1. 1 NTNU, November 2008Norwegian University of Science and Technology (NTNU), June 2009 Scattering Theory of Charge-Current Induced Magnetization Dynamics Kjetil Magne Dørheim Hals (NTNU) Arne Brataas (NTNU) Yaroslav Tserkovnyak (UCLA)

2. 2 NTNU, November 2008 Introduction J. C. Slonczewski, J. Magn. Magn. Mater. 159, L1 (1996) L. Berger, Phys. Rev. B 54, 9353 (1996) Spin-Transfer-Torque Transverse spin current absorbed by the ferromagnet. Incident spin current Transmitted spin current Ferromagnet M Acts as a torque on the magnetization. Definitions:

3. 3 NTNU, November 2008 Introduction Seen in experiments 1998- M. Tsoi et al., Phys. Rev. Lett. 80 (1998), p. 4281. J.Z. Sun, J. Magn. Magn. Mater. 202 (1999), p. 157. E.B. Myers et al. Science 285 (1999), p. 867. J.A. Katine et al. Phys. Rev. Lett. 84 (2000), p. 3149. M. Tsoi et al. Nature 406 (2000), p.46. S.I. Kiselev et al. Nature 425 (2003), p. 380. W.H. Rippard et al. Phys. Rev. Lett. 92 (2004), p. 027201. I.N. Krivorotov et al. Science 307 (2005), p. 228.

4. 4 NTNU, November 2008 Introduction Theory Systems without spin-orbit coupling : Based on: Conservation of angular momentum X. Waintal, E.B. Myers, P.W. Brouwer, D.C. Ralph, Phys. Rev. B 62 (2000), p. 12317. A. Brataas, Yu.V. Nazarov and G.E.W. Bauer, Phys. Rev. Lett. 84 (2000), p. 2481. M.D. Stiles and A. Zangwill, Phys. Rev. B 66 (2002), p. 014407. General systems: Based on: Calculation of exchange-correlation energy. A. S. Nunez and A. H. MacDonald Solid State Commun.,139 (2006), p. 31.

5. 5 NTNU, November 2008 Introduction Theory Example : Magnetoelectronic circuit theory (A. Brataas et al., PRL 84, 2481 (2000) ) LRFerromagnet Scattering matrix r mn,LL t mn,RL Torque on ferromagnet in spin conserving system m,n: Labels transverse modes n=1n=2

6. 6 NTNU, November 2008 Introduction 2) Rashba-Model: Spin-orbit coupling induces an out-of-equilibrium spin density (A. Manchon and S. Zhang Phys. Rev. B 78, 212405 (2008) ). When applying an electric field, the SO-term acts as an effective magnetic field that induces an out-of-eqv. spin density Recent observations: 1) A. Chernyshov, M. Overby, X. Liu, J. K. Furdyna, and L. P. Rokhinson, arXiv:0812.3160: Unpolarized charge currents can switch magnetization in (Ga,Mn)As. N|F|N system

7. 7 NTNU, November 2008 Introduction Call for a general theory!

8. 8 NTNU, November 2008 Introduction Solution strategies 1) Calculate induced out-of-eqv. spin density = cumbersome in general. 2) Easy, compact method: Look at the reciprocal processes. Parametric pumping formula: X(t) Time varying parameter pumps current through the system I

9. 9 NTNU, November 2008 Introduction Our main results: Used Onsager’s reciprocal theorem. Developed a general scattering theory. Applied formalism to a layered GaAs|(Ga,Mn)As|GaAs system. Find critical currents as low as 2.0 * 10 6 A/cm 2.

10. 10 NTNU, November 2008 Outline 1.Introduction to Onsager reciprocal relations. 2.Derivation of formalism. 3.Application 1: System with no spin-orbit coupling. 4.Application 2: GaAs|(Ga,Mn)As|GaAs system.

11. 11 NTNU, November 2008 Onsager Reciprocal Relations {q i |i=1,..,N}{X i |i=1,..,N}{dq i /dt |i=1,..,N} Quantities describing the system Rate of changeForce inducing rate of change

12. 12 NTNU, November 2008 Onsager Reciprocal Relations General form of rate of change in linear response: = 1 if q i even under time reversal -1 if q i odd under time reversal Onsager’s Theorem:

13. 13 NTNU, November 2008 Onsager Reciprocal Relations in N|F|N system Quantity Rate of change Force (X) Magnetic system: Spin system: Charge system: M i dM i /dt (X M ) i =-dF/dM i I s L(R) (X s L(R) ) i = N L - N R I (X c ) z =V L - V R Linear Response: Onsager’s Theorem gives: Normal metal Normal metal Ferro- magnet LR

14. 14 NTNU, November 2008 Onsager Reciprocal Relations in N|F|N system Spin and charge pumped by precessing magnetization: Gives response coefficients: Gives magnetization dynamics: Used:

15. 15 NTNU, November 2008 Summarized Scattering Theory of Charge & Spin-Current Induced Magnetization Dynamics Reference: K.M.D. Hals, A. Brataas, and Y. Tserkovnyak, arXiv:0905.4170

16. 16 NTNU, November 2008 Application 1: Systems with no spin-orbit coupling Scattering matrix given by: Spin-transfer-torque: Agrees with magnetoelectronic circuit theory. Assume spin accumulation in left reservoir, and that length of conductor is larger than the transverse spin coherence length.

17. 17 NTNU, November 2008 Application 2: GaAs|(Ga,Mn)As|GaAs Model: GaAs (Ga,Mn)As z x y Main results: Charge current gives magnetization switching. Critical current density of the order 2.0*10 6 A/cm 2

18. 18 NTNU, November 2008 Application 2: GaAs|(Ga,Mn)As|GaAs

19. 19 NTNU, November 2008 Conclusions Developed a general theory that treats both STT and charge current torques. No SO coupling: Agrees with magnetoelectronic circuit theory. SO systems: Unpolarized charge-current torques give magnetization switching. Interface scattering gives a torque. Impurity scattering gives a bulk torque. Find magnetization switching for currents as low as 2.0* 10 6 A/cm 2 Reference: K.M.D. Hals, A. Brataas, and Y. Tserkovnyak, arXiv:0905.4170

20. 20 NTNU, November 2008 Parameter values GaAs (Ga,Mn)As z x y

21. 21 NTNU, November 2008