Spin-injection Hall effect Spin-injection Hall effect: A new member of the spintronic Hall family Institute of Physics of the Academy of Science of the Czech Republic, Prague, November 18th, 2008 JAIRO SINOVA Texas A&M University Institute of Physics ASCR Research fueled by: 1 Hitachi Cambridge Jorg Wunderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth,, Vít Novák, et al Texas A&M A. Kovalev, M. Borunda, A. Kovalev, et al

2 Anomalous Hall transport: lots to think about Taguchi et al Fang et al Wunderlich et al Kato et al Valenzuela et al SHE Inverse SHE SHE Intrinsic AHE (magnetic monopoles?) AHE AHE in complex spin textures Brune et al

The family of spintronic Hall effects 3 AHE B=0 polarized charge current gives charge-spin current Electrical detection SHE B=0 charge current gives spin current Optical detection SHE -1 B=0 spin current gives charge current Electrical detection j s ––––––––––– iSHE

4 Towards a spin-based non-magnetic FET device: can we electrically measure the spin-polarization? ISHE is now routinely used to detect other effects related to the generated spin-currents (Sitho et al Nature 2008) Can we achieve direct spin polarization detection through an electrical measurement in an all paramagnetic semiconductor system? Long standing paradigm: Datta-Das FET Unfortunately it has not worked: no reliable detection of spin-polarization in a diagonal transport configuration No long spin-coherence in a Rashba SO coupled system

Alternative: Alternative: utilize technology developed to detect SHE in 2DHG and measure polarization via Hall probes J. Wunderlich, B. Kaestner, J. Sinova and T. Jungwirth, Phys. Rev. Lett (2005) Spin-Hall Effect 5 B. Kaestner, et al, JPL 02; B. Kaestner, et al Microelec. J. 03; Xiulai Xu, et al APL 04, Wunderlich et al PRL 05 Proposed experiment/device: Coplanar photocell in reverse bias with Hall probes along the 2DEG channel Borunda, Wunderlich, Jungwirth, Sinova et al PRL 07

material Device schematic - material 6 i p n 2DHG

- i p n 7 trench Device schematic - trench

i p n 2DHG 2DEG 8 n-etch Device schematic – n-etch

VdVd VHVH 2DHG 2DEG VsVs 9 Hall measurement Device schematic – Hall measurement

2DHG 2DEG e h e e ee e h h h h h VsVs VdVd VHVH 10 SIHE measurement Device schematic – SIHE measurement

Photovoltaic Cell Reverse- or zero-biased: Photovoltaic Cell trans. signal Red-shift of confined 2D hole  free electron trans. due to built in field and reverse bias light excitation with = 850nm ( well below bulk band-gap energy) σoσoσoσo σ+σ+σ+σ+ σ-σ-σ-σ- σoσoσoσo VLVL 11 -1/2 +1/2 +3/2 -3/2 bulk Transitions allowed for ħω>E g Transitions allowed for ħω<E g -1/2 +1/2 +3/2-3/2 Band bending: stark effect Transitions allowed for ħω<E g

n2 + + - - Spin injection Hall effect: Spin injection Hall effect: experimental observation n1 (  4) n2 n1 (  4) n2 n3 (  4) Local Hall voltage changes sign and magnitude along the stripe 12

Spin injection Hall effect  Anomalous Hall effect 13

and high temperature operation Zero bias- + + -- + + -- Persistent Spin injection Hall effect 14

THEORY CONSIDERATIONS Spin transport in a 2DEG with Rashba+Dresselhaus SO 15 For our 2DEG system: The 2DEG is well described by the effective Hamiltonian: Hence

16 spin along the [110] direction is conserved long lived precessing spin wave for spin perpendicular to [110] What is special about ? Ignoring the term for now The nesting property of the Fermi surface:

The long lived spin-excitation: “spin-helix” An exact SU(2) symmetry Only Sz, zero wavevector U(1) symmetry previously known: J. Schliemann, J. C. Egues, and D. Loss, Phys. Rev. Lett. 90, (2003). K. C. Hall et. al., Appl. Phys. Lett 83, 2937 (2003). Finite wave-vector spin components Shifting property essential 17

Spin configurations do not depend on the particle initial momenta. For the same x + distance traveled, the spin precesses by exactly the same angle. After a length x P =h/4mα all the spins return exactly to the original configuration. Physical Picture: Persistent Spin Helix Thanks to SC Zhang, Stanford University 18

19 Persistent state spin helix verified by pump-probe experiments Similar wafer parameters to ours

The Spin-Charge Drift-Diffusion Transport Equations For arbitrary α,β spin-charge transport equation is obtained for diffusive regime For propagation on [1-10], the equations decouple in two blocks. Focus on the one coupling S x+ and S z : For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, (2004); Mishchenko, Shytov, Halperin, PRL 93, (2004) 20

Steady state solution for the spin-polarization component if propagating along the [1-10] orientation 21 Steady state spin transport in diffusive regime Spatial variation scale consistent with the one observed in SIHE

Understanding the Hall signal of the SIHE: Anomalous Hall effect Simple electrical measurement of out of plane magnetization Spin dependent “force” deflects like-spin particles I _ F SO _ _ _ majority minority V InMnAs 22

