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

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Spin-polarized transport in ferromagnetic semiconductor / diffusive semiconductor / superconductor junctions

• 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

• H. Takayanagi 髙柳

英明 International Center for Materials NanoArchitechtonics (MANA), NIMS, Tsukuba Tokyo University of Science,Tokyo JST-DFG Workshop on Nano-electronics, March 5-7, 2008, Aschen

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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 Nb/n-InAs/ferromagnetic p-InMnAs junction

S-F-S junction S-N-F junction

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• 1. S-F-S junction Nb/p-InMnAs/Nb structure

Cross-sectional view Top view L = 0.8, 10 μm p-In0.96Mn0.04As

• P ~ 4.4 x 1013 (cm-2)
• μP ~ 71 (cm2/Vs)

at 0.5 K

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Anomalous Hall effect

• Observation of anomalous Hall effect below ~15 K
• Reverse magnetic field is ~ 1000 gauss at 0.5 K.

10 20 30 40 50

• 4000 -3000 -2000 -1000

1000 2000 3000 4000 0.5 K 2 K 4 K 8 K 10 K 15 K 20 K

Hall resistance (Ω) Magnetic field (gauss)

L = 10 μm

Measurement configuration

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TC of Nb electrodes

45 50 55 60 65 70 75 5 6 7 8 9 10

Resistance (Ω) Temperature (K)

TC ~ 8.2 K

TC ~ 8.2 K

Measurement configuration

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0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 2 4 6 8 10 S-F-S N-F-N

Normalized resistance (a.u.) Temperature (K)

L = 0.8 μm

Temperature dependence of resistance

Measurement configuration

(a) S-F-S junction (b) N-F-N junction

Below TC of Nb, temperature dependence of resistance is completely different between the S-F-S and N-F-N junction.

TC (Nb) ~ 8.2 K

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Differential conductance in N-F-N junction

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2

• 6
• 4
• 2

2 4 6 0.5 K 2 K 4 K 6 K 8 K 10 K

Differential conductance (x10-4 S) Voltage (mV)

L = 0.8 μm Although the weak tunneling behavior is observed in low temperatures, we have obtained nearly linear voltage-dependence.

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Differential conductance in S-F-N junction

We have obtained the conductance reduction within V ~ 1.5 mV.

• cf. Nb superconducting energy gap ΔNb ~ 1.5 meV

1 2 3 4 5 6 7 8

• 3
• 2
• 1

1 2 3 0.5 K 2 K 4 K 6 K 8 K 10 K

Differential conductance (x10-4 S) Voltage (mV)

L = 0.8 μm

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Differential conductance in S-F-S junction

0.5 1 1.5 2 2.5 3 3.5

• 6
• 4
• 2

2 4 6 0.5 K 2 K 4 K 6 K 8 K 10 K

Differential conductance (x10-4 S) Voltage (mV)

L = 0.8 μm We have obtained the conductance reduction within V ~ 3mV. 0.5 1 1.5 2 2.5 3 3.5

• 6
• 4
• 2

2 4 6 0.5 K 2 K 4 K 6 K 8 K 10 K

Differential conductance (x10-4 S) Voltage (mV)

L = 0.8 μm

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Comparison between all junctions

0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1

• 6
• 4
• 2

2 4 6 S-F-S S-F-N N-F-N

Normalized conductance (arb. u) Voltage (mV)

T ~ 0.5 K L = 0.8 μm The superconducting electrodes may affect conductance of the junction. The conductance reduction is

• bserved in ONLY S-F-S and

S-F-N junctions.

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Discussion

In Andreev reflection process, the incident electron requires the

• pposite 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. Our experimental results can be qualitatively understood by considering the suppression of Andreev reflection due to spin polarization in p-In0.96Mn0.04As.

• R. J. Soulen Jr. et al., Science 282, p.86 (1998)

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Current injection to SFS JJ

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

• 6
• 4
• 2

2 4 6

Differential conductance (x10-4 S) Voltage (mV)

Iinj = 0 - 3 μA step 0.2 μA (from bottom) T ~ 0.7 K

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• 2. S-N-F junction p-InMnAs/n-InAs/Nb structure

Cross-sectional view Top view L = 0.6 μm (designed)

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Current injection from Nb

1.756 1.758 1.760 1.762 1.764 1.766 1.768

• 6
• 4
• 2

2 4 6

Differential conductance (x10-3 S) Voltage (mV)

Iinj = 0 - 20 μA step 2 μA (from bottom) T ~ 0.7 K

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Current injection from p-InMnAs

1.756 1.758 1.760 1.762 1.764 1.766 1.768

• 6
• 4
• 2

2 4 6

Differential conductance (x10-3 S) Voltage (mV)

