Spontaneous spin current near the interface between ferromagnets and unconventional superconductors

Abstract

Proximity effects between ferromagnets (F) and superconductors (S) with broken time-reversal symmetry ( T) are studied theoretically. For the S side we consider a chiral (p x ±ip y )-wave, and a d x 2− y 2 -wave superconductor, the latter of which can form T-breaking surface state, i.e., (d x 2− y 2 ±is)-state. The Bogoliubov de Gennes equation which describes the spatial variations of the superconducting order parameter and the magnetization is derived and solved numerically. It is found that a spontaneous spin current flows along the interface between the (p x ±ip y )-wave superconductor and the ferromagnet. On the contrary, in the case of a [110] interface of the d x 2− y 2 -wave superconductor, the surface state has a (d±p x ±p y )-wave (or (d x 2− y 2 ±is)-wave) symmetry, and thus no (only charge) spontaneous current arises.