Spin injection from a normal metal into a mesoscopic superconductor

We report on nonlocal transport in superconductor hybrid structures, with ferromagnetic as well as normal-metal tunnel junctions attached to the superconductor. In the presence of a strong Zeeman splitting of the density of states, both charge and spin imbalance is injected into the superconductor. While previous experiments demonstrated spin injection from ferromagnetic electrodes, we show that spin imbalance is also created for normal-metal injector contacts. Using the combination of ferromagnetic and normal-metal detectors allows us to directly discriminate between charge and spin injection, and demonstrate a complete separation of charge and spin imbalance. The relaxation length of the spin imbalance is of the order of several $\mu$m and is found to increase with a magnetic field, but is independent of temperature. We further discuss possible relaxation mechanisms for the explanation of the spin relaxation length.

Figure 1

Scanning electron microscopy image of a section of sample A. An iron (F) and two copper (N) electrodes form tunnel contacts with a superconducting aluminum (S) wire. Examples of two measurement configurations for nonlocal measurements using a normal-metal injector and either a normal-metal (NISIN) or ferromagnetic (NISIF) detector are indicated.

Figure 2

(a) Differential conductance $g_{\mathrm{loc}}$ of an NIS junction as a function of the bias voltage $V_{\mathrm{inj}}$ for different magnetic fields $B$. (b) Data for $B=1.0$ T together with a fit to Eq. (3) and the contributions of the individual spin orientations. (c) Calculated spin injection $g_{\downarrow }-g_{\uparrow }$.

Figure 3

Normalized nonlocal differential conductance ${\widehat{g}}_{\mathrm{nl}}$ for different contact configurations. All data are taken at $T=50\mathrm{mK}$. (a) ${\widehat{g}}_{\mathrm{nl}}$ for the closest pair of electrodes with N as injector, F as detector (NISIF) and for several magnetic fields. (b) ${\widehat{g}}_{\mathrm{nl}}$ for the same contacts and magnetic fields, but now with F as injector and N as detector (FISIN). (c) Difference of the signals from (a) and (b) at $B=1.0\mathrm{T}$. (d) Comparison of NISIF and NISIN data at $B=1.0\mathrm{T}$ for large contact separation $d$. The lines in (c) and (d) are model predictions (see discussion). (e) Comparison of data for opposite field polarity for a pair of contacts of sample C. (f) Hysteresis loop at small magnetic field and fixed injector bias for a pair of contacts of sample C. Arrows indicate the sweep direction.

Figure 4

(a) Nonlocal conductance ${\widehat{g}}_{\mathrm{nl}}$ for several contact distances $d$ at fixed magnetic field $B=1.0$ T. (b) Semilogarithmic plot of the peak area $A$ as a function of contact distance $d$ for different magnetic fields $B$. The lines are fits to an exponential decay. (c) Nonlocal conductance ${\widehat{g}}_{\mathrm{nl}}$ for different temperatures at fixed magnetic field and contact distance. (d) Normalized peak area $A\left(T\right)/A(T=50\mathrm{mK})$ for small contact distances $d$ as a function of temperature $T$, shown for all three samples. The line is a guide to the eye.

Figure 5

(a) Spin (open symbols) and charge imbalance (closed symbols) relaxation lengths ${\lambda }_{Q^{*}}$ and ${\lambda }_S$ as a function of the magnetic field $B$. (b) Spin relaxation length ${\lambda }_S$ as a function of temperature $T$ at fixed magnetic field $B$. (c) Charge imbalance relaxation time ${\tau }_{Q^{*}}$ as a function of the magnetic field $B$, together with fits (see text). (d) Spin relaxation time ${\tau }_S$ as a function of the magnetic field $B$, with an attempt to fit with $\exp (2{\mu }_{\mathrm{B}}B/k_{\mathrm{B}}T)$ (dotted line).

Figure 6

Schematic view of the spin-resolved density of states, including Zeeman splitting and spin-orbit scattering, and various possible relaxation mechanisms. States are partially occupied up to $E=-e{V}_{\mathrm{inj}}$ (see discussion for details). (a) Spin-flip scattering in a spin-degenerate superconductor. (b) Proposed two-stage relaxation mechanism involving spin flips and recombination for bias voltages in the range of the Zeeman splitting. (c) Inelastic spin flips to the upper Zeeman band. (d) Two-stage spin-flip and energy relaxation process at high bias.