phonon enhancement are taken from Kittel. [25]

code N Metal T
n
(K) d
n
(nm) ξ
T
'
(nm) S
sn
exp
N*
n
/N*
s
m
theo
/m
exp

MgPbUW Mg 0 3.08 9.1 0.48 0.572 4.0
AgPbJB Ag 0 4.12 12.1 0.66 0.387 2.2
CuPbJE Cu 0 3.29 10.8 0.98 0.603 2.5
AuPbJD Au 0 2.95 10.2 0.62 0.442 2.9
CdPBJJ Cd 0.8 3.14 11.2 0.39 0.329 1.3
ZnPbUU Zn 1.39 2.6 7.6 0.33 0.430 1.5
AlPbUT Al 2.28 2.15 9.6 0.44 0.833 1.7
InPbUP In 4.1 3.21 13.6 0.30 0.663 1.2
SnPbUN Sn 4.7 3.3 12.0 0.29 0.664 1.0

42
3.2.3 Conclusion

In this project, the superconducting proximity effect of NS double layers is
investigated in terms of the normalized initial slope and in the thin film limit where the T
c

does not depend on the thickness or mean free path. The results of the NS double layers
can be divided into three groups in terms of their discrepancies between experiment and
theory.

(1) Non-coupling ( T
c
= 0 K ): N= Mg, Ag, Cu, Au
There are large deviations between experiment and theory by a factor to the order of
2.5. ( from 2.2 with Ag to 4.0 in Mg )

(2) Weak coupling ( T
c
is low ( < 2.5 K )) : N=Cd, Zn, Al
Deviation is present, but only by a factor of 1.5 (from 1.25 with Cd to 1.7 with Al ).

(3) Intermediate coupling ( T
c
is around half of Pb’s ( ≈ 4.5 K)) : N=In, Sn
The experimental results agree with the theory.

In this project Pb is used as an S film for the NS double layers. Quench condensed Pb is a
strong coupling type superconductor. To make further comparisons with the linear gap
equation theory in the weak coupling frame work, the measurements could be performed
with a weak coupling superconductor such as Zn or Al as an S film. These
superconductors have a lower transition temperature but permit thicker films because of
their larger coherence length with lower temperatures.
43
CHAPTER 4 : MAGNETISM OF Ni THIN FILM ON DIFFERENT METALLIC
SUBSTRATE

4.1 Motivation

The Magnetic Dead Layers (MDLs) of Ni film have been studied theoretically and
experimentally for more than three decades since they were first reported by Liebermann
et al. in 1970. [28] For theoretical investigation, crystal structure of Cu and Ag is mainly
used as the substrate material for the Ni film.

[18][24][38][40][41] On the other hand, for
experimental study, several metals are adopted as substrate films. [8][26][27]
[30][31][33][34]-[36] In this project, the MDL effect is tested with multiple substrate
materials, and the MDL’s dependence on the substrate thickness and film temperature are
investigate with the Anomalous Hall Effect (AHE) and compared with other reports.
When atoms possess magnetic moments in or on the thin film, they scatter the conduction
electrons asymmetrically. This asymmetrical scattering causes the AHE. The AHE for
thin Ni film shows up as a non-linear slope in the Hall curves; R
yx
(B), with a negative
sign (normally). The magnitude of the Anomalous Hall Resistance (AHR) at zero
magnetic field, ΔR
yx
(0) is primarily proportional to the magnetic moment in the z-
component whose direction is perpendicular to the film; ΔR
yx
(0) ∝ M
z
. [5]

44
4.2 Experimental Results

4.2.1 Polyvalent substrate metal

To investigate the dependence of the MDL on substrate materials, eight polyvalent
metals (Mg, Zn, Al, In, Sn, Bi
90
Pb
10
, Pb, and Ga
90
Ag
10
) are used as substrates for Ni film.
All of the Hall measurements of the (Sb)/polyvalent/Ni film systems show qualitatively
the same results. As an example, the Hall curves of the Indium substrate; (Sb)/In/Ni
sandwich structure, are plotted in Fig 4.1(a) and (b). The Fig 4.1(a) is for small coverage
of Ni and Fig 4.1(b) is for larger coverage. The thickness of the In substrate, the
resistance of the (Sb)/In film, and the measurement temperature are 10.7 (at.lay.), 75 (Ω),
and 10 (K), respectively. The numbers on the right side of each curve in Fig 4.1 give the
coverage thickness of the Ni on top of the In substrate in units of atomic layer (at.lay.).

45

Fig 4.1(a) : The Hall curves of small
coverage of Ni on top of In (10.7 at.lay.) at
10K. All of the open squares, full circles,
and open circles are experimental results.
The open squares are for non-coverage of
Ni. The full circles are for linear slope. The
open circles are for non- linear curves. The
numbers on the right side of the each curve
give the coverage thickness of the Ni.

Fig 4.1(b) : The Hall curves of large
coverage of Ni on top of In (10.7 at.lay.) at
10K. All of the open squares, full circles,
and open circles are experimental results.
The open squares are for non-coverage of
Ni. The full circles are for linear slope. The
open circles are for non- linear curves. The
numbers on the right side of the each curve
give the coverage thickness of the Ni.

