Spin waves and the anomalous Hall effect in ferromagnetic (Ga,Mn)As

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for Tintinthe greatest lil’ ferret that ever lived
AcknowledgementsI would like to thank my advisor, Professor Tomasz Dietl, for providing mewith the opportunity to work on many interesting topics and encouraging me toaim high in academic life. Working under the direction of such a successful anddedicated scientist taught me to trust my skills, accept responsibility and work hardto achieve set goals, the things I will certainly benefit from in the future.One of the greatest aspects of my research work has been the cooperation withthe group of Professor Hideo Ohno from Tohoku University, whose groundbreakingexperiments have been an inspiration also for my work. I will ever remain gratefulto Professor Ohno for his kind attitude.It was nice to meet the people of our Institute, especially the fellow membersof the SL2 group. My work would not proceed smoothly without the help of ourgroup’s computing cluster, which was kept running by the expertise of CzarekŚliwa—thank you for this, and your patient tolerance of my numerous attempts tobring the cores down. I regret that I did not pursue research together with youand ̷Lukasz. I have always felt a bit of envy towards the experimentalists in ourgroup, who fight at the frontline of physics, but my only visit in the lab ended uptriggering the fire alarm (thank you, Krzyś!).I would like to thank Professor Jacek Majewski and Rafa̷l Oszwa̷ldowski forproviding me with C. Strahberger’s tight-binding code, which made my work easier.There is also a group of people, whom I could always ask for advice and wordsof encouragement, especially Arek Wójs, Jacek Majewski and Professor WitoldDobrowolski. Their friendship and support are invaluable and helped me a lotduring the darkest moments of my PhD journey.Outside of the institute, Maria and Alex, my partners in crime, you are alwayswelcome to our home no matter how many kitchen appliances you destroy. Seb,thank you for polishing my Englirz. Now that I have more time, I can go backto making my culinary experiments with strange cuisines and crazy cakes on youand Roman. Halina, big thanks for managing everything for us in Poland. To allmy mates from physics forums and blogs, thank you for fascinating discussions onphysics and maths, and all your interest in my poor fate ;-)It was my grandma, who taught me the respect for knowledge and educationfrom my early days, as the indestructible key to my personal independence andfreedom. Remembering in what tough conditions you pursued your goals is thesource of my determination. You are my heroine. (ps. Out of caution I am nottaking philosophy on my exams.) My grandpa, you have always remained the manof truth and justice, showing me the way I can go through my life with peace ofmind.Scientists want to find out the global topology of the Universe to give the firmfoundation to what we believe in. Roman, you defined the global topology of mylife and gave sense to all the things, recognised only locally, unstable or withoutconnection.MyresearchwassupportedbytheScholarshipofthePresidentofPolishAcademyof Sciences, the EC NANOSPIN (FP6-IST-015728) and EC Network SemiSpinNet(PITN-GA-2008-215368) grants.
Page 1: Polish Academy of SciencesInstitute
Page 5 and 6: Curriculum VitaeEducation and Train
Page 7 and 8: Jaszowiec, Poland, 2005, RKKY and Z
Page 9 and 10: ContentsPreface 41 Introduction 132
Page 11: 10.5 Summary . . . . . . . . . . .
Page 14 and 15: to look far to find another example
Page 16 and 17: 1990 was a watershed event in the f
Page 18 and 19: Figure 1.1: Examples of spintronic
Page 20 and 21: values of spin-splitting up to thos
Page 23 and 24: Chapter 3(Ga,Mn)As as a dilutemagne
Page 25 and 26: in the 1970s and became commonly us
Page 27 and 28: GaAsMna 2a 3a 1dFigure 3.1: (Ga,Mn)
Page 29 and 30: 3.3 Mn impuritiesThe (Ga,Mn)As crys
Page 31 and 32: values too large to be explained by
Page 33 and 34: Chapter 4Origin of magnetism in(Ga,
Page 35 and 36: They lead to dramatic spin-dependen
Page 37 and 38: alignment of the Mn moments. The el
Page 39 and 40: Although J(r) describes exchange in
Page 41 and 42: Taking into account the above equat
Page 43 and 44: Bohr radius a ⋆ . One can expect
Page 45 and 46: Chapter 5Band structure of(Ga,Mn)As
Page 47 and 48: I know how to decompose the potenti
Page 49 and 50: k zk xΓΛLΣ K∆QWUZSXk yFigure 5
Page 51 and 52: or antibonding. In semiconductors l
Page 53 and 54:
of the Brillouin zone are illustrat
Page 55 and 56:
5.4.2 Structure inversion asymmetry
Page 57 and 58:
of electrons on the ion’s electro
Page 59 and 60:
Chapter 6Band structure methodsIn t
Page 61 and 62:
the higher-lying ones can be taken
Page 63 and 64:
Parameter Kohn-Luttinger Kane (set
Page 65 and 66:
and Q ǫ and R ǫ are the following
Page 67 and 68:
ThematrixM kso describesthek-depend
Page 69 and 70:
a b c022−0.2−0.41.51.5−2 −1
Page 71 and 72:
It is easy to see that the basis st
Page 73 and 74:
dependence on the interatomic dista
Page 75 and 76:
35 spds*sps*302520151050−5−10L
Page 77:
40-orbital spds ⋆ tight-binding a
Page 80 and 81:
adjacentmagneticmomentsandtheirexci
Page 82 and 83:
consistent and can accommodate any
Page 84 and 85:
which gives for M ′ ≤ N( ) NΩ
Page 86 and 87:
One can associate each lattice spin
Page 88 and 89:
volume. For P carriers, the Fermi e
Page 90 and 91:
FMFigure 7.3: Free energy F of the
Page 92 and 93:
MT1 2 3 4TFigure 7.6: Average magne
Page 94 and 95:
the ions’ magnetisation changes.
