Current Nanospin related theory topics in Prague
in collaboration with Texas and Warsaw
based primarily on Nottingham and Hitachi experimental activities
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,….
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
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
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
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
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)
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
)
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
Strain and doping-depent magnetocrystalline anisotropy
macroscopic elastic theory simulations of strainsGaMnAs
microscopic magneto-crystalline anisotropies
New device functionalities and new opportunity for exploring the rich phenomenologyof magnetocrystalline anisotropies in (Ga,Mn)As
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
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~
Family of I-II-V hosts
- 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
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
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