The negative linear slope at 0.0 at.lay. of Ni coverage on the (Sb)/In substrate film shown
in Fig 4.1(a) and (b), is a typical feature of the disordered thin film. [27] It is obvious that
as the Ni coverage thickness increases, the slope increases, while remaining linear at up
to 3.0 at.lay. The slope of the linear Hall curve; dR
yx
(B)/dB, is plotted on the left in Fig
4.2. This linear slope increases with Ni thickness as mentioned above and diverges when
the Ni thickness reaches between 3.0 and 3.5 at.lay.

46

Fig 4.2 : The magnetic properties of the (Sb)/In/Ni film at 10K. The left curve is for
linear slope; dR
yx
(B)/dB, and the right curve is for the extrapolated value from higher
fields back to zero; R
yx
(0).

Fig 4.1 shows that the Hall curves are no longer linear when the Ni coverage exceeds at
3.0 at.lay. The anomalous Hall resistance (AHR) is caused by the asymmetric scattering
of conducting electrons through the atoms which have the magnetic moments. Therefore
the appearance of the non-linear slope proves that Ni atoms possess magnetic moments.
Further Ni condensation enhances the magnetic moment and transforms the state into
47
ferromagnetic. With Ni coverage higher than 5.0 at.lay., the typical shape of the Hall
curve of the thin ferromagnetic film is exhibited. [30] Demagnetization is strong in the
relatively small magnetic field of up to around 1.5T shown in Fig 4.1(b), so that the Hall
curve has a steep initial slope and a kink at the saturated field. When one extrapolates the
Hall curve from the high magnetic field back to zero, one can evaluate the anomalous
Hall resistance at zero field, R
yx
(0). The AHR R
yx
(0) is proportional to the magnetization
in the z component (perpendicular to the surface of the film) of the total film. The right
part of the Fig 4.2 shows the AHR curve; R
yx
(0), as a function of the Ni thickness. The
absolute value of the R
yx
(0) increases sharply when the Ni thickness exceeds 3.0 atomic
layers. Therefore from this graph one can evaluate the thickness of the Magnetic Dead
Layers (MDL) and in this case the MDL is 3.0 at.lay.

48

Fig 4.3 : A sketch of the total Hall resistance (normal Hall resistance (NHR) +anomalous
Hall resistance (AHR)) versus the magnetic field. R
yx
(0) which is the extrapolated value
from higher field back to zero field shows the AHR at zero field
B (T)
R
yx
(B) (Ω)
Bs (saturated field)
NHR
AHR R
yx
(0)
Bs
NHR + AHR
0
demagnetization
NHR+AHR
(Linear part)
49
In Fig 4.4, the other experimental results with the different substrate materials at 10K are
plotted. Their behavior is similar to the In substrate film; namely, they also have the
magnetic “dead layers” (MDL) where there are no magnetic moments on or in the film.
The experimental results and information for the (Sb)/polyvalent/Ni films are collected in
Table 4.1. All the eight polyvalent substrates suppress the magnetic moments of a few
at.lay. of Ni film and have the “dead layers” in their films.

Fig 4.4 : The AHR R
yx
(0) of (Sb)/polyvalent/Ni film at 10K. The full squares are for the
Bi
90
Pb
10
substrate. The open circles are for the Ga
90
Ag
10
substrate. The full diamonds are
for the Zn substrate.

50
Table 4.1 : The experimental results and information for the (Sb)/polyvalent/Ni films.
The columns give experimental code, substrate material, the thickness of the substrate
(at.lay.), the resistance of the substrate (Ω), and the thickness of the magnetic dead layers
(at.lay.)

In addition the MDL thickness for these films is temperature independent between 5
and 20 K. The AHR R
yx
(0) curve for (Sb)/In/Ni films at three different temperatures; 5,
10, and 20 K, is plotted in Fig 4.5. In the past the MDL based on the In substrate has been
measured using the AHE at 7K and 37 at.lay. of In thickness which is around four times
thicker than this film. [30] The previous result of 3.1 at.lay. is close to our result, 3.0
at.lay. Mg and Sn systems were also measured at 7 K, and their substrate thicknesses
were both roughly 50 at.lay. The MDLs were 2.6 (Mg) and 3.4 (Sn) atomic layers,
respectively. In all these cases, the difference of the MDL in terms of substrate thickness
is less than 0.5 atomic layers, for both the In and Sn substrates, the difference is only 0.1
atomic layers. From the above comparison, we can say that the MDL are essentially
independent of the substrate thickness in the range of 10 to 50 at.lay.
51

Fig 4.5 : The AHR curve versus Ni thickness with the temperature parameter; 5, 10, and
20 K, for the (Sb)/In/Ni sandwich film.
52
To investigate the MDL with thinner substrate films, we reduced the substrate
thickness from 10 to 1.3, 2.0, and 5.0 at.lay. We used Pb as the substrate material because
of how easy it is to control its thickness with high accuracy. 1.3 at.lay. thickness of the Pb
substrate is the practical minimum due to the statistical distribution of the condensed
atoms necessary to a complete film. Furthermore, since the Sb/Ni film also has MDL
between two and four at.lay., Ag film is used as the foundation substrate instead of Sb.
As mentioned later, the (Sb)/Ag/Ni system has no dead layers from 5 to 20K, so that we
can avoid influence from the foundation substrate to the MDL when the Pb film has a
small thickness. The results are plotted in Fig 4.6. The average MDL value is around 2.75
at.lay. It is close to the value of (Sb)/Pb/Ni film which has 2.6 at.lay. of the MDL in
TABLE 4.1. Therefore, the MDL value hardly depends on the thickness of the substrate
of when its thickness is from 1.3 to 10 at.lay.

