From ferromagnetic to nonmagnetic semiconductor spintronics Spininjection Hall

From ferromagnetic to non-magnetic semiconductor spintronics: Spin-injection Hall effect Tomas Jungwirth Institute of Physics ASCR Jairo Sinova, Karel Výborný, Jan Zemen, Jan Mašek, Alexander Shick, František Máca, Jorg Wunderlich, Vít Novák, Kamil Olejník, et al. University of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds, Andrew Rushforth, et al. Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine, Byonguk Park, et al. Texas A&M University Jairo Sinova, Liviu Zarbo, et al.

AMR and GMR (TMR) sensors: dawn of spintronics Inductive read elements Magnetoresistive read elements 1980’s-1990’s

Ferromagnetism & spin-orbit coupling anisotropic magnetoresistance ~ 1% MR effect Ferromagnetism only giant (tunnel) magnetoresistance ~ 100% MR effect magnetization current Lord Kelvin 1857 Fert, Grunberg et al. 1988

Renewed interest in SO induced MRs in ferromagnetic semiconductors Ohno Science ’ 98 ~ 1000% MR effect & gate controlled Wunderlich et al. PRL ’ 06 Schlapps et al. PRB `09 Coulomb blockade AMR: likely the most sensitive spintronic transistors to date p- or n-type FET depending on magnetization non-volatile programmable logic, etc.

SO induced MRs: AMR & anomalous Hall effect Ordinary Hall effect: response in normal metals to external magnetic field via Lorentz force Anomalous Hal effect: response to internal spin polarization in ferromagnets via spin-orbit coupling Hall 1879 B _ Hall 1881 M FL __ FSO I I V V Tc in (Ga, Mn)As upto ~190 K but AHE survives and dominates HE far above Tc OHE AHE Ruzmetov et al. PRB ’ 04

(Ga, Mn)As: simple band structure of the host SC Quantitative AHE theory j=3/2 HH Jungwirth et al. PRL ’ 02 HH & LH Fermi surfaces Spherical HH Kohn-Luttinger 3 D model Rashba and Dresselhaus 2 D models

Intense theory research of AHE in model 2 D R&D systems Nagaosa et al RMP ‘’ 09 in press (ar. Xiv: 0904. 4154)

Taming spins in non-magnetic materials: spin-Hall effect Ordinary Hall effect: response in normal metals to external magnetic field via classical Lorentz force Anomalous Hal effect: response to internal spin polarization in ferromagnets via quantum-relativistic spin-orbit coupling Hall 1879 B _ Hall 1881 __ M FL FSO I I V V Spin Hall effect spin-dependent deflection transverse edge spin polarization _ __ FSO Wunderlich et al. ar. Xives ’ 04 (PRL ’ 05) Kato et al. Science ’ 04 FSO I || E

Polarized EL from a planar LED Theory and experiment: ~10% polarization over ~10 nm wide edge region

More taming of spins by spin-orbit coupling Fe rr om ag ne t Spin-injection from a ferromagnet Wunderlich et al. Nature Phys. ‘ 09

More taming of spins by spin-orbit coupling Spin-injection by incident circularly polarized light + Wunderlich et al. Nature Phys. ‘ 09

More taming of spins by spin-orbit coupling Spin-injection Hall effect + + – – – Spin-dependent deflection due to spin-orbit coupling Wunderlich et al. Nature Phys. ‘ 09

More taming of spins by spin-orbit coupling Spin-injection Hall effect + + – – + – + + + + – – – + + + – Spin-dependent deflection due to spin-orbit coupling transverse (Hall) electrical voltage in steady state Wunderlich et al. Nature Phys. ‘ 09

More taming of spins by spin-orbit coupling Spin-injection Hall effect + + – – + – + + – Built-in electric fields in SC structure another spin-orbit coupling effect which can lead to spin precession Hall voltages measure local spin orientation Bernevig et al. , PRL`06, Wunderlich et al. Nature Phys. ‘ 09

More taming of spins by spin-orbit coupling Spin-injection Hall effect + + – – + + – + – Built-in electric fields in SC structure can be modified by external gate voltage Hall signals changed by gate transverse-voltage spintronic transistor Bernevig et al. , PRL`06, Wunderlich et al. Nature Phys. ‘ 09

More taming of spins by spin-orbit coupling Spin-injection Hall effect VG + + + – – + + – – Built-in electric fields in SC structure can be modified by external gate voltage Hall signals changed by gate transverse-voltage spintronic transistor Bernevig et al. , PRL`06, Wunderlich et al. Nature Phys. ‘ 09

Optical injection of spin-polarized charge currents into Hall bars Ga. As/Al. Ga. As planar 2 DEG-2 DHG photovoltaic cell h h h e VH e e e 2 DHG 2 DEG

Optical spin-generation area near the p-n junction Simulated band-profile 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 1 m from the p-n junction safely outside the spin-generation area and/or masked Hall probes

Experimental observation of the SIHE

SIHE linear in degree of polarization and spatially varying

Spin dynamics in Rashba&Dresselhaus SO-couped 2 DEG > 0, = 0, < 0 k-dependent SO field strong precession & spin-decoherence due to scattering

No decoherence for | | = | | & channel SO field Bernevig et al PRL’ 06 [110] [1 -10]

Diffusive spin dynamics & Hall effect due to skew scattering precession-length (~1 m) >> mean-free-path (~10 nm) ~1 0 nm

Conclusions SIHE: high-T SO only spintronics in non-magnetic systems · Basic studies of spin-charge dynamics and Hall effect in non-magnetic systems with SO coupling · Spin-photovoltaic cell: polarimeter on a SC chip requiring no magnetic elements, external magnetic field, or bias; unconventional laser displacement sensor with the resolution defined by the spin-precession length built in the SC · SIHE can be tuned electrically by external gate and combined with electrical spininjection from a ferromagnet (e. g. Fe/Ga(Mn)As structures)

SIHE vs other spin-detection tools 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 hybrid design & B-field to orient the FM Ohno et al. Nature’ 99, others · spin-LED all-semiconductor requires further conversion of emitted light to electrical signal

· Spin-injection Hall effect non-destructive electrical 100 -10 nm resolution with current lithography in situ directly along the SC channel & all-SC requiring no magnetic elements in the structure or B-field