Fractional vortices in Josephson tunnel junctions with a ferromagnetic interlayer [Elektronische Ressource] / vorgelegt von Judith Pfeiffer

Sujets

• Physik

Informations

• Publié par: eberhard_karls_universitat_tubingen
• Publié le: 01 janvier 2010
• Nombre de lectures: 10
• Langue: English
• Poids de l'ouvrage: 6 Mo

Extrait

Fractional vortices
in Josephson tunnel junctions
with a ferromagnetic
interlayer
DISSERTATION
Zur Erlangung des Grades eines Doktors
der Naturwissenschaften
der Fakult¨at fu¨r Mathematik und Physik
der Eberhard-Karls-Universit¨at zu Tu¨bingen
vorgelegt von
Judith Pfeiffer
aus Schweinfurt
2010Tag der mu¨ndlichen Pru¨fung: 11.01.2010
Dekan: Prof. Dr. W. Knapp
1. Berichterstatter: Prof. Dr. R. Kleiner
2. Berichterstatter: Prof. Dr. D. Ko¨lleHey you,
out there in the cold
Pink FloydAbstract
In this thesis, we study Josephson tunnel junctions with a ferromag-
netic interlayer, so-called SIFS (superconductor-insulator-ferromagnet-
superconductor) Josephson junctions. Conventional 0 Josephson junc-
tions have a current phase relationI =I sin withI >0. In contrast,c c
SIFS Josephson junctions provide the possibility to realize π junctions.
In such structures the superconducting wave function changes its sign
across the barrier, i.e., shifts its phase by π. The current phase rela-
tion of π junctions reads I = I sin, formally with I < 0. Using ac c
step-like thickness of the ferromagnetic barrier, allows to fabricate so-
called 0-π Josephson junctions. The ground state phase in such junc-
tions has a value of 0 deep inside the 0-region, and a value of π deep
inside the π region. Supposed that the critical current densities in both
halves of the 0-π junction are equal, the ground state of the system
consists of a spontaneously formed vortex of supercurrent circulating
aroundthe0-π boundary. Thissupercurrentcorrespondstoalocalmag-
netic flux |Φ| ≤ Φ /2, where Φ = h/2e is the magnetic flux quantum0 0
[BKS78; XMT95; GKK02]. Thus, the localized magnetic field is called
semifluxon. In the framework of this thesis, we examine triplets, 0-π
junctions with their respective 0 and π reference junctions. Samples of
different geometries (linear and annular) and of different lengths (rang-
ingfromtheshorttothelongjunctionlimit)areavailable. Thejunctions
arerealizedinoverlapgeometry,usingNb/Al-Al O /Ni Cu /Nbtech-2 3 60 40
nology [WTK06; WSK07].
Theaimofthisthesiswastwofold: First,wewantedtofigureoutwhether
the additional ferromagnetic interlayer of SIFS junctions modifies the
Josephson physics or leads to additional noise contributions in contrast
to conventionalSIS Josephson junctions, both in the thermal and in the
quantum regime. As a second aim, we studied the properties of 0-π
junctions and characterized the associated fractional flux in detail.
We determined the static and dynamic properties of our samples by
measuring current-voltage characteristics, IVCs, and by measuring the
critical currentI vs. applied magnetic fieldB,I (B). The experimentsc c
4 3were performed using a standard He- and He-cryostat. As a result,
I (B) of the reference junctions and of the 0-π junctions showed a smallc
offsetfromzeromagneticfield. Additionally,I (B) of the 0-π Josephsonc
junctionsrevealedanasymmetricheightofthemaximaandbumpedside
minima. Thisbehaviorismostlikelyduetoafinitemagnetizationofthe
ferromagnetic layer. Regarding the dynamic properties of the reference
junctions, we observednodiscrepancyfromstandardJosephsonphysics.
Depending on the respective experimental conditions, Fiske steps, zerofield stepsand Shapirosteps wereverified,exactlyasexpected fromthe-
ory. In case of short 0-π junctions, half-integer zero field steps were
experimentally verified on the IVCs for the first time. Additionally,
we presented the first experimental observation of various metastable
fluxon/semifluxon configurations in long 0-π junctions. Switching cur-
rent measurements were performed in a dilution refrigerator to study
escapemechanisms ofthe Josephsonphase in SIFS junctions. The effec-
tive potential height as a function of magnetic field and as a function of
temperature was examined using samples in the short limit. Numerical
simulations showed, that the activation energy of SIFS Josephson junc-
tions vs. magnetic field can be described in the framework of standard
shortJosephsonjunction theory. Performingswitchingcurrentmeasure-
ments at different temperatures revealed, that the escape temperatures
coincided perfectly with the bath temperatures, for 0, π as well as 0-π
