Spin-polarized transport in ferromagnetic semiconductor / diffusive - PowerPoint PPT Presentation

JST-DFG Workshop on Nano-electronics, March 5-7, 2008, Aschen Spin-polarized transport in ferromagnetic semiconductor / diffusive semiconductor / superconductor junctions H. Takayanagi 髙柳 英明 International Center for Materials NanoArchitechtonics (MANA), NIMS, Tsukuba Tokyo University of Science,Tokyo T. Akazaki NTT Basic Research Labs., Atsugi Y. Sawa, T. Yokoyama, Y. Tanaka Nagoya University, Nagoya A. A. Golubov University of Twente, The Netherlands H. Munekata Tokyo Institute of Technology, Yokohama 1

Motivation Superconductivity Ferromagnet Appearance of the new quantum phenomena • Josephson current via ferromagnet • Interplay between Andreev reflection or proximity effect and spin polarization Nb/ferromagnetic p-InMnAs/Nb junction S-F-S junction Nb/n-InAs/ferromagnetic p-InMnAs junction S-N-F junction 2

1. S-F-S junction Nb/p-InMnAs/Nb structure L = 0.8, 10 μ m Cross-sectional view p-In 0.96 Mn 0.04 As • P ~ 4.4 x 10 13 (cm -2 ) • μ P ~ 71 (cm 2 /Vs) at 0.5 K Top view 3

Anomalous Hall effect 50 0.5 K 2 K 4 K 40 Hall resistance ( Ω ) 8 K 10 K 15 K 30 20 K 20 10 L = 10 μ m 0 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 Magnetic field (gauss) Measurement configuration • Observation of anomalous Hall effect below ~15 K • Reverse magnetic field is ~ 1000 gauss at 0.5 K. 4

T C of Nb electrodes 75 70 Resistance ( Ω ) 65 60 55 50 T C ~ 8.2 K 45 5 6 7 8 9 10 Temperature (K) Measurement configuration T C ~ 8.2 K 5

Temperature dependence of resistance 4.5 Normalized resistance (a.u.) S-F-S 4.0 N-F-N 3.5 L = 0.8 μ m 3.0 2.5 2.0 T C (Nb) ~ 8.2 K 1.5 1.0 0.5 (a) S-F-S junction 0 2 4 6 8 10 Temperature (K) Below T C of Nb, temperature dependence of resistance is completely different between Measurement the S-F-S and N-F-N junction. configuration 6 (b) N-F-N junction

Differential conductance in N-F-N junction Differential conductance (x10 -4 S) 3.2 0.5 K 3 2 K 4 K 2.8 6 K 8 K 2.6 10 K 2.4 2.2 2 1.8 L = 0.8 μ m 1.6 -6 -4 -2 0 2 4 6 Voltage (mV) Although the weak tunneling behavior is observed in low temperatures, 7 we have obtained nearly linear voltage-dependence.

Differential conductance in S-F-N junction Differential conductance (x10 -4 S) 8 7 6 5 4 0.5 K 2 K 3 4 K 6 K 2 8 K L = 0.8 μ m 10 K 1 -3 -2 -1 0 1 2 3 Voltage (mV) We have obtained the conductance reduction within V ~ 1.5 mV. cf. Nb superconducting energy gap Δ Nb ~ 1.5 meV 8

Differential conductance in S-F-S junction Differential conductance (x10 -4 S) Differential conductance (x10 -4 S) 3.5 3.5 3 3 2.5 2.5 2 2 0.5 K 0.5 K 1.5 1.5 2 K 2 K 4 K 4 K 6 K 1 6 K 1 8 K 8 K L = 0.8 μ m L = 0.8 μ m 10 K 10 K 0.5 0.5 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 Voltage (mV) Voltage (mV) We have obtained the conductance reduction within V ~ 3mV. 9

Comparison between all junctions Normalized conductance (arb. u) 1.1 The conductance reduction is 1.0 observed in ONLY S-F-S and 0.9 S-F-N junctions. 0.8 0.7 0.6 0.5 The superconducting electrodes S-F-S may affect conductance of the T ~ 0.5 K 0.4 S-F-N L = 0.8 μ m junction. N-F-N 0.3 -6 -4 -2 0 2 4 6 Voltage (mV) 10

Discussion In Andreev reflection process, the incident electron requires the opposite spin electron to be removed from the N region for conversion to Cooper pair. In case of S-F junctions, Andreev reflection is limited by the minority spin population. R. J. Soulen Jr. et al., Science 282, p.86 (1998) Our experimental results can be qualitatively understood by considering the suppression of Andreev reflection due to spin polarization in p-In 0.96 Mn 0.04 As. 11

Current injection to SFS JJ Differential conductance (x10 -4 S) 2.2 2.0 1.8 1.6 1.4 1.2 1.0 I inj = 0 - 3 μ A step 0.2 μ A 0.8 T ~ 0.7 K (from bottom) 0.6 -6 -4 -2 0 2 4 6 Voltage (mV) 12

2. S-N-F junction p-InMnAs/n-InAs/Nb structure Top view L = 0.6 μ m (designed) Cross-sectional view 13

Current injection from Nb Differential conductance (x10 -3 S) 1.768 1.766 1.764 1.762 1.760 I inj = 0 - 20 μ A 1.758 step 2 μ A T ~ 0.7 K (from bottom) 1.756 -6 -4 -2 0 2 4 6 Voltage (mV) 14

