1. Spin Hall Effect induced by resonant scattering on impurities in metals Peter M Levy New York University In collaboration with Albert Fert Unite Mixte de Physique CNRS, and Universite Paris-Sud

2. Spin current Spin current without charge current Intrinsic SHE: due to S-0 effects on the wave functions of the lattice Extrinsic SHE: due to S-0 terms of scattering potentials Spin Hall Effect (SHE)

3. w t = thickness x y Detection Ferromagnetic contact nonmagnetic contact Injection of spin-polarized current V  0 S. Zhang, PRL 85, 393 (2000)

4. How the SHE could be used in spintronic applications: Spintronics need currents that are spin polarized. The conventional method of obtaining a polarized current is to pass an ordinary charge current through a ferromagnetic metal. However, it is difficult to integrate ferromagnetic metals with CMOS [silicon-based] circuits that make up the active memory of computers. Therefore there is great interest in finding nonmagnetic metals or semiconductors which are capable of converting charge to spin currents. As we will see the Spin Hall Effect has this potential; this has lead to the current interest in this effect. The origins of the SHE are the same as those that have produced the Anomalous Hall Effect (AHE) which has been known for over 6-7 decades. The AHE is caused by ordinary charge currents and produces additional contributions to the ordinary Hall effect; it is caused by spin-orbit coupling effects on the band structure, defect scattering, and the expression for the electric current (anomalous velocity or side jump). The SHE is caused by the same mechanisms but relies on the presence of a spin- polarized current.

7. Previous work on the SHE: The term Spin Hall Effect was first used by Jorge Hirsch PRL 83, 1834 (1999). The idea of a SHE was first proposed by M. I.Dyakonov and V. I. Perel, Phys. Lett. A 35, 459 (1971). Shufeng Zhang made the first realistic calculation of the signal produced by this Effect in metals with finite spin diffusion lengths. PRL 85, 393 (2000). It was further studied by amongst others: J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A. H. MacDonald, PRL 92, 126603 (2004). Also, see articles by Jairo Sinova in PRB and PRL 2004-2010; and Sinova’s Viewpoint article “Spin Hall effect goes electrical” in Physics 3, 82 (2010).

8. 1/T R H /R 0 Introduction: Hall effect due to magnetic impurities in metals Skew scattering

9. Mn impurities in Cu No contribution to the Hall effect Spin-polarizes the current 1981 The SHE of nonmagnetic Cu alloys could be detected using the spin-polarized current induced by Mn impurities (0.01%) Today The SHE of nonmagnetic conductors can be detected by injecting a spin-polarized current from a ferromagntic contact

10. Nonmagnetic impurities T with large spin- orbit induce SHE revealed by the Mn- induced current spin polarization Cu + y nonmagnetic impurities T + x Mn impurities (y  100-2000 ppm, T=Ir,Lu,Ta, Au) ( x  100 ppm) Mn impurities +field polarize the current without inducing Hall effect by themselves

11. R H  V y /H 1/T skew scat. identified by 1/T contrib. to R H scat

12. A. Fert and O. Jaoul, PRL 28, 303, 1972  H of skew scatt. Side jump  H  c   0 Gd + Lu impurities Ni + various impurities R.Asomoza, AF et al, JLCM 1983

13. j =3/2 j =5/2 Spin-orbit split 5d states of Lu SHE induced by resonant scattering on spin-orbit split impurity d levels Partial wave phase shift analysis of resonant scattering ( Friedel’s virtual bound state model) EFEF Accomodation of one 5d electron ( Z 5d =1 for Lu)

14. Skew scattering: scattering probability to the right  scattering probability to the left  H =  xy /  xx = constant,  xx  c I,  xy  c I x Re-emission to the right at time t Re-emission to the left at time t+  t Side-jump  y = v  t of the center of mass Scattering with side-jump: side-jump of the mass center of the scattered electrons  H =  y/  c I,  xy =  H  xx  (c I ) 2  H =  y/   I  c I yy Re-emission probability to the right = p Re-emission probability to the left = p(1-p) * * the deflection angle  H is characteristic of the scattering asymmetry ExEx j HH x y x y EyEy Spin up el.