Fig 4.6 : The magnetic dead layers of thinner Pb substrate film, 1.3, 2.0, 5.0, and 10.2
at.lay. at 10 K.
53
4.2.2 Noble substrate metal

The MDL of the polyvalent substrates are practically independent from the valence of
the substrate materials; however, the behavior of the Ni on a Ag substrate is totally
different. In this series, 10.4 at.lay. thickness of Ag film is used as the noble metal
substrate. The AHE of the (Sb)/Ag/Ni film is measured at three different temperatures; 5,
10, and 20K. As a result, no MDL is detected. The non-linear slope in the Hall curve
already shows up with 0.6 at.lay.-thickness of Ni at all of the three temperatures. A part
of the Hall curve and the AHR at zero field R
yx
(0) with temperature parameter are plotted
in Fig 4.7 and Fig 4.8, respectively. From these figs we can easily see that the Ag
substrate produces a positive value for AHR R
yx
(0) in the small Ni coverage region of up
to around 2.5 at.lay. of Ni thickness, instead of possessing MDL. This is one of the
remarkable points in this experiment because the sign of the AHR R
yx
(0) of Ni thin film
is normally negative. As one can see in Fig 4.8, the sign of the AHR changes from
positive to negative with increasing Ni thickness. In the positive region, the R
yx
(0)
depends on temperature. The lower temperature the film is, the larger R
yx
(0) value the
film has. The anomalous Hall resistance ΔR
yx
(B) is temperature dependent, however
since the magnetic ions are coupled (no free moment), it is impossible to fit with a
universal plot; ΔR
yx
(B) versus B/T. When the Ni thickness exceeds 2.6 atomic layers, the
AHR changes its sign into negative in three temperatures at the same time. In the
negative area, the R
yx
(0) becomes temperature independent between 5 and 20K.
Therefore the film which initially has some coupled ( or weak coupled ) moments in the
positive area transforms its state into ferromagnetic when the sign switches to negative.
The AgCo system also shows a similar phenomenon [9] with temperature independent
54
and the opposite sign of AHR in small coverage thickness. Also in the cases of Fe on Pb,
In, and Sn [10] and Co on Pb, the same “wrong sign” effect occurs, showing that this
effect is not only for Ni. This phenomenon is not yet solved but the hybridization effect
between the d-band of the transition metal atoms and the conduction band of the substrate
at the interface might be important.

Fig 4.7 : The total Hall resistance curve of (Sb)/Ag/Ni film at 10K.

55

Fig 4.8 : The AHR R
yx
(0) curve versus Ni coverage thickness with temperature parameter.

Next we compare the two magneto-resistance curves of Ag and Al substrate Ni films,
Fig 4.9 and Fig 4.10 with both measured at 10K. They belong to the group of the
(Sb)/noble metal/Ni and (Sb)/polyvalent metal/Ni sandwich films, respectively. The
numbers on the right side of the each curve give the Ni coverage thickness on top of the
substrate surface in units of atomic layers. In both cases, the experimental results for
magneto-resistance show similar tendencies with increasing Ni coverage on top of the
substrate; namely, the magneto resistance changes from positive to negative as Ni
thickness increases. However there is one different point; the Ag substrate film changes
its sign quicker than the Al substrate film. Since the (Sb)/Ag/Ni sandwich film has no
56
MDL, it causes even 0.6 atomic layers of Ni to reduce the field dependence of the
magneto resistance drastically and changes the sign of magneto resistance very quickly.
In the case of (Sb)/Al/Ni, the first few layers of Ni loose their magnetic moment and
contribute to the susceptibility of the film; this means that the (Sb)/Al/Ni film requires a
relatively larger amount of Ni coverage before the sign of its magneto resistance changes.
The different behaviors of the magneto resistances also show that the substrate materials
have great influence on Ni. The curves in the Al substrate film with 6.5 and 7.2 at.lay. of
Ni coverage are in their typical ferromagnetic state. [27] Also, in the ferromagnetic state,
the magneto resisitance is independent of temperature.

Fig 4.9 : Magneto-resistance of (Sb)/Al/Ni
film at 10 K.
Fig 4.10 : Magneto-resistance curve of
(Sb)/Ag/Ni film at 10 K.

