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Electron Transport through Domain Walls in Ferromagnetic Nanowires

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167 pages
Niveau: Supérieur

  • dissertation


Electron Transport through Domain Walls in Ferromagnetic Nanowires Peter Edward Falloon BSc (Hons) MSc, W. Aust. A dissertation submitted to the University of Western Australia & l'Universite Louis Pasteur for the degree of Doctor of Philosophy in co-tutelle

  • physical parameter

  • electron transport through

  • domain wall

  • transport through

  • real physical

  • ferromagnetic nanowires

  • supervisor uwa

  • conductance through

  • spins between


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Electron Transport through Domain Walls in
Ferromagnetic Nanowires
Peter Edward Falloon
BSc (Hons) MSc, W. Aust.
A dissertation submitted to
the University of Western Australia
&
l’Universit´e Louis Pasteur
for the degree of Doctor of Philosophy in co-tutelleiiThesis defence at Strasbourg, 26 June 2006 in front of the jury comprising
Supervisor ULP: Prof. Rodolfo A. Jalabert (IPCMS, Strasbourg)
Supervisor UWA: Assoc. Prof. Robert L. Stamps (UWA, Perth)
Referees: Prof. David M. Edwards (Imperial College, London)
Prof. Klaus Richter (Universitat¨ Regensburg)
Dr. Michel Viret (CEA, Saclay)
Prof. Wolfgang Weber (IPCMS, Strasbourg)
Invited member: Dr. Dietmar Weinmann (IPCMS, Strasbourg)
iiiivAbstract
In this dissertation we present a theoretical study of electron transport through
domain walls, with a particular focus on conductance properties, in order to un-
derstand various transport measurements that have been carried out recently on
ferromagnetic nanowires.
The starting point for our work is a ballistic treatment of transport through the
domain wall. In this case conduction electrons are generally only weakly reflected
by the domain wall, and the principal effect is a mixing of transmitted electron
spins between up and down states. For small spin-splitting of conductance electrons
the latter can be characterized by an appropriate adiabaticity parameter. We then
incorporate the effect of spin-dependent scattering in the regions adjacent to the
domain wall through a circuit model based on a generalization of the two-resistor
theoryofValetandFert. Withinthismodelwefindthatthedomainwallgivesriseto
an enhancement of resistance similar to the giant magnetoresistance effect found in
ferromagneticmultilayersystems. Theeffectislargestinthelimitofanabruptwall,
for which there is complete mistracking of spin, and decreases with increasing wall
width due to the reduction of spin mistracking. For reasonable physical parameter
values we find order-of-magnitude agreement with recent experiments.
Going beyond the assumption of ballistic transport, we then consider the more
realistic case of a domain wall subject to impurity scattering. A scattering matrix
formalism is used to calculate conductance through a disordered region with either
uniform magnetization or a domain wall. By combining either amplitudes or proba-
bilities we are able to study both coherent and incoherent transport properties. The
coherent case corresponds to elastic scattering by static defects, which is dominant
atlowtemperatures, whiletheincoherentcaseprovidesaphenomenologicaldescrip-
tionoftheinelasticscatteringpresentinrealphysicalsystemsatroomtemperature.
vIt is found that scattering from impurities increases the amount of spin mistracking
of electrons travelling through a domain wall. This leads, in the incoherent case,
to a reduction of conductance through the domain wall as compared to a uniformly
magnetized region. In the coherent case, on the other hand, a reduction of weak
localization and spin-reversing reflection amplitudes combine to give a positive con-
tribution to domain wall conductance, which can lead to an overall enhancement of
conductanceduetothedomainwallinthediffusiveregime. Areductionofuniversalnce fluctuations is found in a coherent disordered domain wall, which can
be attributed to a decorrelation between spin-mixing and spin-conserving scattering
amplitudes.
To treat the total effect of a disordered domain wall on the conductance of
a nanowire, we extend the scattering matrix approach to incorporate the regions
