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Current Nanospin related theory topics in Prague
in collaboration with Texas and Warsaw
based primarily on Nottingham and Hitachi experimental activities
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Range of materials or model systems
- 2D models with simple Rashba spin-orbit coupled bands
- Dilute-moment ferromagnetic semiconductors:
still simple bands yet strongly exchange and SO split
dilute moment – tunable, weak dipolar fields, smaller STT currents
AsAsGaGa
MnMn
- Systems with complex bands but room Tc: FeNi, CoFe, CoPt,….
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Technical issues
- Analytical calculations (Rashba model)
k.p semiphenomenological modelling (typical for semiconductors) extensive library of home-made routines
spd-tight-binding modelling (half way between phenomenological and ab initio) home-made codes
Full ab initio heavy numerics (transition metals based structures) standard full-potential libraries, home-made relativistic ab-initio codes
- Conclusions derived from bulk band structures total energy calculations, Boltzmann and Kubo transport equations
Device specific modeling Landauer-Buttiker formalism
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Extraordinary magnetoresistance (AHE/SHE, AMR, STT)
B
V
I
_
+ + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _ _ FL
Ordinary magnetoresistance:response in normal metals to external magnetic field via classical Lorentz force
Extraordinary magnetoresistance:response to internal magnetization in ferromagnets via quantum-relativistic spin-orbit coupling
e.g. ordinary (quantum) Hall effect
I
_ FSO
FSO
_ __majority
minority
Ve.g. anomalous Hall effect
or anisotropic magnetoresistance
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Intrinsic vs. extrinsic AHE in Rashba 2D systems
semicalssical Boltzmann eq.
intrinsic skew scattering side jump
group velocity distribution function
quantum Kubo formula
int. skew side jumpsc.
Solvable analytically
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Proposed experimental setup
skew scattering term: - absent in 2DEG for two-band occupation
- absent in 2DHG for any band occupation
extenting the study to:
- 4-band spherical Kohn-Luttinger model
- full 6(multi)-band model of DMSs
- ab initio band structures of metals
Rashba
spherical K-L model
so far microscopic calculations of intrinsic AHE only in these systems
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Origin of non-crystalline and crystalline AMR in GaMnAs
~(k . s)2 ~Mx . sx
SO-coupling – spherical model FM exchange spiitting
hot spots for scattering of states moving M R(M I)> R(M || I)
Boltzmann eq. in relax. time approximation 1st order Born approximation
4-band spherical Kohn-Luttinger model
ky
kxk
x
kx
k y
k y
M
M
1/k (M)
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M
[110]
current
))
theory
exp.
spherical model: non-crystalline AMR only
full 6-band Hamiltonian:non-crystalline andcrystalline AMR
- explains sign of non-crystalline AMR
- consistent with experimentally seen increasing role of crystalline terms with increasing compensation
- large AMR dominated by crystalline terms in ultrathin layers not explained by bulk theory
Mcurrent
)
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Mn
Ga
As Mn
Ferromagnetism mediated by As p-orbital-like band states: - basic SO coupling related symmetries similar to familiar GaAs, unchanged by MnGa
- carriers with strong SO coupling and exchange splitting due to hybridization with MnGa d-orbitals
px
py
- straightforward means for relating intuitive physical pictures with microscopic calculations
- compare with ferro metals: model of scattering of non-SO-coupled non-exchange-split s-state carriers to localized d-states difficult to match with ab initio theories with mixed s-d carriers
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Strain and doping-depent magnetocrystalline anisotropy
macroscopic elastic theory simulations of strainsGaMnAs
microscopic magneto-crystalline anisotropies
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New device functionalities and new opportunity for exploring the rich phenomenologyof magnetocrystalline anisotropies in (Ga,Mn)As
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Close relatives to GaMnAs with new degrees of freedomn-type DMSs, higher Tc,…
III = I + II Ga = Li + Zn• GaAs and LiZnAs are twin semiconductors
• Prediction that Mn-doped are also twin ferromagnetic semiconductors
• No limit for Mn-Zn (II-II) substitution
• Independent carrier doping by Li-Zn stoichiometry adjustment
Limited confidence in ab initio calc.Reasonable confidence when comparingto GaMnAs bench-mark material
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L
As p-orb.
Ga s-orb.As p-orb.
EF
Electron mediated Mn-Mn coupling in n-type Li(Zn,Mn)As
similar to hole mediated coupling in p-type (Ga,Mn)As
Tc~
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Family of I-II-V hosts
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- theoretical exploration of I-II-V’s I-Mn-V’s I-(II,Mn)V DMSs- MOCVD growth of the most promising theory candidates- MBE growth to achieve better stoichiometry control for the promising MOCVD materials
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MnI formation in mixed (Al,Ga)As and Ga(As,P)
higher in (Al,Ga)As
and Ga(As,P)
than in GaAs
smaller interstitial space
only in Ga(As,P)
Less interstitials in Ga(As,P)more interstitials in (Al,Ga)As
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L
As p-orb.
Ga s-orb.As p-orb.
EF
n-type AlAs with int. Mn only
Comparable Tc to n-type hosts withsubstitutional Mn moments
electrons can mediateFM coupling for both subst.and int. Mn