57
4.2.3 Alkali substrate metal

To investigate the properties of the alkali metal substrate films, we used potassium K
as an example. The K substrate has a thickness of 9.3 at.lay. and resistance of 432Ω AT
10K. The resistance of (Sb)/K/Ni film at 10K and zero film is shown in Fig 4.11. As Fig
4.11 shows, in the case of potassium, the resistance actually increases from its initial
value of 432Ω to a peak of around 3500Ω (factor of 7) at 1.2 at.lay. thickness of Ni. After
the peak, the resistance decrease normally as the Ni thickness increases, but remains
relativelly high (more than 500Ω). The anomalous Hall conductance (AHC) L
yx
(0) is
calculated from the ohmic resistance R
xx
(0) and the anomalous Hall resistance R
yx
(0).

( )
( )
( ) [ ] ( ) [ ]
( )
( ) [ ]
2
xx
yx
2
yx
2
xx
yx
yx
0 R
0 R
0 R 0 R
0 R
0 L ≈
+
=

The AHC L
yx
(0) is plotted in Fig 4.12. It is obvious that L
yx
(0) already has finite value
with 1.2 at.lay. of Ni thickness and increases monotonically.

58

Fig 4.11 : the resistance of (Sb)K/Ni film
10 K.
Fig 4.12 : the AHC of (Sb)/K/Ni film at at
10 K.

In Fig 4.13 the magneto resistance curve of the sandwich film is plotted for different
thicknesses of Ni coverage. The experimental results are totally different from the
polyvalent and noble substrate systems; all curves show negative magneto resistance. The
field dependence of the magneto resistance changes with Ni coverage thickness. At first, 1.2
atomic layer of the Ni coverage strengthens the field dependence of the magneto resistance
drastically. Then the additional Ni atoms reduce the field dependence step by step. With a
thickness of more than 3.1 at.lay. and a magnetic field of more than 2T, the field
dependence becomes less than that of the original K film. As Ni thickness increases, the
width of the peak curve narrows and sharpens.

59

Fig 4.13 : Magneto-resistance of (Sb)/K/Ni.
60
4.3 Discussion

The MDL of the polyvalent substrate using the AHE

The Hall resistance curve R
yx
(B) in Fig 4.1(a) has linear curves up to 3.0 at.lay. of Ni
coverage. Fig 4.14 shows the temperature dependence of the linear slope between 5 and
20K. The horizontal and vertical axis represents measurement temperature and the linear
slope, respectively, with the parameter of Ni thickness. It is obvious that the linear slope
is independent of the temperature between 5 and 20K.

Fig 4.14 : The temperature dependence of the linear slope of the (Sb)/In/Ni sandwich
structure.
61
The AHR; R
yx
(0), of the thin film is proportional to the magnetic moment in z-
component; ΔR
yx
(0) ∝ M
z
. [5] The magnetic susceptibility is

B
M
B
M
o o
∂
∂
= = μ μ χ

The susceptibility caused by the AHE of thin film is in the z component and the magnetic
moment B is (0, 0, B).

dB
dRyx
dB
B dR
B
B R
B
M
B
yx
B
yx
B
z
z
o z
) 0 (
) ( ) (
0 0 0
= =
∂
∂
∝
∂
∂
=
= = =
μ χ

With this, one can evaluate the susceptibility of the sandwich thin film from its slope.
The slope is proportional to the magnetic susceptibility.

dB
dRyx ) 0 (
∝ χ

The linear slope is temperature independent between 5 and 20 K and this result is shown
in Fig 4.14. The temperature dependence and proportionality to the susceptibility of the
linear slope indicates that the state of the (Sb)/In/Ni sandwich film at less than the 3.0
at.lay. of Ni coverage meets the condition for Pauli paramagnetic states. Therefore we
can say that the films with linear slopes have lost their magnetic moments.

62
The difference in slope from the original In film is caused by the enhanced Pauli
susceptibility of the Ni film; χ = (1-NU)
-1
χ
o
. Now, (1-NU)
-1
is the Stoner enhancement
factor with the density of states for the d-electrons at Fermi energy; N, and the energy
shift due to the exchange interaction between spin up and spin down electrons; U. χ
o
is
the Pauli susceptibility. The physics is as follows. At the interface between Ni and In
films, the magnetic d-electrons of Ni atoms hybridize with conduction electrons from In
film. This hybridization decreases the density of states in d-electrons; N, and causes the N
value to be less than N
o
which is the value of the bulk state. As a result, the product NU
becomes less than 1 and suppresses the possession of magnetic moments in the Ni atoms,
so that the film is magnetically dead. As Ni atoms are added to the film, the additional Ni
atoms increase the NU value and enlarge the linear slope. When the NU value reaches 1,
it makes the enhancement factor; (1-NU)
-1
, diverge, the Hall curve; R
yx
(B), become non-
linear, and the film possess magnetic moments. [5]