Iinj = 0 - 20 μA step 2 μA (from bottom) T ~ 0.7 K

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Proximity Effect

Normal Superconductor Pair potential Pair potential Superconductor Ferromagnetic Normal Ferromagnetic

Spin Injection

(In,Mn)As / InAs junction Fe / Si junction

Superconductor Ferromagnetic Pair potential Exchange field Ferromagnetic Superconductor

( ) exp( / )

S S

h x h x = − ξ

F

h

x

h

Inverse proximity effect

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Mean free path

L l <<

Usadel Equation

ˆ ˆ ˆ ˆ , D G G i H G x x ∂ ∂ ⎛ ⎞ ⎡ ⎤ + = ⎜ ⎟ ⎣ ⎦ ∂ ∂ ⎝ ⎠

:Green’s function

ˆ G

D :Diffusion constant

: pair potential

( ) x Δ

: Quasiparticle energy

ε

( ) F S

h

: Exchange field in F(S)

Hamiltonian for spins

b

R

x

L − Ferro Electrode

d

R

' b

R Super

L x − ≤ ≤

x >

( ) ( )

3 3 2

ˆ ( ) ˆ ˆ ˆ ( ) ( )

F S

h H h x i x + − ⎧ ⎪ = ⎨ + − + Δ ⎡ ⎤ ⎪⎣ ⎦ ⎩ ε τ ε τ τ

Boundary condition: Conservation at the interface : Bulk value ( ) x Δ → ∞ = Δ

: Pauri matrix

ˆi τ

( )

1,2,3 i =

Theoretical Model

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Calculation Method

DOS, Conductance, etc. Usadel Eq. Gap Equation

Green’s function Pair potential Selfconsistently

• Golubov. et. al. (1994)

Green’s function

: F(S) Coherence length

( )

F S

ξ

Constant hF Exponential decay of hS

F

h h ≥

Due to the barrier at the interface

Exchange field Ferromagnetic Superconductor

( ) exp( / )

S S

h x h x = − ξ

F

h

x

h

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Model for the Experiment

For path ② Current injection from Ferromagnetic Ferromagnetic Normal

*

1 2

i

I I −

*

1 2

i

I I +

* i

I S S F F

*

1 2

i i

V RI =

i

V V V − Electrode Electrode

Ferro(F) Super(S)

① ② Normal(N)

i

I

V V −

i

V

Virtual voltage for the current injection

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Zero-bias conductance peak by current injection

Conductance for a FS-SF junction (1)

i

V

i

V

eV/Δ0 1

• 1

σT h = σT eV/Δ0

• 2
• 1

1 2 0.2 0.4 0.6 0.8 1.0 1.2 h =

Vi /Δ = 0 Vi /Δ = 0.5 Vi /Δ = 1 Vi /Δ = 1.5

Exchange field Ferro Super

F

h

x

h =

i

V V V −

i

I

F S S F

i

V :Corrensponds to current injection

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i

V

i

V

σT eV/Δ0

1

• 1

= Δ h

1

i

h eV =

σ

T

• 2
• 1

1 2 0.2 0.4 0.6 0.8 1.0 1.2 eV/ Δ0

Vi /Δ = 0 Vi /Δ = 0.5 Vi /Δ = 1 Vi /Δ = 1.5

Exchange field Ferro Super

h

F

h

x

i

V V V −

i

I

F S S F

i

V :Corresponds to current injection

Conductance for a FS-SF junction (2)

Inverse proximity effect Zero bias peak is suppressed by the synergistic effect of the current injection and exchange field in the S.

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Theory

1

i

h eV =

σ

T

• 2
• 1

1 2 0.2 0.4 0.6 0.8 1.0 1.2 eV/ Δ0

Vi /Δ = 0 Vi /Δ = 0.5 Vi /Δ = 1 Vi /Δ = 1.5

Comparison with experimental results

σT eV/Δ0

• 2
• 1

1 2 0.2 0.4 0.6 0.8 1.0 1.2

h =

Vi /Δ = 0 Vi /Δ = 0.5 Vi /Δ = 1 Vi /Δ = 1.5

Experimen t

hS = 0 hS = 0

1.756 1.758 1.760 1.762 1.764 1.766

• 6
• 4
• 2

2 4 6

Differential conductance (x10-3 S) Voltage (mV)

Iinj = 0 - 20 μA step 2 μA (from bottom) T ~ 0.7 K

1.756 1.758 1.760 1.762 1.764 1.766

• 6
• 4
• 2

2 4 6

Differential conductance (x10-3 S) Voltage (mV)

Iinj = 0 - 20 μA step 2 μA (from bottom) T ~ 0.7 K

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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.