Spintranszport és spindinamika nanorendszerekben Simon Ferenc

Transcription

1 Spintranszport és spindinamika nanorendszerekben Simon Ferenc BME

2 Motivation Outline - Spintronics intro -Experimental methods -The Elliott-Yafet theory -Its generalization -Dessert

3 Spintronics 1996 DARPA project title by Stuart A. Wolf Low R High R Local geometry Non-local

4 Spin-Orbit Coupling Classical Electrodyn.: interacts with Factor 2! Types of internal E field: Intrinsic (atomic) Dresselhaus Bychkov-Rashba e.g. GaAs heterolayers, gate bias

5 Suggested device: Datta-Das spin FET Fabian et al. RMP 2004 Tipically: T 1 =10 6 τ spin-mean free path >> mean free path

6 Non-local resistance measurement Tombros et al. Nature 2007

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

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

9 Historical understanding of CESR Observations for alkali metals: depends on alkali width increases with increasing T Too large line broadening, wrong T dependence gives ΔB inhom >1 T broad lines ( /sec). Motional narrowing: τ sec gives ΔB hom 10 mt decreasing with increasing T Explanation: SO coupling induces relaxation (Elliott 1954 )

10 Symmetry breaking: Spin Relaxation mechanisms bulk, e.g. GaAs (Dresselhaus) heterolayer (Bychkov-Rashba) Courtesy of J. Fabian EY: the more the scattering the shorter the T 1 DyP: the more the scattering the longer the T 1

11 The Elliott-Yafet theory: Without SOC pure spin up/down states e.g. atomic basis SO mixes vertical-k spin up/down states Mixing strength: For a crystal with inversion: Presence of a near band needed Inversion time reversal SO does not split spin up-down in the same band

12 The Elliott-relation g-factor shift: H Z + gives Scattering: Yafet 1964: valid to lowest T Monod-Beuneu diagram Beuneu and Monod, PRB 18, 2422 (1978).

13 The Elliot-Yafet mechanism

14 Anomalous spin-lattice relaxation (or line-width) in MgB 2 Anomaly appears above 150 K No magnetic field- No thermal history dependence It is a true electronic effect Reproduced by Rettori et al Monod et al F. Simon et al. PRL 87, (2001). J. Fabian, 2001: I do not have a clue

15 The generalized Elliott-Yafet theory In EY: τ does not play a role, treated to lowest order For elemental metals Δ 10 ev Hint: A. Jánossy check the Adrian paper F. Adrian PRB 1996 SO field fluctuating with τ Rigorous derivation: Kubo formalism, Mori-Kawasaki theory (Balázs Dóra, MPI Dresden)

16 BS of MgB 2 J. Kortus et al. PRL 86, 4686 (2001). 4 For MgB 2 at 400 K, Γ=0.24 ev Energy (ev) π π π σ σ σ Γ M K Γ A L Γ Γ -0.3

17 Fitting the data 14 Single gap does not work 12 CESR Line-width (mt) Mg 11 B 2 σ Two gap model: 2 π T (K)

18 Alkali fullerides Unique properties: Large EPC - quadratic Γ -large residual Γ 0 (disorder) Gunnarsson. RMP 2001 Hou et al. SSC 1995, Jánossy et al. PRL 1993, Nemes et al. PRB 2000

19 Dóra and Simon, PRL 2009

20 Consequences of the generalized EY theory I.: Saturation of relaxation rate Saturation of transport (ρ) Ioffe-Regel criterion: Saturation of relaxation rate BW Γ Δ Γ High temperature spin mean-free path (800 K): Au Cu Ag K 3 C nm 100 nm 180 nm 180 nm Use molecular metals for spintronics!

21 Consequences of the generalized EY theory II.: EY to DyP crossover if Γ<<Δ then Γ s α Γ EY if Γ>>Δ then Γ s α 1/Γ DyP Large scattering acts like symmetry breaking

22 Graphene v F large, SO small Heavy debate: measured T 1 is ps Tombros et al. Nature Theory: 3 orders of magn. longer! Intrinsic Bychkov-Rashba Ripples Dora, Muranyi, Simon EPL accepted

23 Our approach 1. Take the transport experiment serious 2. Study model systems Values for the intrinsic SO in graphene Graphene DFT: Our analysis: Other systems LiC 6 : MgB 2 : 1-10 μev (J. Fabian, P. Guinea) 4 mev 1 mev 3 mev

24 MgB 2 graphene

25 EY or DyP? Answer: both

26 Feasibility of bulk ESR in graphene Suggestion: Li doped graphene

27 Collaborators: Balázs Dóra The rest of the team in action... András Jánossy Ferenc Murányi László Forró Paul Canfield Cedomir Petrovic Sergey Budko Special thanks: Attila Virosztek Jaroslav Fabian Phillippe Monod