1. Spin-orbit coupling induced magneto-resistance effects in ferromagnetic semiconductor structures: TAMR, CBAMR, AMR Tomas Jungwirth University of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds, Andrew Rushforth, Tom Foxon, et al. University & Hitachi Cambridge Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri, Byonguk Park, et al. Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Mašek, Vít Novák, Kamil Olejník, Ludvík Smrčka, Jan Kučera, Nataliya Goncharuk, et al. University of Texas Allan MaDonald, Maxim Trushin,et al. Texas A&M Jairo Sinova, et al. Wuerzburg University Charles. Gould, Laurens Molenkamp, et al.

2. Experimental observation of (ohmic) AMR Lord Kelvin 1857 Inductive read elementsMagnetoresistive read elements AMR sensors: dawn of spintronics Now often replaced by GMR or TMR but still extensively used in e.g. automotive industry magnetization current 1980’s-1990’s

3.  ss sdsd sdsd itinerant 4s: no exch.-split no SO localized 3d: exch. split SO coupled Theory of AMR: current response to magnetization via spin-orbit coupling Model for transition metal FMs: Banhart&Ebert EPL‘95 Miscroscopic theory: relativistic LDA & Kubo formula theory experiment ? Smit 1951 FeNi

4. x=0.07% 1% 2.5% 7% Jungwirth et al. PRB ’07 <<0.1% Mn ~0.1% Mn >1.5% Mn ~ Mn Ga acceptor: electrical conduction similar to conventional p-doped GaAs Renewed research interest in AMR due to FS like (Ga,Mn)As metallic insulating Ohno. Science ’98

5. (Ga,Mn)As Ni d  /dT~c v TcTc  h+ h+  h+ h+ Mn moment: Ferromagnetism reminiscent of conventional metal band FMs (Fe, Co, Ni,..) Novak et al. PRL ’08 Renewed research interest in AMR due to FS like (Ga,Mn)As >1% Mn ~ ferromagnetic TcTc

6. Baxter et al. PRB ’02, Jungwirth et al. APL’02, ‘03 Renewed research interest in AMR due to FS like (Ga,Mn)As AMR’s of order ~1-10%: - routine characterization tool - semi-quantitatively described assuming scattering of valence-band holes

7. SET Resistor Complexity of the device design Magnitude, control, and tuneability of MR DOS  Simple direct link between band structure and transport Tunneling DOS  TAMR Chemical potential  CBAMR Scattering lifetimes  ohmic AMR heterostructures bulk micro-structures MTJ

8. Magnetic anisotropies in (Ga,Mn)As valence band Dietl et al. PRB ’01, Abolfath et al. PRB ‘01 exchange-split HH bands and LH bands in (Ga,Mn)As: anisotropic due to crystal, SO coupling and FM exchange field M j=3/2 HH degenerate HH bands and LH bands in GaAs: anisotropic surface and spin- texture due to crystal and SO coupling in As(Ga) p-orbitals HH & LH Fermi surfaces

9. TAMR: spectroscopy of tunneling DOS anisotropy M M Selectivity tuned by choice of barrier, counter-electrode, or external fields GaMnAs barrier electrode V bias  B inpl Giddings et al. PRL ’04 k - resolved tunneling DOS

10. TAMR: spectroscopy of tunneling DOS anisotropy M M GaMnAs AlOx Au Non-selective barrier and counter- electrode  only a few % TAMR Gould et al. PRL ’04

11. TAMR: spectroscopy of tunneling DOS anisotropy M M Giraud et al. APL ’05, Sankowski et al. PRB’07, Ciorga et al.NJP’07, Jerng JKPS ‘09 Giraud et al. Spintech ’09 n-GaAs:Si p-(Ga,Mn)As Very selective p-n Zener diode MTJs  B inpl

12. TAMR: spectroscopy of tunneling DOS anisotropy M M Extra-momentum due to Lorentz force during tunneling Giraud et al. Spintech ’09  B inpl n-GaAs:Si p-(Ga,Mn)As Very selective p-n Zener diode MTJs

13. & electric & magnetic control of CB oscillations SourceDrain Gate VGVG VDVD Q CBAMR: M-dependent electro-chemical potentials in a FM SET Wunderlich et al. PRL ’06 [ 110 ] [ 100 ] [ 110 ] [ 010 ] M 

14. Huge MRs controlled by low-gate-voltage: likely the most sensitive spintronic transistors to date Wunderlich et al. PRL ’06 Schlapps et al. arXiv:0904.3225

15. SET Resistor Chemical potential  CBAMR Tunneling DOS  TAMR Scattering lifetimes  AMR  DOS Simple direct link between band structure and transport MTJ

16. Simplicity of the microscopic picture of AMR in (Ga,Mn)As -- Mn Ga M CBAMR,TAMR: SO & FM polarized bands ohmic AMR: main impurities – FM polarized random Mn Ga  can consider bands with SO coupling only SET MTJ Resistor

17. AMR: M vs current (non-crystalline) term can be separated and dominates in (Ga,Mn)As Simplicity of the microscopic physical picture in (Ga,Mn)As TAMR: current direction is cryst. distinct  inseparable M vs current term CBAMR: only el.-chem potentials  no M vs current term M cryst. axis current M cryst. axis current M cryst. axis current SET MTJ Resistor

18. KL Hamiltonian in spherical approximation Heavy holes Electro-magnetic impurity potential of Mn Ga acceptor Rushforth PRL’07, Trushin et al. arXiv:0904.3785, Vyborny et al. arXiv:0906.3151 current M Ga Key mechanism for AMR in (Ga,Mn)As: FM impurities & SO carriers in non-cryst.-like spherical bands

19. Pure magnetic Mn Ga impiruties: positive AMR, current - - Backward-scattering matrix elements

20. current - - Backward-scattering matrix elements Electro-magnetic Mn Ga impiruties: negative AMR,

21. AMR= - 20  2 -1 24  4 -2  4 +1 p [10 21 cm -3 ] AMR current - -  ~ screened Coulomb potential  all scatt. backward scatt. Electro-magnetic Mn Ga impiruties: negative AMR,

22. current - - AMR= - 20  2 -1 24  4 -2  4 +1 p [10 21 cm -3 ] AMR  ~ screened Coulomb potential  all scatt. backward scatt. Electro-magnetic Mn Ga impiruties: negative AMR,

23. Straightforward intuition for AMR in Rashba and Dresselhaus 2DEGs & exact analytical solutions to full integral Boltzmann equation  SO-coupled 2DEGs are ideal testbed to study AMR Trushin et al. arXiv:0904.3785