Spintronics: a step closer to the "The Emperor's New Mind" Ferenc Simon

Transcription

1 Spintronics: a step closer to the "The Emperor's New Mind" Ferenc Simon TU-Budapest, Institute of Physics

2 Outline -I. Intro, spintronics -II. SOC,spin-relaxation mechanisms -III. The intuitive unified theory of SR -IV. Monte Carlo approach to SR

3 Motivation: sustainable development in electronics Empirical Moore s law Doubling every two years Challenges: - Sustainable development -Economical operation Landauer principle: 1 bit information: k B T log2 B 0 0 S 0 k B ln2

4 Spintronics is enabled by motion of spins Giant magnetoresistance (GMR) 1988 (2007 Nobel prize, Fert and Grünberg) Spin-valve: low R Momentum relaxation resistivity Electrons: collisions sec Mean free path: high R Spin flip: Diffusion! Spin diffusion length: 10-8 sec (due to weak SOC) Central issue: spin-lifetime/decoherence/relaxation

5 Non-local resistance measurement Local geometry Non-local Tombros et al. Nature 2007

6 Hanlé type spin-precession 1D Bloch equation: Tombros et al. PRL 2008

7 B=0 B 0 Electron spin resonance S=1/2 T 1 spin-lattice relaxation S=-1/2 H Z =g B BS h g First CESR on Na: Griswold, Kip, Kittel, PR 88, 951 (1952). Measurables: Intensity Width Resonance field/frequency MAGNETIC FIELD (T)

8 1955, First evidence for spin-diffusion First CESR on Na: Griswold, Kip, Kittel, PR 88, 951 (1952). Theory: F. J. Dyson, Theory of electron diffusion and the skin effect, Phys. Rev. (1955). Skin-depth Length scales: -Skin depth, (electrodynamics,, f) -Spin diffusion length, (T 1, Dysonian Lorentzian

9 Outline -I. Intro, spintronics -II. SOC,spin-relaxation mechanisms -III. The intuitive unified theory of SR -IV. Monte Carlo approach to SR

10 Spin-orbit coupling E B Electrodynamics: v Interacts with electrons magnetic moment Types of internal E field: Intrinsic (atomic) Dresselhaus e.g. GaAs Bychkov-Rashba heterolayers+electric field Proximity nearby large SOC layers

11 Role of inversion symmetry Time reversal: k, > and k, > degenerate, even with SOC 1.4 inversion 1.4 broken (GaAs) Energy (arb.units) Energy (arb.units) k k, > and k, > are degenerate Effective, k-dep. magnetic field k

12 inversion Phenomenology of spin-relaxation broken 1/ s α1/ 1/ s α s α s α1/ Elliott-Yafet (1954) Dy akonov Perel (1971) 1 st order pert. theory motional narrowing

13 The Elliott-Yafet theory: Without SOC pure spin up/down states SOC mixes spin up/down states Time dependent perturbation theory: Proportional resistivity and ESR width!

14 The Dy akonov-perel theory: internal fields SOC (L) (k) B(k) (k) Energy (arb.units) k Condition: < << 1 or L << Result: Exceptions: large magn. field: s α

15 Outline -I. Intro, spintronics -II. SOC,spin-relaxation mechanisms -III. The intuitive unified theory of SR -IV. Monte Carlo approach to SR

16 Advances in the theory and experiments of spin-relaxation in metals and semiconductors Simon et al., Phys. Rev. Lett. 101, (2008). Dora and Simon, Phys. Rev. Lett. 102, (2009). Dora, Muranyi, Simon, Eur. Phys. Lett. 92, (2010) Boross et al., Sci. Rep. 3, 3233 (2013). Kiss et al., Sci. Rep. 6, (2016). Szolnoki et al., Sci. Rep. 7, 9949 (2017). Szolnoki et al., Phys. Rev. B. 96, (2017).

17 Anomalous spin-lattice relaxation (or line-width) in MgB 2 Anomaly appears above 150 K No magnetic field- No thermal history dependence No purity, no isotope, No sample type dependence It is a true electronic effect F. Simon et al. PRL 87, (2001). Reproduced by Rettori et al Monod et al. 2001

18 The generalized Elliott-Yafet theory FS et al. PRL 101, (2008). In EY: does not play a role, treated to lowest order For elemental metals 10 ev 400 K-en, =0.24 ev Large EPC! Where is the small gap?

19 Unified theory of spin relaxation

20 The model: 2 DEG L: interband matrix elements L: intraband Dynamic spin susceptibility:

21 The unified theory Boross, Dóra, Kiss, Simon, Sci. Rep. 3, 3233 (2013).

22 The Grand Unified Theory of spin-relaxation EY, DP: long known EY : 2008 DP : 2013 a: SciRep 2016 b: SciRep 2017 c,d: top. insulators Dóra, Simon Sci. Rep Non Lorentzian response

23 The intuitive unification I. Szolnoki, Dóra, Kiss, Fabian, Simon, PRB 2017 Add 2 virtual states+magnetic field Rename the states

24 The intuitive unification II. The EY result in the DP language? Precession for A and B electrons+between scatterings Fabian, Zutic et al. Acta Phys. Slovaca 2007

25 Outline -I. Intro, spin-spectroscopy -II. SOC,spin-relaxation mechanisms -III. The intuitive unified theory of SR -IV. Monte Carlo approach to SR

26 A Monte Carlo approach to spin-relaxation Szolnoki et al. SciRep 2017 The model: 1. Polarized spin ensemble 2. Evolution due to (k) 3. New random k 2DEG+Bychkov-Rashba Yields the dynamic Spin-susceptibility in clean & dirty limits

27 Validation of the model: clean and dirty limits Analytic result on for 2DEG BR+DR SOC 2DEG BR+Many body (finite ) Burkov and Balents, PRB 69 2 (2004).

28 Interesting analogy: NMR motional narrowing 1 =3 =0.1 A. Abragam: Principles of Nuclear Magnetism I( ) (arb.u.) =1 = (arb.u.)

29 Realistic systems: 3D Dresselhaus (e.g. GaAs) Clean limit: dephasing T 2* =1/ Intermediate limit: Non-exponential decoherence Dephasing+memory loss Dirty (DP) limit: Single exponential relaxation

30 Loschmidt-echo in spin relaxation Invert (k) at a given time reversal reversal echo echo echo envelope M z (t) time (units of ) Distinguish dephasing and relaxation/decoherence

31 Conclusion EY and DP can be unified The MC is useful to tackle SR for both DP and EY for arbitrary Future: include the effects of cyclotron effects

32 Acknowledgements András Jánossy László Forró Balázs Dóra Annamária Kiss Jaroslav Fabian Lénárd Szolnoki Gábor Csősz ERC Starting Grant: MTA Lendület: