Chudnovsky Symposium, Mar.13&14, 2009 2 Wayne M. Saslow Texas A&M University Spintronics in Non-uniform Magnetic Conductors: Dynamics with a Bend or a Twist Phys. Rev. B 76, 184434 (2007). Bend or Twist: Domain Wall or Vortices
Chudnovsky Symposium, Mar.13&14, 2009 3 What Phenomena Occur? Spin Seebeck Effect A temperature gradient causes spin-polarized currents. "Observation of the spin Seebeck effect", K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa and E. Saitoh, Nature 455, 778-781 (9 October 2008). Spin Transfer Torque (bulk) A spin-polarized current transfers angular momentum and torque to the magnetization. Now “well-known”. Spin Pumping (bulk) Dynamics of the magnetization causes spin-polarized current flow. "Universal Electromotive Force Induced by Domain Wall Motion", S. A. Yang, G. S. D. Beach, C. Knutson, D. Xiao, Q. Niu, M. Tsoi, and J. L. Erskine, Phys. Rev. Lett. 103, 067201 (2009).
Chudnovsky Symposium, Mar.13&14, 2009 4 What Theoretical Approach? Irreversible Thermodynamics Local thermodynamics holds initially. Equations of motion taken to ensure that local thermodynamics holds at all future times. Non-negative heating rate R (even under t => -t). R is a sum of products of thermodynamic fluxes j with corresponding thermodynamic forces: R=-j si dT/dx i +… Thermodynamic fluxes are proportional to thermodynamic forces. Irreversible thermodynamics doesn’t give coefficients. Onsager relations for cross-coupling coefficients.
Chudnovsky Symposium, Mar.13&14, 2009 5 Time-Reversal Signature (TRS) is Crucial: Irreversibility = Dissipative Response Reversibility = Reactive Response Thermodynamic densities and thermodynamic forces (affinities) have well-defined signatures under time-reversal. Time-derivatives (e.g. dM/dt) and fluxes (e.g. j) have intrinsic time- reversal signature (TRS). Each part of the time-derivatives and fluxes allowed by irreversible thermodynamics has a definite TRS; same TRS as intrinsic makes them reactive; opposite TRS from intrinsic makes them dissipative. Examples: (1) Mass moving through a fluid: force has even intrinsic TRS; Stokes’ damping force has odd TRS. These are opposite, so Stokes’ damping is dissipative. (2) Insulating solid (NaCl): Entropy current has odd intrinsic TRS; temperature gradient has even TRS. These are opposite, so thermal conduction is dissipative.
Chudnovsky Symposium, Mar.13&14, 2009 6 One-Band Conductor Thermodynamic variables (densities): entropy s and number n, with even TRS. Thermodynamic forces: gradients of temperature and electrochemical potential, with even TRS. Real-space vector index i. For this system, all thermodynamic fluxes have odd intrinsic TRS. entropy flux number flux current flux Thermodynamic forces have even TRS; all these fluxes are dissipative. Subject to Onsager Relation (ensures equal dissipation rates for the two cross-terms)
Chudnovsky Symposium, Mar.13&14, 2009 7 One-Band Conductor - Heating Rate Rate of entropy production Oscillate voltage Phase-lock heating rate
Chudnovsky Symposium, Mar.13&14, 2009 8 Two-Band Conductor Thermodynamic variables (densities): entropy s and number n 1 and n 2, with even TRS. Thermodynamic forces: gradients of temperature and electrochemical potentials, with even TRS. Real-space vector index i. Thermodynamic fluxes with odd intrinsic TRS All these fluxes are dissipative. Subject to Onsager Relations