63
CHAPTER 5 ; Ni on Pb, MAGNETICALLY DEAD or ALIVE ?

5.1 Motivation

Meservey et al. [36][37] investigated the proximity effect of ferromagnetic metal films
with the spin-polarized tunneling method. They detected about 3 at.lay. of Magnetic
Dead Layers (MDLs) of Ni on Al substrates. Then Moodera and Meservey produced a
new sensor to improve the sensitivity with the RF oscillator method [8][34][35] and
measured Pb/Ni double layers with 9 nm (about 30 at.lay.) thickness of Pb substrate as
part of a 14MHz oscillator. When the Pb substrate changes its state from normal
conducting into superconducting, it increases the frequency of the oscillator by around 60
kHz. They observed the T
c
-reduction of the Pb film due to the Ni deposition on it. 0.4 nm
(about 1.8 at.lay.) of Ni coverage makes the transition temperature fall below 4.2 K. They
also observed a similar effect with Fe deposition whose thickness is only about 1/80 of Ni
thickness. From these experimental results they concluded that not only isolated Fe atoms
but also isolated Ni atoms deposited on the surface of Pb substrate at 4.2 K possess
magnetic moments. Furthermore, although magnetic moments were present on the Ni
atoms deposited on the Pb, the Hall-effect measurement did not detect them. [34]
However, they do not try to give a concrete value for this reduced moment of Ni atoms.
Therefore, we revisit the Pb/Ni system to measure the magnetic scattering of Ni with the
method of Weak Localization (WL); quantum interference. It is well known that the pair
breaking mechanism in superconductivity and the dephasing in weak localization are in
many aspects identical. In this series, we use only very thin Pb films between 1.3 and 5
at.lay. deposited on top of the Ag substrate with about 37 at.lay. thickness, because we
64
make the Ag substrate suppress the superconductivity of the extremely thin Pb film with
the SPE and avoid the Azlamazov-Larkin fluctuations. [21] We have two measurement
methods (1) the Anomalous Hall Effect (AHE) and (2) the Weak Localization (WL) in
this project.

5.2 Experimental results

5.2.1 The MDL by the Anomalous Hall Effect (AHR)

Fig 5.1 shows the experimental results of the anomalous Hall resistance ΔR
yx
(B) with
2.0 at.lay. of the Pb thickness at 10 K. The MDL is 2.5 at.lay. As mentioned in section
4.2.1., extrapolating the anomalous Hall curve from the high magnetic field back to zero,
one can evaluate the anomalous Hall resistance at zero field, R
yx
(0). All experimental
results with the different thicknesses of Pb film at 10K are plotted in Fig 5.2. From these
results we can see that the thickness of the MDL is almost independent from the Pb
substrate thickness (see also Fig 4.6). The concrete value of the MDLs are collected in
TABLE 5.1. These results also support the fact that the Pb film covers the Ag substrate
completely and homogeneously, because if not, the MDL region would not show up.

65

Fig 5.1 : The Anomalous Hall curve
ΔR
yx
(B) versus magnetic field. The
thickness of Pb is 2.0 at.lay. and the
measurement temperature is at 10 K. The
numbers on the right side of the each curve
give the Ni coverage thickness. The
maximum MDL is 2.5 at.lay.
Fig 5.2 : The AHR at zero field R
yx
(0) of
Ag/Pb/Ni film at 10 K with different
thickness of the Pb film.

TABLE 5.1 : The MDL values in Ag/Pb/Ni sandwich film at 10 K by the AHE. The first
column gives the thickness of the Pb film in at.lay.

d
Pb
(at.lay) d
MDL
(at.lay)
1.3 2.5
2.0 2.5
5.0 3.3
10.2 2.6
66
5.2.2 The MDL by the Weak Localization (WL)

We also measure the magneto resistance to investigate the dephasing of the
conduction electrons due to the Ni atoms deposited on top of the Pb film in Ag/Pb/Ni
sandwich film. Fig 5.3 shows the experimental results of the magneto resistance R
xx
(B)
with 1.3 at.lay. of the Pb thickness at 10 K. The numbers on the right side of the each
curve give the Ni coverage thickness. The open and full circles are the experimental data
and the full curves are theoretical fits with two fitting parameters, B
*
i
and B
*
so
.

Fig 5.3 : Magneto resistance versus magnetic field. The Ag/Pb/Ni sandwich film has 1.3
at.lay. of Pb thickness at 10 K. The open and full circles are the experimental data and the
full curves are theoretical fits yielding the singlet and triplet dephasing rates.

67
S. Hikami, et al. derived the following quantum conductance correction by using the
Weak Localization theory in 1980. [37]















−








π
=
Δ
T S
2
2
2
B
B
2
3
B
B
2
1
2
e
R
R
f f
η
(5.2.2-1)

R is the resistance per square, ΔR/R
2
= -ΔG is the (negative) correction in conductance,
and the function f(x) is given by the following equation.

( ) ( )






+ Ψ + =
x
1
2
1
x ln x f
(5.2.2-2)

Ψ(z) is the digamma function. Also in equ (5.2.2-1) B
S
and B
T
are both the characteristic
field for singlet and triplet dephasing, respectively. They are given by the following
equation.

