Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems
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Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems Tomas Jungwirth Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Mašek, Vít Novák, Kamil Olejník, et al. Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine, Elisa de Ranieri, Byonguk Park, et al. University of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds, Andrew Rushforth, et al. Texas A&M Jairo Sinova, et al. University of Texas Allan MaDonald, et al. Extraordinary magnetoresistance: AMR, AHE Ordinary magnetoresistance: response in normal metals to external magnetic field via classical Lorentz force B Extraordinary magnetoresistance: response to internal spin polarization in ferromagnets via quantum-relativistic spin-orbit coupling anisotropic magnetoresistance _ _ _ _ _ _ _ _ _ _ _ Lord Kelvin 1857 FL +++++++++++++ V I M __ FSO I ordinary Hall effect 1879 V anomalous Hall effect 1881 Spin-orbit coupling nucleus rest frame E Q 40 r r 3 1 B 0 0 v E 2 v E c Lorentz transformation Thomas precession electron rest frame I Qv H SO 0 I r B 4 r 3 g B e SB S vE 2 2 2mc From 1950’s microscopic model interpretations – often controversial AMR: Mott’s model of transport in metals ss sd ss sd itinerant 4s: no exch.-split no SO Smit 1951 localized 3d: exch. split SO coupled AHE Karplus&Luttinger 1954 (then partly forgotten till 2000’s) Berger 1970 Smit 1955 From 1990’s numerics based on relativistic ab initio band strucrure & Kubo formula Scattering considered essential for both AMR and AHE alloys like FeNi (treated in CPA) AMR AHE Numerically successful but difficult to connect with microscopic models due to complex bands in metals Banhart&Ebert EPL‘95 Khmelevskyi ‘PRB 03 AMR sensors: dawn of spintronics in early 1990’s Magnetoresistive read element Inductive read/write element In mid 1990’s replaced in HDD by GMR or TMR but still extensively used in e.g. automotive industry From late 1990’s AMR and AHE studied in novel ferromagnets Ferromagnetic DMS GaMnAs with much simpler 3D band structure than metals Ga As-p-like holes As Bso Mn Mn-d-like local moments Bex + Bso Jungwirth et al. RMP’06 Dietl et al. Semicond. and Semimet. ‘08 Semiquantitative numerical description of AMR and AHE in GaMnAs Jungwirth et al. RMP’06 Dietl et al. Semicond. and Semimet. ‘08 AMR in GaMnAs DMS: from full numerics to microscopic mechanism Anisotropic scattering rate: non-crystalline and crystalline AMR Spherical model: non-crystalline AMR only M current M [110] Rushforth et al. PRL‘07 current AMR in GaMnAs DMS: from full numerics to microscopic mechanism Non-crystalline AMR mechanisms: 1) Polarized SO bands 2) Polarized impurities & SO bands M MGa current current Leading AMR mechanism in DMSs Rushforth et al. PRL‘07 Microscopic mechanism of AHE in GaMnAs DMS Jungwirth et al PRL‘02 AHE explained by the revived intrinsic mechanism Note: Inspired to explain AHE in pure Fe,etc by intrinsic AHE Experiment sAH 1000 (W cm)-1 Theroy sAH 750 (W cm)-1 Yao et al PRL‘04 2D SO-coupled systems simplest band-structures offer most detailed and complete understanding of the AMR and AHE Rashba SO-coupled 2DEG AMR in 2D SO-coupled systems We will discuss a detailed theory analysis in Rashba-Dresselhaus 2D systems Experimentally not studied in 2D systems yet; we will comment on experiments in related 3D DMS systems