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

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 A. Brataas, Yu.V. Nazarov and G.E.W. Bauer, Phys. Rev. Lett. 84 (2000), p M.D. Stiles and A. Zangwill, Phys. Rev. B 66 (2002), p General systems: Based on: Calculation of exchange-correlation energy. A. S. Nunez and A. H. MacDonald Solid State Commun.,139 (2006), p. 31.

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 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, (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: : Unpolarized charge currents can switch magnetization in (Ga,Mn)As. N|F|N system

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

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

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

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:

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

21 NTNU, November 2008