adjacent to the domain wall, thus providing a microscopic equivalent of the circuit
model studied for a ballistic wall. It is found that scattering in the adjacent regions
leads to an increase in domain wall magnetoconductance as compared to the effect
foundbyincludingonlythescatteringinsidethewall. Thisincreaseismostdramatic
in the limit of narrow walls, but is also significant in the limit of wide walls.
Finally, we apply our model to calculate the spin-transfer torque exerted by a
spin-polarized current on a domain wall. Within the circuit model we find expres-
sions for the spin-transfer torque and corresponding domain wall velocity, ignoring
pinning effects.
vi“If you didn’t mind wasting the best years of your youth,
graduate student life ...was paradise.”
— Emanuel Derman
viiviiiAcknowledgements
I would firstly like to thank my supervisors, A. Prof. Robert Stamps and Prof.
RodolfoJalabert,fortheirguidanceduringthisPhD.DuringmytimeinStrasbourg,
Rodolfo provided invaluable insight and feedback on my work, and went out of his
way to give me the chance to participate in the french physics community. Bob
was a constant source of new ideas, good advice, and enthusiasm for physics, and
from him I learned a new way to approach problem solving. I would also like to
thank Dietmar Weinmann, with whom it has been a great pleasure to collaborate
throughout my thesis, and who is the third supervisor of this PhD in all but name.
For their help throughout the arduous process of arranging the co-tutelle pro-
gramme in which this thesis has been carried out, I sincerely thank the staff at the
UWA Graduate Research School and the ULP Bureau des ´etudes doctorales. I am
alsoverygratefultohavereceivedfinancialsupportfromtheAustraliangovernment
through an Australian Postgraduate Award, the University of Western Australia
through a Jean Rogerson Fellowship, and the European Union through the Marie
Curie Early Stage Researcher programme.
It is a pleasure to acknowledge Dr. Paul Abbott and Dr. Michael Trott for their
expertassistancewithabroadrangeofcomputationalphysicsissues. IalsothankA.
Prof. Jingbo Wang for use of the “Nye” computer cluster and Dr. Michael Eilon for
general computer support at UWA. For their correspondence on questions relating
to the typesetting of this thesis, I thank Andr´e Wobst and Andy Buckley.
I’d like to thank all my fellow postgraduate students in the UWA School of
Physics, past and present, for making it a great place to be part of. The following
people, among many others, will be fondly remembered: Paul Brayshaw, for the
angry exchanges providing sources of puzzlement (10); StuartHatch, forthemusical
ixeducation; ChrisHines,forthejuggling,homebrew,andunixexpertise; Dr.Joo-Von
Kim, for the many discussions about physics and Macs–and for having the bright
idea to do a co-tutelle; Dr. Peter Loxley, for the wide-ranging discussions and games
of office handball–both of which helped to while away many an afternoon; and, for
the sporting memories, the Fetahs: Nicole Gorham, Milan Mari´c, Shane McCarthy,
Neil Riste, Holly Rose, and Neil Somers.
Du cot´e fran¸cais, j’aimerais remercier les autres th´esards que j’ai rencontr´es
`a l’IPCMS, qui ont support´e mon fran¸cais et qui m’ont accueilli a` bras ouverts,
´en particulier: Ahmed Nait-Abdi, Madjid Abes, Elise Gambetti-C´esare, Romaric
Montsouka, Julien V´enuat, Vincent Vlaminck, et Guillaume Weick.
J’adresse une mention sp´eciale a` Gabriel Vasseur, co-th´esard et ami, pour les
innombrables discussions que nous avons eues sur l’informatique, la physique et la
nature de la recherche. J’ai beaucoup appr´eci´e nos sessions jam et les journ´ees
snowboard. Merci ´egalement de m’avoir aid´e a` comprendre les subtilit´es de la
langue fran¸caise avec tant de rigueur. J’esp`ere que j’aurai l’occasion de te renvoyer
l’ascenseur, si jamais tu viens a` Zihuatanejo.
On a personal level, I thank my family and the Lourdes family for their under-
standing during my seemingly interminable years at university.
Finally, and most importantly, I thank my girlfriend Cresandra Roslyn Lourdes,
for always being there. Without your constant love and support, this thesis would
never have been finished. Merci.
PEF 28/6/2006
x

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