Trushin, Vyborny et al PRB in press (arXiv:0904.3785) AHE in 2D SO-coupled systems Detailed theory analysis completed Nagaosa et al RMP ‘to be published (arXiv:0904.4154) We will discuss 2D AHE related experiment: Spin-injection Hall effect in a planar photo-diode Heuristic link between spin-texture of 2D SO bands, impurity potentials and AMR Short-range magnetic impurity potential Short-range electro-magnetic impurity potential Non-crystalline AMR>0 in Rashba 2D system Rashba Hamiltonian Eigenspinors Non-crystalline AMR>0 in Rashba 2D system Scattering matrix elements current ( ) Large non-crystalline AMR>0 in Rashba 2D system with electro-magnetic scatterrers Scattering matrix elements of current current ( ) Negative and positive and crystalline AMR in Dresselhaus 2D system Dresselhaus Rashba current AMR in (Ga,Mn)As modeled by j=3/2 Kohn-Luttinger Hamiltonian KL Hamiltonian Heavy holes Magnetic part of the impurity potential Scattering matrix elements of Compare with spin-1/2 Negative AMR in (Ga,Mn)As due to electro-magnetic MnGa impiruties Rashba Kohn-Luttinger current AMR in 2D Rashba system from exact solution to integral Boltzmann eq. = const. for or independent of averages to 0 over Fermi cont. quasiparticle life-time AMR in 2D Rashba system from exact solution to integral Boltzmann eq. transport life-time transport life-time is a good first approximation to AMR AMR in 2D Rashba system from exact solution to integral Boltzmann eq. contains only cos and sin harmonics analytical solution to the integral Boltzmann eq. Spintronic Hall effects in magnetic and non-magnetic (2D) systems AHE ++++++++++ jqs ––––––––––– SHE Ferromagnetic (polarized charge current) jq nonmagnetic (unpolarized charge current) Co/Pt p-AlGaAs etched 2DHG i-GaAs 2DEG n--doped AlGaAs Wunderlich et al. IEEE 01, PRL‘05 Spin-injection Hall effect: Hall measurement of spin-polarized electrical current injected into non-magnetic system ++++ –––– –––– ++++ Spin-polarizer (e.g. ferromagnet, s light) jqs nonmagnetic Wunderlich et al. Nature Phys. in press, arXives:0811.3486 Optical injection of spin-polarized charge currents into Hall bars GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell ni p 2DHG 29 Optical injection of spin-polarized charge currents into Hall bars GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell - ni p 2DHG 30 Optical injection of spin-polarized charge currents into Hall bars GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell p i n 2DHG 2DEG 31 Optical injection of spin-polarized charge currents into Hall bars GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell h h h h h h e VH e e e e e 2DHG 2DEG 32 Optical spin-generation area near the p-n junction Simulated band-profile Vb h h h h h h e e e e e VL e VH2 2DHG 2DEG p-n junction bulit-in potential (depletion length ) ~ 100 nm self-focusing of the generation area of counter-propagating e- and h+ Hall probes further than 1m from the p-n junction safely outside the spin-generation area and/or masked Hall probes Spin transport in a 2DEG with Rashba+Dresselhaus SO H 2DEG 2k 2 * k ys x k xs y k xs x k ys y s (k Vdis (r )) 2m o2 P 2 1 1 5.3 A for GaAs, 2 2 3 E g ( E g so ) * weak spin orbit coupling regime: 0 B k with B 10 eV A 3 for GaAs, 2 z * Ez , ( 5meV) System can be described by a set of spin-charge diff. Equation: Schliemann, et al., Phys. Rev. Lett. 94, 146801 (2003) Bernevig, et