Page 96 and 97:
Because of the spin-orbit coupling
Page 98 and 99:
my perturbation calculus invalid. H
Page 100 and 101:
Due to the equality ∆ = NSβ/V, t
Page 102 and 103:
102
Page 104 and 105:
of the lattice ions. It ignores the
Page 106 and 107:
52with angular momentum L = 0 do no
Page 108 and 109:
in the vicinity of the Γ point, in
Page 110 and 111:
shinskii-Moriyaexchange. Someofthem
Page 112 and 113:
emaining terms).I want to obtain th
Page 114 and 115:
where excitation modes are spin wav
Page 116 and 117:
SPIN−WAVE DISPERSION ω q(meV)654
Page 118 and 119:
the coefficients of the q-dependent
Page 120 and 121:
where p αβ = A µναβ q µq ν
Page 122 and 123:
stiffness tensors in a similar mann
Page 124 and 125:
Figure9.7: Cycloidalspinstructurein
Page 126 and 127:
yφxK surf0 , l = 0 l = 1 ... l = L
Page 128 and 129:
two pictures is especially apparent
Page 130 and 131:
due to the multiplicity of the vale
Page 132 and 133:
hh COMPOSITIONso COMPOSITION0.80.60
Page 134 and 135:
mean-field Brillouin function (8.1)
Page 136 and 137:
ters for numerical simulations, I s
Page 138 and 139:
EXCHANGE STIFFNESS (pJ/m)0.40.30.20
Page 140 and 141:
the employed Landau-Lifshitz equati
Page 142 and 143:
netisation. The basic theoretical m
Page 144 and 145:
M z [242] and has a weak anisotropy
Page 146 and 147:
the periodic parts of the modified
Page 148 and 149:
model used must also have enough ro
Page 150 and 151:
The multiband tight-binding methods
Page 152 and 153:
AH CONDUCTIVITY σ xy(S/cm)10080604
Page 154 and 155:
AH CONDUCTIVITY σ xy(S/cm)14012010
Page 156 and 157:
the negative AHE conductivity is ob
Page 158 and 159:
Figure 10.10: Hall conductivity vs.
Page 160 and 161:
160
Page 162 and 163:
crystals, which provide full contro
Page 164 and 165:
form of statistical DMFT (statDMFT)
Page 166 and 167:
FigureA.1: Relationsbetweensoftware
Page 168 and 169:
168
Page 170 and 171:
a str strained lattice constanta
Page 172 and 173:
U Dzyaloshinskii-Moriya vectorV cry
Page 174 and 175:
gdzieL ′ = F ′ +2G M = H 1 +H 2
Page 176 and 177:
której wartość pola średniego
Page 178 and 179:
[12] G. Binasch, P. Grünberg, F. S
Page 180 and 181:
[42] M. A. Ruderman and C. Kittel.
Page 182 and 183:
[69] H. Munekata, A. Zaslavsky, P.
Page 184 and 185:
[92] J. Zemen, J. Kučera, K. Olejn
Page 186 and 187:
[118] C. Zener. Interaction between
Page 188 and 189:
[143] J. Jancu, R. Scholz, F. Beltr
Page 190 and 191:
[171] T. E. Ostromek. Evaluation of
Page 192 and 193:
[199] C. Gourdon, A. Dourlat, V. Je
Page 194 and 195:
[221] H. B. Callen. Green function
Page 196 and 197:
[249] G. Sundaram and Q. Niu. Wave-
Page 198 and 199:
[275] K. Y. Wang, K. W. Edmonds, R.
Page 200 and 201:
[300] D. J. Garcia, K. Hallberg, an
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Spin waves and the anomalous Hall effect in ferromagnetic (Ga,Mn)As

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