Spin Currents in a 2D Electron Gas

Transcription

1 Spin Currents in a 2D Electron Gas Joshua Folk UBC Asilomar, 2007

2 Thanks to: My group Sergey Frolov (postdoc) Ananth Venkatesan (postdoc) Mark Lundeberg (PhD) Wing Wa Yu (Masters) Yuan Ren (Masters) Chung-Yu Lo (Masters) George Kamps (Undergrad) Heterostructures W. Wegscheider (Regensburg, Germany) Funding CIFAR, CFI, NSERC

3 Motivations Why measure spin current? - Spintronics (quantum and classical) - Hard to infer spin physics from charge transport Why measure in semiconductors (vs metals)? - Spin physics of interacting electrons - Exquisite control of material system - Electrical control of spin

4 Measuring spin currents electrically: a polarizer/analyzer geometry Spin injector (polarizer) Spin detector (analyzer) A V

5 Nonlocal geometry generates pure spin currents (spin currents without charge currents) Jedema, van Wees et al, Nature 2002; see also Johnson and Silsbee, PRL A Charge current flows to left, spin current to right V

6 Nanostructures in GaAs/AlGaAs electron gas Gate Voltage(s) Gates This material: n e = cm 2 µ = cm 2 /V s mfp 50µm Bias Voltage

7 V Device geometry A Charge current flows to left, spin current to right 300μm

8 V Device geometry 1μm channel width A Charge current flows to left, spin current to right 300μm

9 V Device geometry 1μm channel width Quasiballistic: momentum relaxation length ~ 20um, >> channel width A Charge current flows to left, spin current to right 300μm

10 V Device geometry A Charge current flows to left, spin current to right Point contact injector/detectors

11 Quantum point contact: A spin injector without ferromagnets In-plane B=10T Quantized Conductance B = 0T B =10T A g (e 2 /h) Vgate 1µm Gate voltage (mv) Spin-resolved plateau, transmits only spin up

12 Spin injectors are spin detectors too Equilibrium spin population No voltage detected Nonequilibrium spin population Voltage records μup - μdown when spin selective

13 V Detecting spin currents Detector spacing 10μm In-plane B=10T A

14 Detecting spin currents Detector spacing 10μm x Injector Gate Voltage (mv)

15 Temperature Dependence 2.0x10-6 B=10T 2.2K 1.1K 600mK 200mK 1.5 Nonlocal Voltage Injector Gate (mv) Enhanced g factor in low density QPC spin current still significant at T=2.2K!

16 Diffusion Length V spin (x) λ s e x λs 2L λ s = 50µm Assumes constant detector polarization

17 Diffusion Length V spin (x) λ s e x λs Assumes infinite channels λ s (channel length >> )

18 Finite channels Nonlocal Voltage (V) 500x L=90um L=150um Injector Gate (mv)

19 Finite channels Nonlocal Voltage (V) 500x L=90um L=150um V spin (x) λ s sinh( L x λs ) for channel length L 2 e L λs Injector Gate (mv)

20 Finite channels Nonlocal Voltage (V) 500x L=90um L=150um V spin (x) λ s sinh( L x λs ) for channel length L 2 also gives e L λs 2L λ s = 50µm Injector Gate (mv) independent of contact polarization

21 Spin relaxation time Total channel resistance implies 20um momentum relaxation length 2L λ s = 50µm τ s 1ns How does this depend on: Magnetic field? Electron-electron interactions? Nonequilibrium chemical potential? ( )

22 Contact Polarization R V spin (x) I inj 2L P injp det λ s e x λs = 50

23 Contact Polarization R V spin (x) I inj 2L P injp det λ s e x λs = 50 R spin = V spin I inj P inj P det

24 Absolute magnitude of spin signal R V spin (x) I inj 2L P injp det λ s e x λs = 50 Spin current flows to the left and right. Absolute magnitude depends on device details (not fully diffusive!) E.g. perpendicular field of mT can strongly enhance or suppress spin current

25 Other Nonlocal Signals Thermoelectric Voltage (?) V P I 2 = (I dc + I 0 sin(ωt)) 2 e s = I 2 dc + 2I dci 0 sin(ωt) + sin 2 (ωt) = 50 Lockin measurement

26 Other Nonlocal Signals x Thermoelectric Voltage (?) DC Bias Voltage (mv) V P I 2 = (I dc + I 0 sin(ωt)) 2 e s = I 2 dc + 2I dci 0 sin(ωt) + sin 2 (ωt) = 50 Lockin excitation 17Hz Lockin measurement 1.5x Nonlocal Voltage at 17Hz Injector Gate (mv)

27 Other Nonlocal Signals Thermoelectric Voltage (?) V P I 2 = 50 Phase coherent effects (nonlocal UCF) = (I dc + I 0 sin(ωt)) 2 e s = I 2 dc + 2I dci 0 sin(ωt) + sin 2 (ωt) 2.0x K 1.1K 600mK 200mK 1.5 Nonlocal Voltage see also Lerescu, van Wees et al Injector Gate (mv)

28 Other Nonlocal Signals Detector Gate B = 10T B = 0 Injector Gate Spin signal dominates over other nonlocal signals, and most other signals disappear for T>500mK

29 Conclusions: Electrical generation and detection of spin currents Long mean free path enables spin transfer over long distances Spin relaxation length can be determined independent of contact polarization characteristics Flexibility of gated channel geometry in 2D electron gas provides a tool to study spin relaxation over a wide range of parameters (temperature, field, density, # of modes in