Current injection from p-InMnAs Differential conductance (x10 -3 S) 1.768 1.766 1.764 1.762 1.760 I inj = 0 - 20 μ A 1.758 step 2 μ A T ~ 0.7 K (from bottom) 1.756 -6 -4 -2 0 2 4 6 Voltage (mV) 15

Proximity Effect Spin Injection Pair potential Ferromagnetic Normal Superconductor Normal (In,Mn)As / InAs junction Fe / Si junction Pair potential Pair potential Ferromagnetic Superconductor Ferromagnetic Superconductor Exchange field Ferromagnetic Inverse proximity effect Superconductor h F = − ξ h x ( ) h exp( x / ) h S S x 0 16

Theoretical Model l << Mean free path L Usadel Equation ' R R ∂ ∂ b b ⎛ ⎞ ⎡ ⎤ + = ˆ ˆ ˆ , ˆ Ferro ⎜ ⎟ Electrode R Super D G G i H G 0 ⎣ ⎦ d ∂ ∂ ⎝ ⎠ x x x − L 0 ˆ G :Green’s function D :Diffusion constant ε Hamiltonian for spins : Quasiparticle energy ( ) ⎧ ε + − τ Δ − ≤ ≤ ˆ ⎪ ( ) h ( ) x : pair potential L x 0 F 3 = ⎨ ˆ H ( ) ⎡ ε + − ⎤ τ + Δ τ x > ⎪⎣ ˆ ˆ ( ) h x ⎦ i ( ) x ⎩ h 0 : Exchange field in F(S) S 3 2 ( ) F S ( ) i = τ 1,2,3 ˆ i : Pauri matrix Boundary condition: Conservation at the interface Δ → ∞ = Δ ( x ) : Bulk value 0 17

Calculation Method Green’s function Selfconsistently Gap Equation Usadel Eq. Pair potential Golubov. et. al. (1994) Green’s function DOS, Conductance, etc. Exchange field Ferromagnetic Constant h F Superconductor h F = − ξ h x ( ) h exp( x / ) h Exponential decay of h S S S x ≥ 0 Due to the barrier at the interface h h F ξ : F(S) Coherence length ( ) F S 18

Model for the Experiment V V F 1 Electrode − * I I For path ② i Normal(N) 2 * S I i ① ② I V i i Ferro(F) Super(S) 1 S + * I I i 2 F Electrode − 1 = V * V RI i i − 2 V V Virtual voltage for the Current injection from Ferromagnetic i current injection Normal Ferromagnetic 19

Conductance for a FS-SF junction (1) Exchange field I i Ferro Super h − F F S S F V V h = 0 V x i 0 V :Corrensponds to current injection i h = 0 σ T V V i i 1.2 1.0 0.8 σ T 0.6 0.4 h = 0 0.2 -2 -1 0 1 2 0 1 -1 eV/ Δ 0 eV/ Δ 0 V i / Δ = 0 V i / Δ = 1 0 0 V i / Δ = 0.5 V i / Δ = 1.5 Zero-bias conductance peak by current injection 0 0 20

Conductance for a FS-SF junction (2) Inverse proximity effect I Exchange field i − Ferro Super F S S F V V h V F i h V :Corresponds to current injection x i 0 = Δ h σ T 0 V V i i 1.2 1.0 0.8 T σ 0.6 h eV = 1 0.4 i 0.2 -2 -1 0 1 2 0 1 -1 eV / Δ 0 eV/ Δ 0 V i / Δ = 0 V i / Δ = 1 Zero bias peak is suppressed by the synergistic 0 0 V i / Δ = 0.5 V i / Δ = 1.5 0 0 effect of the current injection and exchange 21 field in the S.

Comparison with experimental results Theory Experimen 1.2 Differential conductance (x10 -3 S) t 1.766 1.0 1.764 0.8 T σ 1.762 0.6 h h S = 0 eV = 1.760 1 0.4 i I inj = 0 - 20 μ A 1.758 0.2 -2 -1 0 1 2 step 2 μ A eV / Δ 0 T ~ 0.7 K (from bottom) 1.756 -6 -4 -2 0 2 4 6 V i / Δ = 0 V i / Δ = 1 0 0 Voltage (mV) V i / Δ = 0.5 V i / Δ = 1.5 0 0 Differential conductance (x10 -3 S) 1.766 1.2 1.764 1.0 1.762 0.8 σ T h S = 0 1.760 0.6 I inj = 0 - 20 μ A 1.758 0.4 step 2 μ A h = 0 T ~ 0.7 K (from bottom) 0.2 1.756 -2 -1 0 1 2 -6 -4 -2 0 2 4 6 eV/ Δ 0 Voltage (mV) V i / Δ = 0 V i / Δ = 1 22 0 0 V i / Δ = 0.5 V i / Δ = 1.5 0 0

Summary 1. Nb/ p-InMnAs /Nb junctions. ● Suppression of Andreev reflection due to spin polarization in p-InMnAs 2.Nb/n-InAs/ferromagnetic p-InMnAs junction ● We can study the conductance of two types of junctions; one is with the inverse proximity effect and the other is without the inverse effect. ● Our theoretical model explains both experimental results. 23