coupling. Using microwave spectroscopy, we observed harmonic, sub-
harmonic and superharmonic pumping. The experimental data of the
eigenfrequenciesof short and intermediate length samples showed a per-
fect agreement with the pointlike junction theory.
Overall we conclude, that we do observe peculiarities of the ferromag-
netic interlayer in SIFS Josephson junction. Nevertheless, we did not
find any indication for additional noise contributions due to the pres-
ence of the ferromagnetic layer. Thus, regarding quantum applications,
the usability of SIFS Josephson junctions is not restricted due to poor
noiseproperties. Inmanyaspects,shortSIFSsamplesarewelldescribed
by the short Josephson junction theory. In the case of 0-π junctions, we
developed a deep understanding of the associatedfractional flux. Its oc-
currence was experimentally observed in several experiments, as it had
been predicted in theory.
iiContents
Introduction 1
I Basics 5
1 Josephson physics 6
1.1 Superconductivity . . . . . . . . . . . . . . . . . . . . . . 6
1.2 The Josephson relations . . . . . . . . . . . . . . . . . . . 7
1.3 Short Josephson junctions . . . . . . . . . . . . . . . . . . 10
1.3.1 RCSJ model . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Magnetic field dependence . . . . . . . . . . . . . . 13
1.3.3 Resonances in short junctions: Fiske steps and
Shapiro steps . . . . . . . . . . . . . . . . . . . . . 15
1.4 Long Josephson junctions . . . . . . . . . . . . . . . . . . 17
1.4.1 The sine-Gordon equation . . . . . . . . . . . . . . 17
1.4.2 Resonances in long junctions: zero field steps . . . 21
1.5 The pendulum analog . . . . . . . . . . . . . . . . . . . . 21
2 Fractional vortices in Josephson junctions 24
2.1 0-π Josephson junctions . . . . . . . . . . . . . . . . . . . 24
2.2 Semifluxons . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Static properties of 0-π junctions: a fingerprint of the
semifluxon . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3 Josephson junctions in the quantum regime 33
3.1 The washboard potential . . . . . . . . . . . . . . . . . . . 33
3.2 Escapemechanisms of the Josephsonphase in point junc-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Thermal activation . . . . . . . . . . . . . . . . . . 35
iiiiv Contents
3.2.2 Macroscopic quantum tunneling . . . . . . . . . . 39
3.2.3 Resonant activation . . . . . . . . . . . . . . . . . 41
3.3 Consequencesoffinitelengthandphasediscontinuitypoints
on the escape mechanisms . . . . . . . . . . . . . . . . . . 43
4 Josephson junctions with a ferromagnetic barrier 47
4.1 Introduction: history and state of the art . . . . . . . . . 47
4.2 Theory ofπ junctions . . . . . . . . . . . . . . . . . . . . 50
4.2.1 Microscopic origin . . . . . . . . . . . . . . . . . . 50
4.2.2 Diffusive vs. clean limit . . . . . . . . . . . . . . . 53
4.3 Fabrication of 0-π SIFS Josephson
junctions with reference junctions . . . . . . . . . . . . . . 56
II Results 59
5 Conventional characterization of SIFS
Josephson Junctions 60
5.1 Samples and measurement techniques . . . . . . . . . . . 61
5.2 Static properties of 0-π SIFS junctions . . . . . . . . . . . 64
5.2.1 Magnetic field dependence of short 0-π junctions . 64
5.2.2 Magnetic field dependence of long 0-π junctions . . 67
5.3 DynamicpropertiesofshortandintermediateSIFSJoseph-
son junctions . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.1 Half-integer zero field steps . . . . . . . . . . . . . 75
5.3.2 Fiske steps . . . . . . . . . . . . . . . . . . . . . . 79
5.3.3 Shapiro steps . . . . . . . . . . . . . . . . . . . . . 82
5.4 Dynamic properties of long 0-π SIFS junctions . . . . . . 85
5.4.1 Experimental data . . . . . . . . . . . . . . . . . . 85
5.4.2 Numerical analysis . . . . . . . . . . . . . . . . . . 86
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Escape of the Josephson phase in SIFS junctions: From
thermal to quantum regime 91
6.1 Samples and measurement techniques . . . . . . . . . . . 92
6.2 Escape rate measurements of short SIFS Josephson junc-
tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.2.1 Phase escape in magnetic field . . . . . . . . . . . 96
6.2.2 Phase escape at different temperatures . . . . . . . 103
6.3 Microwave spectroscopy of short and intermediate length
SIFS Josephson junctions . . . . . . . . . . . . . . . . . . 108Contents v
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Summary 117
Zusammenfassung 122
A Samples 128
Bibliography 131