Long-Range Spin-Polarized Quasiparticle Transport in Mesoscopic Al Superconductors with a Zeeman Splitting

We report on nonlocal transport in multiterminal superconductor-ferromagnet structures, which were fabricated by means of $e$-beam lithography and shadow evaporation techniques. In the presence of a significant Zeeman splitting of the quasiparticle states, we find signatures of spin transport over distances of several $\mu \mathrm{m}$, exceeding other length scales such as the coherence length, the normal-state spin-diffusion length, and the charge-imbalance length. The relaxation length of the spin signal shows a nearly linear increase with magnetic field, hinting at a freeze-out of relaxation by the Zeeman splitting. We propose that the relaxation length is given by the recombination length of the quasiparticles rather than a renormalized spin-diffusion length.

Figure 1

Scanning electron microscopy image of a sample together with the measurement scheme with the injection (inj) and detection (det) circuits.

Figure 2

(a) Local differential conductance $g_{\mathrm{loc}}=d{I}_{\mathrm{inj}}/d{V}_{\mathrm{inj}}$ of one junction as a function of injector bias $V_{\mathrm{inj}}$ for different applied magnetic fields $B$. (b) The same data plotted on a color scale. The lines indicate the regions where a single spin band dominates conductance.

Figure 3

Normalized nonlocal differential conductance $g_{\mathrm{nl}}/G_{\mathrm{inj}}{G}_{\det }$ as a function of injector bias $V_{\mathrm{inj}}$ for different applied magnetic fields $B$ for one pair of contacts (a), nonlocal conductance of a pair of contacts of the NISIN reference sample (b), the data from panel (a) plotted on a color scale (c), and calculated differential spin current (d).

Figure 4

(a) Normalized nonlocal differential conductance $g_{\mathrm{nl}}/G_{\mathrm{inj}}{G}_{\det }$ as a function of the bias voltage $V_{\mathrm{inj}}$ for different contact distances $d$ at fixed magnetic field $B$ (b) peak area $A$ (for the peak at $V_{\mathrm{inj}}<0$) as a function of $B$ for different $d$ (c) semi-logarithmic plot of $A$ as a function of $d$ for different $B$, together with fits to an exponential decay (d) relaxation length ${\lambda }_{\mathrm{S}}$ derived from these fits as a function of $B$, together with the charge imbalance length ${\lambda }_{Q^{*}}$ of the reference NISIN structure, and the normal-state spin diffusion length ${\lambda }_{\mathrm{N}}$ derived from nonlocal spin-valve experiments.