Chudnovsky Symposium, Mar.13&14, 2009 9 Uniform Insulating Magnet (No Diffusion) Thermodynamic variables (densities): magnetization M has odd intrinsic TRS. Thermodynamic forces: torque MxH has even intrinsic TRS. New Element - Structure Constant has odd intrinsic TRS. Equation of motion (vectors indicate spin-space) First (Larmor) term has even TRS, which matches the intrinsic TRS of dM/dt, so no damping. Second (Landau-Lifshitz) term has odd TRS, so damping. Many other authors also get LL damping with their versions of irreversible thermodynamics (Baryakhtar, Iwata, Barta). Irreversible thermodynamics does not give the put-in-by-hand, self-referential Gilbert damping, with dM/dt in place of - MxH for the last term on the RHS. W.F. Brown’s Fokker-Planck theory inputs, rather than derives, Gilbert damping. No Onsager relations
Chudnovsky Symposium, Mar.13&14, 2009 10 Uniform Conducting Magnet Thermodynamic variables (densities): Thermodynamic forces: torque Structure Constant Output - equation of motion and fluxes Spin and space variables are independent. Onsager Relations Spin Seebeck implied by Stiles&Zangwill, etc. Spin Seebeck (j by grad T)
Chudnovsky Symposium, Mar.13&14, 2009 11 Experimental Spin Seebeck Effect Oct. 2008 Nature observation by Japanese group: K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa & E. Saitoh
Chudnovsky Symposium, Mar.13&14, 2009 12 Nonuniform Conducting Magnet with Flow of Magnetization Q - I Thermodynamic variables (densities): Thermodynamic forces: torque Structure Constants Flux of Magnetization Output - equation of motion for M Spin transfer torque (dM/dt by grad )
Chudnovsky Symposium, Mar.13&14, 2009 13 Nonuniform Conducting Magnet with Flow of Magnetization Q - II Flux of Magnetization Output - fluxes Many Onsager Relations New, Non-Dissipative Onsager Relations Spin pumping (j by MxH)
Chudnovsky Symposium, Mar.13&14, 2009 14 Experimental Spin Pumping Observed via Vortex Core motion (Yang et al) Proposed Observation via Domain Wall Motion (Barnes & Maekawa, Duine, Saslow)
Chudnovsky Symposium, Mar.13&14, 2009 15 Adiabatic vs Non-Adiabatic Spin Transfer Torque and Spin Pumping L terms are dissipative (odd TRS, opposite even TRS of dM/dt). Associated with misleadingly-named Adiabatic Spin Transfer Torque and Adiabatic Spin Pumping. Think of adiabatic as adiabatic-in-space, not adiabatic-in-time. L’ terms are non-dissipative (even TRS, same as even TRS of dM/dt). Associated with misleadingly- named Non-adiabatic Spin Transfer Torque and Non-adiabatic Spin Pumping. Spin Transfer Torque, Spin Pumping, Spin Seebeck effects have all been observed, the Spin Pumping effect only recently. What about other theories of Spin Transfer Torque and Spin Pumping? They all use a form of the Spin- Berry phase (up and down spins have different phases). Space-derivative of Spin-Berry phase gives Spin Transfer Torque: current is proportional to gradient of a phase, as for a superfluid. Time-derivative of Spin-Berry phase gives Spin Pumping (relative change of up and down phases rotates magnetization). These theories are appropriate to a superconducting magnet, not an ordinary conducting magnet. These theories give opposite TRS for thermodynamic forces than for ordinary conducting magnets. They have the Onsager symmetries reversed (L L’), and they call the adiabatic spin transfer torque and adiabatic spin pumping terms non-dissipative; whereas they are in fact dissipative.
Chudnovsky Symposium, Mar.13&14, 2009 16 Truth In Advertising Early theories by Berger and Slonczewski. Very heuristic, physically motivated, but not easily-understood. Likely had no influence on recent theories of bulk spin pumping. But definitely predicted surface spin pumping and surface spin transfer torque. First recent theory of bulk spin pumping: S. E. Barnes and S. Maekawa, Phys. Rev. Lett. 98, 246601 (2007). Called it “spin motive” force. Additional theory by R. Duine, Phys. Rev. B 77, 014409 (2008). Called it “spin pumping”. Further theory by U Texas group of Niu, one of whom (Yang) is lead author on the paper from the Erskine-Tsoi group, reporting the observation of bulk spin pumping. “Universal emf induced by domain wall motion”.