al., Phys. Rev. Lett. 97, 236601 (2006) Weber, et al., Phys. Rev. Lett. 98, 076604 (2007) Spin dynamics in a 2DEG with Rashba Dresselhaus SO Steady state solution for the out of plane spin-polarization component pZ ( x[1 1 0] ) exp[ q x[1 1 0] ] ~2~ 2 ~4 L ~2~ 2 ~ 4 14 1 L2 L1 4 1 q | q | exp( i ) , | q | ( L1 L2 L2 ) , 2 arctan L~ 2 L~ 2 2 2 1 Spin-diffusion along the channel of injected spin- electrons ~ L1/ 2 2m | | 2 SO-length ~1m SO-length (~1m) >> mean-free-path (~10 nm) Spin-diffusion along the channel of injected spin- electrons see also Bernevig et al., PRL‘06 Local spin-dependent transverse deflection due to skew scattering Skew-scattering Hall effect H 2DEG 2k 2 * k ys x k xs y k xs x k ys y s (k Vdis (r )) 2m o2 P 2 1 1 5.3 A for GaAs, 2 2 3 E g ( E g so ) * 0 B k with B 10 eV A 3 for GaAs, 2 z * Ez Spin injection Hall effect: theoretical estimate Local spin polarization calculation of the Hall signal Weak SO coupling regime extrinsic skew-scattering term is dominant A. Crepieux and P. Buno, PRB ’01 e H ( x[1 1 0] ) 2 n pz ( x[1 1 0] ) ni * Large Hall angles – comparable to AHE in metals Vb h SIHE device realization h h h h h e e e e e VL e VH2 n3,n2,n1: local SIHE 2DHG 2DEG 3 2 1 0 n0: averaged-SIHE / AHE Spin-generation area Unmasked and masked SIHE devices 5.5m 50 25 0 -25 Vb= 0V Measured SIHE phenomenology RH2 [W] -50 50 25 0 Vb Vb= -10V -25 -50 h h h h h e 2DHG 2DEG e e e e VL e VH2 20 R L [k W ] h s- 10 s0 s+ 0 0 25 50 tm [s] 75 2 SIHE: spatially dependent, linear, strong H1 Skew scattering H [ 10 -3 ] 1 + - - + Bso + 0 -1 - - -2 + -1.0 -0.5 0.0 0.5 1.0 0.5 1.0 s s 10 H0 (x3) 10 H2 ] 5 5 0 H [ 10 -3 -3 H [ 10 ] H2 H1 (x3) H3 (x3) -5 s- -10 0 10 -5 s+ 20 30 tm [s] 40 0 -10 50 -1.0 -0.5 0.0 s s SIHE vs AHE (a) s- s- 0 H2 H3 -10 -20 I [ A] 20 s0 -10 2 2 -2 -4 0 20 Vb=+5V 40 tm [s] 60 80 H2 H3 -20 4 Vb=-5V s- s0 0 4 0 s- s0 10 I [ A] V H [ V] 10 s0 V H [ V] 20 0 -2 -4 Vb=-0.5V 0 20 Vb=+0.5V 40 tm [s] 60 80 SIHE survives to high temperatures -3 H [10 ] 5 s- 100K 160K (x2) 220K (x3) 0 -5 s+ 0 30 60 90 120 150 180 tm [s] Spin-detection in semiconductors Datta-Das transistor Magneto-optical imaging non-destructive lacks nano-scale resolution and only an optical lab tool MR Ferromagnet electrical requires semiconductor/magnet Ohno et al. Nature’99, others hybrid design & B-field to orient the FM spin-LED all-semiconductor requires further conversion of emitted light to electrical signal Spin-detection in semiconductors Crooker et al. JAP’07, others Magneto-optical imaging non-destructive lacks nano-scale resolution and only an optical lab tool MR Ferromagnet electrical requires semiconductor/magnet Ohno et al. Nature’99, others hybrid design & B-field to orient the FM spin-LED all-semiconductor requires further conversion of emitted light to electrical signal Spin-injection Hall effect non-destructive electrical 100-10nm resolution with current lithography in situ directly along the SC channel & all-SC requiring no magnetic elements in the structure or B-field Application of SIHE Spin-photovoltaic cell: polarimeter on a SC chip requiring no magnetic elements, external magnetic field, or bias; form IR to visible light depending on the SC Spin-detection tool for other device concepts (e.g. Datta-Das transistor) Basic studies of quantum-relativistic spin-charge dynamics and AHE also in the intriguing strong SO regime in archetypal 2DEG systems