Effect of contacts on spin lifetime measurements in graphene
Outline
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- Overview of spin injection experiment and nonlocal resistance
- Analytic solution including effect of contacts
- Fitting the solution to real data
- Limitations of fitting regimes
Device geometry
- L : contact spacing
- D : diffusion constant
- τ : spin lifetime
- λ=√Dτ
- ω=gμBB/ħ
- μs=12(μ↑−μ↓)
- J↑↓=σ↑↓∇μ↑↓
- JC↑↓=Σ↑↓(μN↑↓−μF↑↓)c
- J=J↑+J↓
- Js=J↑−J↓
D∇2μs−μsτ+ω×μs=0
V∝μNs(x=L)
J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Žutić, Acta Physica Slovaca 57, 565 (2007).
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M. Popinciuc, C. Józsa, P. J. Zomer, N. Tombros, A. Veligura, H. T. Jonkman, and B. J. van Wees, Phys. Rev. B 80, 214427 (2009).
Tunneling contacts
Finite contact resistance
- RC=5×105kΩ
- τ=427ps
- D=0.014m2/s
- λ=2.5μm
Infinite contact resistance
- τ=427ps
- D=0.014m2/s
W. Han, K. Pi, K. M. McCreary, Y. Li, J. J. I. Wong, A. G. Swartz, and R. K. Kawakami, Phys. Rev. Lett. 105, 167202 (2010).
Transparent contact
Finite contact resistance
- RC=3kΩ
- τ=130ps
- D=0.021m2/s
- λ=1.66μm
Infinite contact resistance
- τ=78ps
- D=0.01m2/s
- λ=1.4μm
W. Han, K. Pi, K. M. McCreary, Y. Li, J. J. I. Wong, A. G. Swartz, and R. K. Kawakami, Phys. Rev. Lett. 105, 167202 (2010).
Transparent contacts
Finite contact resistance
- RC=0.3kΩ
- τ=800×104ps
- D=0.015m2/s
- λ=350μm
W. Han, K. Pi, K. M. McCreary, Y. Li, J. J. I. Wong, A. G. Swartz, and R. K. Kawakami, Phys. Rev. Lett. 105, 167202 (2010).
Limits
- ❱ r→∞ or λ/r≪1
- r terms are negligible.
- Scale and zeros set by τ and D.
- ❱ ωτ≫1 & λ/r>1
- Zeros set by D only.
- Normalized case scales as f/f0∝(λ/r)2√ωτ.
- Can fit to increased τ with moderate decrease in r.
T. Maassen, I. J. Vera-Marun, M. H. D. Guimarães, and B. J. van Wees, Phys. Rev. B 86, 235408 (2012).