*
i s i S
B B 2 B B = + =
(5.2.2-2)

*
SO
*
i
S SO i T
B
3
4
B
B
3
2
B
3
4
B B
+ =
+ + =
(5.2.2-3)

B
i
, B
SO
, and B
S
are the characteristic fields for inelastic, Spin-Orbit, and Magnetic
scattering, respectively. The characteristic fields B
n
are connected with the corresponding
68
characteristic relaxation times τ
n
(corresponding scattering times) with the following
relationship.

eD 4
B
n n
η
= τ
(5.2.2-4)

, where D = 1/(e
2
NRd) is the diffusion constant, R the resistance per square, d the
thickness of the film, and N is the density of state. [21] From equation (5.2.2-4) we can
obtain the B
n
τ
n
value of the Ag/Pb/Ni film, B
n
τ
n
, ≈ 3.0 x 10
-13
Ts. It varies slightly for
different multi-layers. The additional dephasing rate 1/τ
φ
due to the Ni deposition is
plotted in Fig 5.4 as a function of the Ni thickness at 10 K. The numbers on the right side
of each curve are thickness of the Pb inside the sandwich films in units of at.lay. The
open squares give the experimental data of (Sb)/Ag/Ni film where the Ni atoms are
directly deposited on top of Ag substrate. In this case, the film already possesses the
magnetic moment below one at.lay. of Ni coverage thickness and behaves quite
differently from others.

69

Fig 5.4 : The additional dephasing rate 1/τ
φ
due to the Ni coverage on top of the Pb
substrate versus Ni thickness at 10 K. The numbers on the right side of each curve are
thickness of the Pb inside the sandwich films. The open squares give 1/τ
φ
for (Sb)/Ag/Ni
film (Ni directly deposited on top of Ag substrate).

70
From the above two figures, Fig 5.3 and Fig 5.4, we can see that the additional dephasing
due to the Ni on Pb is very small up to 1.5 at.lay. thickness of Ni. Now we evaluate the
dephasing rate of the Ag/Pb/Ni sandwich film which has 2.0 at.lay of Pb film using
equation (5.2.2-4). The additional characteristic field B
n
can be directly determined by
magneto resistance measurements. When the Ni thickness is 1.5 at.lay., the corresponding
field ΔB
i
* is given as ΔB
i
* ≈ 0.01 (T). With the product value mentioned before, B
n
τ
n
, ≈
3.0 x 10
-13
Ts, we can obtain the additional dephasing rate, 1/τ
φ
≈ 3.0 x 10
10
s
-1
. Now, this
rate is the average for an electron propagating all over the Ag/Pb/Ni film. The time that
the electron spends in the Ni film is proportional to the fraction d
Ni
N
Ni
/(d
Ag
N
Ag
+d
Pb
N
Pb
+d
Ni
N
Ni
), so that the actual dephasing in the Ni film is given by the factor
of (d
Ag
N
Ag
+d
Pb
N
Pb
+d
Ni
N
Ni
)/d
Ni
N
Ni
≈ d
Ag
N
Ag
/d
Ni
N
Ni
. Therefore, the dephasing rate in the
Ni film is following.

( )
1 10
Ni Ni
Ag Ag
WL
Ni
s 10 0 . 3
N d
N d
1
−
ϕ
× × ≈
τ
(5.2.2-5)

71
5.3 Comparison with the results from the RF oscillator method

Moodera and Meservey observe that even at only 0.2 at.lay. of Ni coverage the Ni
atoms reduce the T
c
of a Pb film with 9 nm thickness. [34] Then they explain that Cooper
pairs are dephased or depaired due to the Ni atoms possessing magnetic moments, even
though their thickness is around 0.2 at.lay. on top of the Pb film. To compare the
dephasing rate with ours, we also evaluate the dephasing rate of the Pb/Ni double layers
that they measured. Now the Ni film on top of the Pb substrate has 1.5 at.lay. and reduces
the transition temperature by about 2.5 K. We suppose that this T
c
-reduction is due
entirely to the (magnetic) dephasing rate 1/τ
φ
. In the linear approximation, a weak
coupling superconductor follows the relation below between a dephasing rate 1/τ
φ
and T
c
-
reduction.

ϕ
τ
π
≈ Δ
8
T k
c B
η
(5.3-1)

For the strong coupling superconductor Pb one obtains a correction factor of 1.4 but we
disregard this here. [39] From this relation and the value of the T
c
-reduction, we can
evaluate the dephasing rate, 1/τ
φ
≈ 8 k
B
ΔT
c
/πħ ≈ 8.0 x 10
11
s
-1
in the Pb/Ni double layers.
As mentioned before, we have d
Pb
N
Pb
/d
Ni
N
Ni
as the factor of the dephasing rate in the Ni
film. Therefore, the dephasing rate in the Ni film is as follows.

