Spontaneous spin current near the interface between unconventional superconductors and ferromagnets

TL;DR

This paper theoretically investigates the proximity effect at ferromagnet-superconductor interfaces with broken time-reversal symmetry, revealing spontaneous spin currents in chiral p-wave superconductors and conditions for pure spin current flow.

Contribution

It introduces a theoretical model analyzing spin and charge currents at F/S interfaces with unconventional superconductors, highlighting the emergence of spontaneous spin currents in chiral p-wave states.

Findings

Spontaneous spin current flows along the interface in chiral p-wave superconductors.

No spin current is observed in d-wave superconductors with surface states.

Pure spin current can exist without charge current in F/S/F trilayer systems with antiparallel magnetizations.

Abstract

We study theoretically the proximity effect between ferromagnets (F) and superconductors (S) with broken time-reversal symmetry (${\cal T}$). A chiral $(p_x\pm ip_y)$-wave, and a $d_{x^2-y^2}$-wave superconductor, the latter of which can form ${\cal T}$-breaking surface state, i.e., $(d_{x^2-y^2} \pm is)$-state, are considered for the S side. The spatial variations of the superconducting order parameters and the magnetization are determined by solving the Bogoliubov de Gennes equation. In the case of a chiral $(p_x\pm ip_y)$-wave superconductor, a spontaneous spin current flows along the interface, but not in the case of a $d_{x^2-y^2}$-wave superconductor. For F/S$(p_x+ip_y)$/F trilayer system, total spin current can be finite while total charge current vanishes, if the magnetization of two F layers are antiparallel.