AC/DC spin current in ferromagnet/superconductor/normal metal trilayer systems

TL;DR

This paper investigates AC and DC spin currents in a ferromagnet/superconductor/normal metal trilayer, revealing temperature and thickness-dependent behaviors, including a coherence peak and a transition in current dependence on superconductor thickness.

Contribution

It introduces a detailed derivation of AC and DC spin currents in a trilayer system and applies the QTCI method to efficiently evaluate complex spin current calculations.

Findings

Temperature dependence shows a coherence peak in spin currents.

Spin current dependence on superconductor thickness exhibits a transition at certain frequencies.

Numerical results demonstrate the influence of microwave frequency and layer thickness on spin currents.

Abstract

Spin pumping with superconductors has been extensively studied, particularly in double-layer systems. In this study, we investigate spin pumping in a trilayer system comprising a ferromagnetic insulator (FMI), a superconductor (SC), and a normal metal (NM). We derive the AC and DC spin currents in the NM layer induced by spin motion in the FMI under circularly polarized microwave irradiation. If we treat the spin motion as classical, the AC spin current is expressed. On the other hand, if we treat the spin motion as quantum quasiparticles, the DC spin current is derived. After these derivations, while the computational cost of evaluating the spin current is extremely high, we mitigate this using the Quantics Tensor Cross Interpolation (QTCI) method. We present numerical results showing the dependence of the spin current on temperature, microwave frequency, and superconductor layer thickness. Notably, the temperature dependence of AC and DC spin currents exhibits a coherence peak. Furthermore, we have discovered a transition structure in the dependence of the spin current on the thickness of the superconductor layer, where the dependence changes after a particular frequency.