1. Magneto-transport anisotropy phenomena in GaMnAs and beyond 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, Alexander Shick. Jan Zemen, Jan Mašek, Vít Novák, Kamil Olejník,, et al. University of Texas Allan MaDonald, Maxim Trushin,et al. Texas A&M Jairo Sinova, et al. University of Wuerzburg Charles. Gould, Laurens Molenkamp, et al.

2. Observations made from studies of AMR phenomena in GaMnAs (outline) 1. More than just bulk AMR in ohmic devices: TAMR, CBAMR 2. In DMSs bulk AMR has the simplest intuitive picture 3. TAMR and CBAMR are transferable to room-T metal FMs & AFMs

3. 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 Problems with small magnitude and scaling magnetization current 1980’s-1990’s

4.  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

5. 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

6. (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

7. 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

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. 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

10. 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

11. 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

12. 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

13. 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

14. & 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 

15. Huge MRs controlled by low-gate-voltage: likely the most sensitive spintronic transistors to date Wunderlich et al. PRL ’06 Schlapps et al. PRB ‘09

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

17. 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

18. 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

19. KL Hamiltonian in spherical approximation Heavy holes Electro-magnetic impurity potential of Mn Ga acceptor Rushforth PRL’07, Trushin et al. PRB ‘09, Vyborny et al. PRB ‘09 current M Ga Key mechanism for AMR in (Ga,Mn)As: FM impurities & SO carriers in non-cryst.-like spherical bands

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

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

22. 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,

23. 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,

24. Negative and positive and crystalline AMR in R&D 2D system Dresselhaus Rashba current

25. AMR in 2D R&D and 3D KL system from exact solution to integral Boltzmann eq. analytical solution to the integral Boltzmann eq. contains only cos  and sin  harmonics

26.  ss sdsd sdsd itinerant 4s: no exch.-split no SO localized 3d: exch. split SO coupled AMR in transition/noble metals Model for transition metal FMs: Banhart&Ebert EPL‘95 Miscroscopic theory: relativistic LDA & Kubo formula theory experiment ? Smit 1951 FeNi

27. ab intio theory Wunderlich et al., PRL ’06,Shick, et al, PRB '06 TAMR and CBAMR predictions for metals Anisotropy in DOS Anisotropy in chemical potential

28. ab intio theory TAMR in SO-coupled FMs experiment Experimental observation of large and bias dependent TAMR Shick et al PRB ’06, Parkin et al PRL ‘07, Park et al PRL '08 Park et al PRL '08

29. Experimental observation of CBAMR in metals Bernand-Mantel et al Nat. Phys.‘09

30. Consider TM combinations containing Mn e.g. FM Mn/W  upto ~100% TAMR spontaneous moment magnetic susceptibility spin-orbit coupling Optimizing TAMR/CBAMR in transition-metal structures Shick, et al PRB ‘08 But most transition/noble metals with Mn are AFMs!

31. AFM spintronics Zero stray field in compensated AFMs Ultrafast dynamics of spin excitations

32. spin-dnspin-up Mn 2 Au Predicted strong AFM with no frustration

33. spin-dnspin-up MnIr Conventional AFM

34. Element specific MAE (meV) *MAE accuracy ~0.01 meV Magnetic moments (m B ) Local Mn-atom moment contributes only little to the MAE Most of the MAE comes from zero moment Au, Ir atoms

35. Each of localized 3d(Mn)- sublattices  induces the magnetic moment on 5d-site Strong 5d-SOC produces the MAE Summing over 3d(Mn)- sublattices  = 0 - non-zero! complies with t-reversal symmetry of AFM Strong 5d-SOC x 3d(Mn)-exchange filed x local susceptibility produce the MAE

36. TAMR and CBAMR ADOS([  ’  ’  = [DOS  –DOS[  ’,  ’]]/ DOS[  ’,  ’] and ATDOS = [TDOS  –TDOS[  ’,  ’]]/TDOS[  ’,  ’] ADOS ADOS([001]-[110]) ~ 50 % ATDOS ATDOS([001]-[110]) ~ 20 % Hard [001]-to-easy [110] Sizable TAMR and CBAMR in AFMs  =E f [001]-E f [110]=-2.5 mV

37. [100] [010] 1% strain Easy [110]  Easy [010] at <1% strain ADOS110010 ADOS([110]-[010]) ~ 20 % Strain-induced TAMR Effect of in-plane strain – moment reorientations and TAMR ATDOS110010 ATDOS([110]-[010]) ~ 20 %

38. GMR/TMR and spin-torque relay on coherence & quality of interfaces  in principle possible but likely very difficult to build AFM spintronics on these effects Instead bulid AFM spintronics on a set of magnetic anisotropy phenomena Piezo- (or other) electric control of AF moment orientation & TAMR (CBAMR)

39. Observations made from studies of AMR phenomena in GaMnAs (summary) 1. More than just bulk AMR in ohmic devices: TAMR, CBAMR 2. In DMSs bulk AMR has the simplest intuitive picture 3. TAMR and CBAMR are transferable to room-T metal FMs & AFMs