Spin relaxation of conduction electrons Jaroslav Fabian (Institute for Theoretical Physics, Uni. Regensburg)

Transcription

1 Spin relaxation of conduction electrons Jaroslav Fabian (Institute for Theoretical Physics, Uni. Regensburg) :Syllabus: 1. Introductory description 2. Elliott-Yafet spin relaxation and spin hot spots 3. Spin-orbit coupling in zincblende (detour: spin transistors) 4. Dyakonov-Perel mechanism: complete derivation 5. Experimental facts for GaAs 6. Spin relaxation in GaAs 2DEG 7. (Extrinsic) Spin Hall effect Literature: I. Zutic, J. Fabian, and S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004).

2 1. Introductory description

3

4 Bloch equations to get T 1 and T 2, start with a microscopic model, derive kinetic equations for spin, and compare with Bloch equations.

5

6

7 2. Elliott-Yafet mechanism the more scattering, the more spin relaxation R. J. Elliott, Phys. Rev. 96, 266 (1954). Y. Yafet, in Solid State Physics Vol. 14, ed. F. Seitz and Turnbull, p. 2 (1963). J. Fabian and S. Das Sarma, Phys. Rev. Lett. 81, 5624 (1998). [realistic calculations]

8 Spin relaxation in metals: Elliott-Yafet theory R. J. Elliott, Phys. Rev. B 96, 266 (1954) Y. Yafet, in Solid State Physics, Vol. 14, p.2 (1963)

9 Elliott-Yafet formalism a >> b spin-flip Eliashberg function

10 Some useful relations Elliott relation: Yafet relation: Spin relaxes at scattering events

11 Phonon-induced spin relaxation in aluminum J. Fabian and S. Das Sarma, Phys. Rev. Lett. 83, 1211 (1999) 2002

12 3. Spin-orbit coupling in zincblende semiconductors

13 spin-orbit coupling in zincblende systems what happens when inversion symmetry is broken

14 specific forms (a) bulk Dresselhaus bulk Dresselhaus G. Dresselhaus, Phys. Rev. 100, 580 (1955). (b) two dimensions, growth direction n, linear in k terms!!! 2d Dresselhaus, BIA (bulk inversion asymmetry) Bychkov-Rashba, SIA (structure inversion asymmetry) Yu. A. Bychkov and E. I. Rashba, J. Phys. C 17, 6039 (1984); JETP Lett. 39, 78 (1984)

15 Dresselhaus (BIA) and Bychkov-Rashba (SIA) field patterns SIA BIA [001] BIA [111] BIA [110] From: I. Zutic, J. Fabian, S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004)

16 Detour: spin transistors

17 Datta-Das Spin FET S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990) From: I. Zutic, J. Fabian, S. Das Sarma, Rev. Mod. Phys. 76, 323 (2004) Low temperatures, spin coherence Single channel transport Spin injection issues Uniform spin-orbit coupling Efficient spin-orbit coupling modulation

18 Hot-electron spin tunneling transistor Fermi level I C CoFe M 1 Emitter ev EB Al O 2 3 I E Fermi level CoFe M 2 3 Base GaAs 4 Collector Hybrid structures Large magnetocurrent Useful for interface characterization Spin filter Large base current small or no gain V EB V BC A S. Van Dijken, X. Jiang, and S. Parkin, Phys. Rev. Lett. 90, (2003)

19 Magnetic Bipolar Transistor active forward mode N emitter forward reverse magnetic P base N collector j e j b j c V BE w b<< Lbn V BC J. Fabian, I. Zutic and S. Das Sarma, Appl. Phys. Lett. 84, 85 (2004); J. Fabian and I. Zutic, Phys. Rev. B 69, (2004).

20 4. Dyakonov-Perel mechanism the more scattering, the less spin relaxation M. I. Dyakonov and V. I. Perel, Sov. Phys. Solid State 13, 3023 (1971).

21 The Boltzmann equation with spin

22 net number of collisions leading to state k

23 the collision term

24 result spin Larmor precession

25 solution of the BE

26 elastic scattering: k =k

27

28

29 result:

30 discussion Spin relaxes between scattering events

31 motional narrowing why 1/τ s τ p random spin walk

32 5. GaAs bulk

33 Spin relaxation in bulk n-gaas relaxation tim e(ns) τ τ τ τ τ τ R. I. Dzhioev et al., Phys. Rev. B 66, (2002)

34 6. GaAs 2d structures Dresselhaus BIA Bychkov-Rashba SIA

35 2d anisotropic spin relaxation SIA BIA [001] BIA [111] BIA [110]

36 Spin relaxation in GaAs/AlGaAs QW 0.10 SpinRelaxation R ate(ps -1 ) E1e (mev) A. Malinowsky et al., Phys. Rev. B 62, (2000)

37 7. (Extrinsic) Spin Hall Effect (SHE) skew spin scattering M. I. Dyakonov and V. I. Perel, Phys. Lett. 35A, 459 (1971).

38 Mott spin-orbit scattering k k Awschalom s group web site

39 Theory of ESHE

40 solution

41 Experiment: spin accumulation at edges k k Awschalom s group web site Y. K. Kato et al. Science Express (2004)