23 Anomalous Hall effect (scaling with ρ) Dyck et al PRB 2005 Kotzler and Gil PRB 2005 Co films Edmonds et al APL 2003 GaMnAs Strong SO coupled regime Weak SO coupled regime

Intrinsic deflection Side jump scattering 24 Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling. ~τ 0 or independent of impurity density Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump. independent of impurity density Skew scattering Asymmetric scattering due to the spin- orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators. ~1/n i STRONG SPIN-ORBIT COUPLED REGIME (Δ so >ħ/τ) V imp (r) Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin- orbit coupling in the periodic potential (electronics structure) E SO coupled quasiparticles

25 WEAK SPIN-ORBIT COUPLED REGIME (Δ so <ħ/τ) Side jump scattering from SO disorder Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump. independent of impurity density  λ*  V imp (r) Skew scattering from SO disorder Asymmetric scattering due to the spin- orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators. ~1/n i  λ*  V imp (r) The terms/contributions dominant in the strong SO couple regime are strongly reduced (quasiparticles not well defined due to strong disorder broadening). Other terms, originating from the interaction of the quasiparticles with the SO- coupled part of the disorder potential dominate. Better understood than the strongly SO couple regime

26 AHE contribution Type (i) contribution much smaller in the weak SO coupled regime where the SO-coupled bands are not resolved, dominant contribution from type (ii) Crepieux et al PRB 01 Nozier et al J. Phys. 79 Two types of contributions: i)S.O. from band structure interacting with the field (external and internal) ii)Bloch electrons interacting with S.O. part of the disorder Lower bound estimate of skew scatt. contribution

Spin injection Hall effect: Theoretical consideration Local spin polarization  calculation of the Hall signal Weak SO coupling regime  extrinsic skew-scattering term is dominant 27 Lower bound estimate

The family of spintronics Hall effects SHE -1 B=0 spin current gives charge current Electrical detection AHE B=0 polarized charge current gives charge-spin current Electrical detection SHE B=0 charge current gives spin current Optical detection 28 SIHE B=0 Optical injected polarized current gives charge current Electrical detection

29 SIHE: a new tool to explore spintronics nondestructive electric probing tool of spin propagation without magnetic elements all electrical spin-polarimeter in the optical range Gating (tunes α/β ratio) allows for FET type devices (high T operation) New tool to explore the AHE in the strong SO coupled regime

Why is AHE difficult theoretically in the strong SO couple regime? AHE conductivity much smaller than σ xx : many usual approximations fail Microscopic approaches: systematic but cumbersome; what do they mean; use non-gauge invariant quantities (final result gauge invariant) Multiband nature of band-structure (SO coupling) is VERY important; hard to see these effects in semi-classical description (where other bands are usually ignored). Simple semi-classical derivations give anomalous terms that are gauge dependent but are given physical meaning (dangerous and wrong) Usual “believes” on semi-classically defined terms do not match the full semi-classical theory (in agreement with microscopic theory) What happens near the scattering center does not stay near the scattering centers (not like Las Vegas) T-matrix approximation (Kinetic energy conserved); no longer the case, adjustments have to be made to the collision integral term Be VERY careful counting orders of contributions, easy mistakes can be made. 30

Boltzmann semiclassical approach: easy physical interpretation of different contributions (used to define them) but very easy to miss terms and make mistakes. MUST BE CONFIRMED MICROSCOPICALLY! How one understands but not necessarily computes the effect. Kubo approach: systematic formalism but not very transparent. Keldysh approach: also a systematic kinetic equation approach (equivalent to Kubo in the linear regime). In the quasi-particle limit it must yield Boltzmann semiclassical treatment. Microscopic vs. Semiclassical AHE in the strongly SO couple regime 31

32 Recent progress: full understanding of simple models in each approach Semi-classical approach: Gauge invariant formulation; shown to match microscopic approach in 2DEG+Rashba, Graphene Sinitsyn et al PRB 05, PRL 06, PRB 07 Borunda et al PRL 07, Nunner et al PRB 08 Sinitsyn JP:C-M 08 Kubo microscopic approach: Results in agreement with semiclassical calculations 2DEG+Rashba, Graphene Sinitsyn et al PRL 06, PRB 07, Nunner PRB 08, Inoue PRL 06, Dugaev PRB 05 NEGF/Keldysh microscopic approach: Numerical/analytical results in agreement in the metallic regime with semiclassical calculations 2DEG+Rashba, Graphene Kovalev et al PRB 08, Onoda PRL 06, PRB 08 – – – – – – – – – – – jqsjqs nonmagnetic Spin-polarizer current injected optically Spin injection Hall effect (SIHE) Up to now no 2DEG+R ferromagnetis: SIHE offers this possibility

33 CONCLUSIONS Spin-injection Hall effect observed in a conventional 2DEG - nondestructive electrical probing tool of spin propagation - indication of precession of spin-polarization - observations in qualitative agreement with theoretical expectations - optical spin-injection in a reverse biased coplanar pn- junction: large and persistent Hall signal (applications !!!)