( )
1 11
Ni Ni
Pb Pb
SC
Ni
s 10 0 . 8
N d
N d 1
−
ϕ
× × ≈
τ
(5.3-2)
72
Now we compare the dephasing rates in the Ni film between the superconducting and
weak localization measurement. The ratio of the two rates is

120
10 0 . 3
10 0 . 8
65 . 0 90
98 . 2 90
10 0 . 3
10 0 . 8
d
d
1
1
ratio
10
11
10
11
Ag Ag
Pb Pb
WL
Ni
SC
Ni
≈
×
×
×
×
×
=
×
×
×
γ
γ
=
τ
τ
=
ϕ
ϕ
(5.3-3)

Here we have replaced the ratio N
Pb
/N
Ag
by the ratio of their Sommerfeld constants γ
Pb
/γ
Ag
= 2.98 / 0.65, [28] and plugged in the film thicknesses, d
Pb
= 9 nm (Moodera and
Meservey’s experiment) [34] and d
Ag
= 9 nm (our experiment). The order of the ratio of
the dephasing rates is 10
2
. It is very obvious that the dephasing rate evaluated by the T
c
-
reduction of Pb film is much larger than the dephasing rate measured by the weak
localization.
73
5.4 Discussion

To start, we consider the reason that the dephasing rate derived from the T
c
-reduction
is so much higher compared to that from the weak localization results. There are some
common dephasing processes between superconductor and weak localization for each
electron. The “pair propagator” in the superconductor and weak localization are shown in
Fig 5.5 and Fig 5.6, respectively. In the superconductor case, the propagator is a Cooper
pair consisting of two electrons with opposite momentums and spins. One electron with
spin up travels from the position A to B, meanwhile its time reversed partner with spin
down propagates from the position B to A (see Fig 5.5). On the other hand, in the weak
localization case (see Fig 5.6) two partial waves of a single electron travel in the opposite
direction and along a closed loop. For the dephasing process the closed path is not
important. The essential thing is that the both propagators move along time reversed
paths. The partial electron waves traveling clockwise and counterclockwise interact with
the environment. The electron-phonon interaction, interaction with the Fermi sea, and
magnetic scattering cause changes in energy and phase between the two partial waves.
However, there is no interaction between the two partial waves, because they belong to
the same electron. This is a remarkable difference from the propagator of a
superconductor.
74

In the superconductor case, electrons making the Cooper pair interact with the same
environment and pass through the same dephasing, similar to the weak localization case.
For these processes the dephasing of weak localization is the same as the pair breaking in
superconductivity. However, these electrons are affected by the dephasing process more
often than those in the weak localization because there are inter-particle interactions
between the two electrons and these interactions influence the phase coherence of the pair
propagator consisting of the two electrons. Next we consider following three inner-
particle interactions. (a) the electron-electron interaction, (b) the thermal effect (finite
temperature), and (c) the Coulomb interaction.

B
A
Fig 5.5 Fig 5.6
Fig 5.5 : The pair propagator of a Cooper pair in a superconductor.
Fig 5.6 : The particle-particle propagator in weak localization.
75

(a) The electron-electron interaction;
Two electrons attract each other through exchanging phonons and keep coherence.
This interaction causes superconductivity.

(b) The thermal effect;
The coherence of the two electrons decays with time due to the finite temperature, as
mentioned before (see the section (3.1.5-(1))).

(c) The Coulomb interaction;
The Coulomb interaction between the two electrons causes dephasing or “pair
weakening”, when the transition metal atoms exist on/in the superconductor. [45]

The balance of creation (a) and decay (b) determine the transition temperature of the
superconductor.
76
Now we focus on the Coulomb interaction (c). When transition metal atoms (d-atoms)
such as Ni are put on / in a superconductor, they change the properties of the
superconductor drastically. When the two electrons making a Cooper pair jump into d-
states of a d-atom like Ni and repel each other due to the overlap, they make the
superconductivity weaken. In the Pb/Ni double layer case, Cooper pairs in the
superconducting Pb film penetrate the Ni film below the transition temperature. The d-
atoms possess d-resonance states, and one can divide the states into three groups.

(1) No Coulomb interaction between d-electrons with opposite spin.

(2) A finite Coulomb interaction between d-electrons with opposite spin, but no
magnetic moment.

(3) A sufficiently strong Coulomb interaction to break the symmetry between d-electrons
with opposite spin, and to develop a magnetic moment.

The phenomenon of case (3) is known to cause “pair breaking”. Furthermore; since not
only case (2) but also case (1) reduces the transition temperature, the effect of these cases
is often called “pair weakening”. This effect has been investigated in the 1970’s [44]. In
the first case, especially, even though the Coulomb repulsion does not influence the two
d-electrons as an inner particle interaction, we can still observe T
c
-reduction. The
physical picture of the “pair weakening” case is simply expressed in the following way.
Here we consider its dynamic interpretation with the time reversible process. When the
two electrons of a Cooper pair jump into the two d-states of a d-atom, their pair
77
amplitude (pair propagator) still decays due to the finite temperature. However, during
their stay in d-states, these electrons are screened from the attractive electron-phonon
interaction. Since the exchange of phonons between the two electrons supports their
coherence and makes the superconducting state, this screening effect weakens the
superconductivity. The fraction of the staying time in the d-states (d-resonance) is
roughly N
d
/N
fe
where N
d
is the density of states of the d-resonance of all d-atoms, and N
fe

is the density of states of the free conduction electrons. Therefore, the attractive
interaction is reduced by a factor (1- N
d
/N
fe
). This causes the T
c
-reduction.

