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