1. Spintronics Research Center, AIST, Tsukuba, Japan Spin rotation after a spin-independent scattering. Spin properties of an electron gas in a solid Journal of Magnetism and Magnetic Materials 356 (2014) 52–67 V. Zayets For details: http://staff.aist.go.jp/v.zayets/spin2_intro_26.html

2. Pauli model for non-magnetic metals, Zener model, Stoner model and s-d model for ferromagnetic metals Models of an electron gas in a solid Classical model of spin-up/spin-down bands Ignores frequent spin rotations Proposed model of TIS/TIA assemblies Includes frequent spin rotations

3. Three possibilities to fill a delocalized electronic state Filling electronic states at different energies 3 undistinguishable states This quantum- mechanical property of an electron causes the spin rotation

4. Spin rotation after a spin-independent scatterings

5. Spin-independent scatterings Scatterings, after which the number of states is conserved Scatterings, after which the number of states is not conserved “spin”+”spin” “full”+”empty” “spin”+”spin” “full”+”empty”

6. TIA and TIS assemblies Time-inversion symmetrical assembly (TIS) Distribution of spin directions in assemblies Time-inversion asymmetrical assembly (TIA) represents electrons of spin accumulations All spin directions One spin directions represents electrons without spin accumulation

7. Spin statistics Charge energy distribution Thermo statistics Spin energy distribution Balance of scatterings Fermi-Dirac statistics Spin statistics

8. Charge energy distribution Fermi-Dirac statistics Spin energy distribution Spin statistics Without spin accumulationWith spin accumulation Spin accumulation Classical modelProposed model

9. Electron gas in magnetic field. Pauli paramagnetism. Ferromagnetic metals Proposed model Classical model non-magnetic metal without magnetic field non-magnetic metal under magnetic field ferromagnetic metal

10. Spin polarization of electron gasbalance between spin pumping and spin relaxation Spin pumping Spin relaxation is spin life time Spin pumping in a magnetic field Spin pumping in a magnetic field is precession damping time is a phenomenological damping parameter k~4/3 when magnetic field is weak Gilbert damping of spin precession Electron gas in magnetic field. Pauli paramagnetism. Ferromagnetic metals

11. Spin Torque. Interaction of two spin accumulations spin accumulated electrons rotates toward spin direction of injected electrons Example (1) (2) (3) Spin Torque Additional spin relaxation

12. Spin-Torque Current Spin Current Spin-Torque Current Aligning all spin-accumulated electrons in one direction over whole sample Diffusion of spin direction Diffusion of spin accumulation Spin Torque due to Spin-Torque Current Additional spin relaxation

13. Origin of Spin-Transfer Torque Step 1 Under an applied voltage a drift current flows between electrodes Step 2 Spin is accumulated at the tunnel barrier (1)(2) (3) (4)

14. Origin of Spin-Transfer Torque Step 4 Spin-torque current flows between electrodes making continuous changing of spin direction of conduction electrodes from electrode to electrode Step 5 In regions, where angle between the conduction s-electrons and localized d-electrons is non-zero, there is a spin precession of the s- and d- electrons around a common axis Step 3 Spin accumulation diffuses from the tunnel barrier deep into electrodes making a gradient of the spin accumulation

15. For more details, visit http://staff.aist.go.jp/v.zayets/spin2_intro_26.html