78
5.5 Conclusion

We compare the experimental results and their interpretation from the two different
measurement methods; the T
c
-reduction of superconducting Pb films, and the weak
localization. From this comparison we find a much smaller dephasing than the T
c
-
reduction method would suggest. We conclude that

(1) Our experimental results and those by Moodera and Meservey do not contradict.
(2) Our experimental results and the conclusion given by Moodera and Meservey
contradict.
(3) The dephasing calculated from weak localization is much smaller than that from the
T
c
-reduction method.
(4) The reduction of the superconducting transition temperature is not due to dephasing
by magnetic scattering but due to the resonance scattering of Cooper pairs by
non-magnetic d-states.

The combined investigation of magnetic dead Ni layers on top of a superconductor, and
the T
c
-reduction and dephasing of weak localization would be very strong methods to
research the formation of magnetic moments in d-metals.

79
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82
Appendix : The “Local Peak” in the Magneto Resistance curve of the (Sb)/Pb/Ni
sandwich film

Fig (A.1) shows the magneto resistance curves; R
xx
(B)- R
xx
(0), of the (Sb)/Pb/Ni film
as a function of the applied field B at 10 K. The thickness of the Pb substrate and the
resistance of the (Sb)/Pb film are 10.2 (at.lay.) and 287 (Ω), respectively. The numbers on
the right side of each curve give the coverage thickness of the Ni on top of the Pb
substrate in units of atomic layer (at.lay.).

Fig (A.1) : The magneto resistance; R
xx
(B)- R
xx
(0), of the (Sb)/Pb/Ni film versus applied
magnetic field B at 10 K. The open circles are measured in the MDL region. The full
squares are measured out of the MDL region.
83
The magneto resistance changes from positive to negative as Ni thickness increases. In
addition, at over 4.0 at.lay. of the Ni coverage the magnetic resistance shows unusual
behavior with the applied magnetic field, especially between -1 and +1 T. We can see
that above 4.4 at.lay. of the Ni coverage thickness the magneto resistance has a “local
peak” in the vicinity of the zero field (0T) and kinks around -1 and 1 T. From the
anomalous Hall curve we can estimate the saturated field B
s
where all magnetic moments
align to the z-direction (parallel to the magnetic field). Since the “local peak” shows up
around 0 T and inside of the saturated field B
s
, it is expected that the peak might be due
to both the disordered magnetic moments of Ni and the interface between the Ni and Pb
substrate. To investigate the relation between the local peak and the Pb/Ni interface, we
compare these results with the magneto-resistance of the Ag/Pb/Ni film with 5.0 at.lay. of
the Pb thickness between Ag and Ni. However, we do not observe a local peak for the
Ag/Pb/Ni films which have 1.3, 2.0 and 5.0 at.lay. of Pb thickness between the Ag and Ni.
Fig(A.2) shows the magneto resistance curve of Ag/Pb/Ni film. It is obvious that there is
no local peak. Therefore it shows that the “local peak” is not due to the interface between
Ni and Pb, but the origin is not understood.
84

Fig(A.2) : the magneto resistance curve of Ag/Pb/Ni film at 10K.

Abstract (if available)

Abstract When a thin superconducting film (S film) is condensed onto a thin normal conducting film (N film), the first layers of the S film loose their superconductivity. This phenomenon is generally called the "superconducting proximity effect(SPE)". As an investigation of SPE we focus on the transition temperature of extremely thin NS double layers in the thin regime. Normal metal is condensed on top of insulating Sb, then Pb is deposited on it in small steps. The transition temperature is plotted in an inverse Tc-reduction 1/dTc=1/(Ts-Tc) versus Pb thickness graph. To compare our experimental results with the theoretical prediction, a numerical calculation of the SN double layer is performed by our group using the linear gap equation. As a result, there are large discrepancies between the experimental and theoretical results generally. The results of the NS double layers can be divided into three groups in terms of their discrepancies between experiment and theory.(1) Non-coupling(Tc=0K):N= Mg, Ag, Cu, Au. There are large deviations between experiment and theory by a factor to the order of 2.5. (2) Weak coupling (Tc is low(<2.5K):N=Cd, Zn, Al. Deviation is present, but only by a factor of 1.5. (3) Intermediate coupling(Tc is around half of Pb's(4.5K)): N=In, Sn. The experimental results agree with the theory.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Tateishi, Go (author)

Core Title Investigation of the superconducting proximity effect (SPE) and magnetc dead layers (MDL) in thin film double layers

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Physics

Publication Date 03/12/2009

Defense Date 11/20/2008

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

Tag magnetic dead layers,OAI-PMH Harvest,superconducting proximity effect,thin metal film

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Bergmann, Gerd (committee chair), Haas, Stephan (committee member), Lu, Jia Grace (committee member), Nakano, Aiichiro (committee member), Thompson, Richard S. (committee member)

Creator Email go_tateishi@yahoo.co.jp,gotateishi@hotmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2019

Unique identifier UC1487946

Identifier etd-Tateishi-2569 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-213147 (legacy record id),usctheses-m2019 (legacy record id)

Legacy Identifier etd-Tateishi-2569.pdf

Dmrecord 213147

Document Type Dissertation

Rights Tateishi, Go

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu