Transcript Slide 1
Spin-orbit coupling induced magneto-resistance effects in ferromagnetic semiconductor structures: TAMR, CBAMR, AMR Tomas Jungwirth Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Mašek, Vít Novák, Kamil Olejník, Ludvík Smrčka, Jan Kučera, Nataliya Goncharuk, et al. 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. Texas A&M Jairo Sinova, et al. University of Texas Allan MaDonald, Maxim Trushin,et al. Wuerzburg University Charles. Gould, Laurens Molenkamp, et al. 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 Theory of AMR: current response to magnetization via spin-orbit coupling Model for transition metal FMs: itinerant 4s: no exch.-split no SO localized 3d: exch. split SO coupled Miscroscopic theory: relativistic LDA ss sd ss sd Smit 1951 & Kubo formula theory experiment FeNi Banhart&Ebert EPL‘95 ? 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 >1.5% Mn ~ metallic 7% 2.5% ~0.1% Mn 1% insulating x=0.07% <<0.1% Mn Jungwirth et al. PRB ’07 Renewed research interest in AMR due to FS like (Ga,Mn)As (Ga,Mn)As d/dT~cv Mn moment: Ferromagnetism reminiscent of conventional metal band FMs (Fe, Co, Ni,..) Ni h+ Tc h+ (Ga,Mn)As >1% Mn ~ ferromagnetic Tc Novak et al. PRL ’08 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 Magnitude, control, and tuneability of MR Simple direct link between band structure and transport Complexity of the device design SET Chemical potential micro-structures CBAMR DOS MTJ heterostructures Tunneling DOS TAMR bulk Resistor Scattering lifetimes ohmic AMR Magnetic anisotropies in (Ga,Mn)As valence band degenerate HH bands and LH bands in GaAs: j=3/2 anisotropic surface and spintexture due to crystal and SO coupling in As(Ga) p-orbitals 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 TAMR: spectroscopy of tunneling DOS anisotropy k - resolved tunneling DOS electrode barrier GaMnAs M Giddings et al. PRL ’04 Vbias Binpl M Selectivity tuned by choice of barrier, counter-electrode, or external fields TAMR: spectroscopy of tunneling DOS anisotropy Gould et al. PRL ’04 M M Au AlOx GaMnAs Non-selective barrier and counterelectrode only a few % TAMR TAMR: spectroscopy of tunneling DOS anisotropy M p-(Ga,Mn)As M n-GaAs:Si 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 TAMR: spectroscopy of tunneling DOS anisotropy M p-(Ga,Mn)As M Extra-momentum due to Lorentz force during tunneling n-GaAs:Si Very selective p-n Zener diode MTJs Binpl Giraud et al. Spintech ’09 CBAMR: M-dependent electro-chemical potentials in a FM SET Wunderlich et al. PRL ’06 Source [110] M [100] [110] Q VD Drain Gate VG [010] (Q Q0 ) 2 U & Q0 CG [VG VM ( M )] 2C ( M ) C & VM e CG electric & magnetic control of CB oscillations 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 Simple direct link between band structure and transport Chemical potential CBAMR SET DOS Tunneling DOS TAMR MTJ Scattering lifetimes AMR Resistor Simplicity of the microscopic picture of AMR in (Ga,Mn)As SET CBAMR,TAMR: SO & FM polarized bands M MTJ MnGa - Resistor ohmic AMR: main impurities – FM polarized random MnGa can consider bands with SO coupling only MnGa - Simplicity of the microscopic physical picture in (Ga,Mn)As SET current 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 Resistor AMR: M vs current (non-crystalline) term can be separated and dominates in (Ga,Mn)As M cryst. axis 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 Vimp ˆ ˆ ˆ ~ 1 eM sˆ 1 eM j / 3 Rushforth PRL’07, Trushin et al. arXiv:0904.3785, Vyborny et al. arXiv:0906.3151 Pure magnetic MnGa impiruties: positive AMR, Vimp (M || I) (M I) ˆ ~ eM j Backward-scattering matrix elements | ˆjx | ~ | 0 | ˆjx | ~ | 0 | ˆjx | ~ | 0 | | current ˆj y | ~ | 0 ˆj y | ~ | 0 - - Electro-magnetic MnGa impiruties: negative AMR, Vimp (M || I) (M I) ˆ ˆ ~ 1 eM j / j current Backward-scattering matrix elements | 1ˆ ˆjx / j | ~ | | 0 | 1ˆ ˆjx / j | ~ | | 0 | 1ˆ ˆjx / j | ~ | 0 | 1ˆ ˆj y / j | ~ | 0 - - Electro-magnetic MnGa impiruties: negative AMR, Vimp (M || I) (M I) ˆ ˆ ~ 1 eM j / 3 ~ screened Coulomb potential p [1021 cm-3] current AMR all scatt. backward scatt. AMR= - 202-1 244-2 4+1 - - Electro-magnetic MnGa impiruties: negative AMR, Vimp (M || I) (M I) ˆ ˆ ~ 1 eM j / 3 ~ screened Coulomb potential p [1021 cm-3] current AMR all scatt. backward scatt. AMR= - 202-1 244-2 4+1 - - 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