Magnetism and Matter MM-2: Electronic and magnetic properties - PowerPoint PPT Presentation

Mitglied der Helmholtz-Gemeinschaft Magnetism and Matter MM-2: Electronic and magnetic properties Stefan Blügel Peter Grünberg Institut and Institute for Advanced Simulation Forschungszentrum Jülich, Germany Lecture MM-2, 20, Sept. 2018 Prof. Dr. Stefan Blügel, | ESM-2018 Krakow Folie 1

Mitglied der Helmholtz Gemeinschaft 1. Elliott-Yafet Parameter & spin-relaxation Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 2

Unquenching the orbital moment by spin- Mitglied der Helmholtz Gemeinschaft orbit interaction The spin-orbit interaction is in the wave function! 1 st order perturbation theory: Orbital moment: MAE due to MCA: (2 nd order perturbation) For d-states Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 3

Concept of spin relaxation Mitglied der Helmholtz Gemeinschaft Injection of Equilibration of spin population spin population "me T 1 Bloch equation: For B=0 : Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 4

Spin degeneracy in nonmagnetic solid Mitglied der Helmholtz Gemeinschaft without spin orbit interaction degenerate states Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 5

Spin mixing by spin-orbit coupling (Elliott, Mitglied der Helmholtz Gemeinschaft 1954) Usually: degenerate states | b 2 |: Ellio5-Yafet parameter n’ E(k) Perturba(on theory: n Δ k Rule of thumb: k Δ small à | b 2 | large Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 6

Importance for spin relaxation (Elliott 1954; Mitglied der Helmholtz Gemeinschaft Yafet 1963) Usually: degenerate states | b 2 |: Elliott-Yafet parameter momentum spin Spin-flip Scattering event scattering overlap probability: + (impurity spin-orbit effects) phonon Spin-relaxation rate: or impurity Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 8

Example: Mitglied der Helmholtz Gemeinschaft Elliott-Yafet parameter in Cu, Au Usually: degenerate states | b 2 |: Elliott-Yafet parameter fcc Cu fcc Au Fermi surface Fermi surface 0.094 0.004 Average: Average: 0.002 0.022 0.001 0.021 different scale Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 9

Momentum and spin relaxation time Mitglied der Helmholtz Gemeinschaft 1% Ga impurities in Cu Momentum relaxation time (fs) Spin relaxation time (fs) Relative difference: Factor 1000 Swantje Heers, PhD Thesis, FZJ 2011 (see also D. Fedorov et al, PRB 2008) Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 10

Gedanken -experiment Mitglied der Helmholtz Gemeinschaft Injection of spin population Equilibration Case A time T 1 A Injection of spin population Equilibration Case B time T 1 B A ≠ T 1 Should we expect that T 1 B ? Yes, if the material structure is anisotropic: Anisotropy of Elliott-Yafet parameter b 2 ! Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 11

12 Mitglied der Helmholtz Gemeinschaft Anisotropy in hcp-Os spin hot-spots injected electrons 0.5 1 ⇠ h b 2 k i FS b 2 T 1 k 0.048 ≈ 1 = 20 0 giant anisotropy + 59% 0.077 ≈ 1 13 spin-flip hot area Zimmermann et al. , PRL (2012) Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 12

13 Mitglied der Helmholtz Gemeinschaft Trends across the periodic table cubic 57 71 72 73 74 75 76 77 78 79 L L H T W R O Ir P A … a u f a e s t u cubic crystals [001] [111] 0.2% 0.9% 0.4% 0.1% ˆ Anisotropy 5.7% ˆ s s Zimmermann et al. , PRL (2012) Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 13 V ↓ ˆ s ↑↓ ˆ s ˆ s ⇒ ⇒ ⇒ ⇒

14 Mitglied der Helmholtz Gemeinschaft Trends across the periodic table hexagonal 57 71 72 73 74 75 76 77 78 79 L L H T W R O Ir P A … a u f a e s t u hcp hcp crystals c -axis ab -plane 150% 200% 830% 88% Anisotropy ˆ ˆ s s Zimmermann et al. , PRL (2012) Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 14 ˆ ˆ s s ↑↓ ⇒ ⇒ ⇒ = ⇒ ⇒

Spin-Orbit Coupling: Mitglied der Helmholtz Gemeinschaft Space Inversion Symmetry Elemental solids (Cu, Si, Al….) For a given band ν the following two states have the same energy Proof: time reversal space inversion q.e.d. Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 16

What happens when Mitglied der Helmholtz Gemeinschaft space inversion symmetry broken (GaAs, InSb, interfaces, surfaces, ...) Time reversal + space inversion symmetry: Time reversal only ! , Effective spin-orbit (“magnetic”) field Ω: Time reversal symmetry: I. Zˇuti ́c, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004) . Lecture MM-2, | ESM-2018, Krakow, Sept 20 2018 Prof. Dr. Stefan Blügel. | http://www.fz-juelich.de/pgi/Bluegel_S Folie 17