Spin-orbit coupling induced magneto-resistance effects in ferromagnetic

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. Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Mašek, Vít Novák,Kamil Olejník, Ludvík Smrčka, Jan Kučera, Nataliya Goncharuk, et al. University & Hitachi Cambridge Jorg Wunderlich, Andrew Irvine,Elisa de Ranieri, Byonguk Park, etal. Texas A&M Jairo Sinova, et al. University of Texas Allan MaDonald, Maxim Trushin,et al. Wuerzburg University Charles. Gould, Laurens Molenkamp, et al.

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

3. ss sd ss 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: Smit 1951 ? Miscroscopic theory: relativistic LDA & Kubo formula theory experiment FeNi Banhart&Ebert EPL‘95

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

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

6. 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 Baxter et al. PRB ’02, Jungwirth et al. APL’02, ‘03

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

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

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

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

11.  p-(Ga,Mn)As n-GaAs:Si 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 Very selective p-n Zener diode MTJs Binpl Giraud et al. Spintech ’09

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

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

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

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

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

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

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

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

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

21. p [1021 cm-3] AMR 202-1 AMR= - 244-2 4+1 - - Electro-magnetic MnGa impiruties: negative AMR,  ~ screened Coulomb potential  current all scatt. backward scatt.

22. p [1021 cm-3] AMR 202-1 AMR= - 244-2 4+1 - - Electro-magnetic MnGa impiruties: negative AMR,  ~ screened Coulomb potential  current all scatt. backward scatt.

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