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

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Nanospin Meeting, Prague, Czech Republic, 2007, Magnetic stiffness andanomalous Hall effect in ferromagnetic (Ga,Mn)Asconference talks:14thInternationalConferenceonModulatedSemiconductorstructures(MSS-14), Kobe, Japan, 2009, Effect of inversion asymmetry on anomalous Halleffect in ferromagnetic (Ga,Mn)AsXXXVIIInternationalSchoolonthePhysicsofSemiconductingCompounds,Jaszowiec, Poland, 2008, Anomalous Hall effect in (Ga,Mn)As29th International Conference on the Physics of Semiconductors, Rio deJaneiro, Brazil, 2008, Anomalous Hall effect in (Ga,Mn)AsXIIWorkshoponSemimagneticSemiconductors, Obory, Poland, 2007, MagneticStiffness in (Ga,Mn)As Ferromagnetic SemiconductorsMAG-EL-MAT Network New materials for magnetoelectronics, Bedlewo,Poland, 2005, RKKY model with Zeeman splittingconference posters:30th International Conference on the Physics of Semiconductors, Seoul, Korea,2010, Spin waves in (Ga,Mn)As5th International School and Conference on Spintronics and Quantum InformationTechnology, Cracow, Poland, 2009, Effect of inversion asymmetryon anomalous Hall effect in ferromagnetic (Ga,Mn)AsXXXVIIIInternationalSchoolonthePhysicsofSemiconductingCompounds,Krynica, Poland, 2009, Effect of inversion asymmetry on anomalous Hall effectin ferromagnetic (Ga,Mn)AsPolish-Japanese Join Meeting, Leszno, Poland, 2007, Magnetic stiffness andanomalous Hall effect in ferromagnets1st WUN Worldwide University Network International Conference on SpintronicMaterialsandTechnology,York, GreatBritain, 2007, Anomalous HallEffect in Ferromagnetic (Ga,Mn)AsXXXVI International School on the Physics of Semiconducting Compounds,Jaszowiec, Poland, 2007, Magnetic Stiffness and Anomalous Hall Effect in(Ga,Mn)AsXXXV International School on the Physics of Semiconducting Compounds,Jaszowiec, Poland, 2006, High Order Anisotropy Terms in (Ga,Mn)AsXXXIV International School on the Physics of Semiconducting Compounds,6
Jaszowiec, Poland, 2005, RKKY and Zener contributions to magnetic stiffnessin (Ga,Mn)AsXXXIII International School on Physics of Semiconducting Compounds,Jaszowiec, Poland, 2004, Beyond the Stoner-Wolfarth approach to magneticproperties of as grown (Ga,Mn)Asseminars:Theory and modelling of nanostructures, Faculty of Physics, University ofWarsaw, 2008 Anomalous Hall effect in dilute magnetic semiconductorsTheory and modelling of nanostructures, Faculty of Physics, University ofWarsaw, 2007 Spin waves in dilute magnetic semiconductorsSeminar on microwave spectroscopy, IP PAS, 2005, Analytical solutions forRKKY coupling in dilute magnetic semiconductorsOther activitiesHelp in the organisation of the Spintech conference in Cracow, Poland,2009; Taking part in the Science Picnic in Warsaw representing the Collegeof Science; Voluntarily tutoring young studentsPublicationsWerpachowska, A., Exact and approximate methods of calculating the sumof states for classical non-interacting particles occupying a finite number ofmodes, Phys. Rev. E 84, 041125 (10/2011)Werpachowska, A. and T. Dietl, Theory of spin waves in ferromagnetic(Ga,Mn)As, Phys. Rev. B 82, 085204 (8/2010)plus online supplement Löwdin calculus for multiband Hamiltonians,arXiv:1101.5775 (1/2011)Werpachowska, A. and T. Dietl, Theory of spin waves in ferromagnetic(Ga,Mn)As,ICPS30 Proceedings (subm. 7/2010, accepted for publication)Werpachowska,A.andT.Dietl,Effect of inversion asymmetry on the anomalousHall effect in ferromagnetic (Ga,Mn)As,Phys. Rev. B 81, 155205 (4/2010)Chiba, D., A. Werpachowska, M. Endo, Y. Nishitani, F. Matsukura, T.Dietl, and H. Ohno, Anomalous Hall Effect in Field-Effect Structures of(Ga,Mn)As, Phys. Rev. Lett. 104, 106601 (3/2010)7
Page 1 and 2: Polish Academy of SciencesInstitute
Page 3 and 4: AcknowledgementsI would like to tha
Page 5: Curriculum VitaeEducation and Train
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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