Anisotropic supercurrent due to inhomogeneous magnetization in ferromagnet/superconductor junctions

We investigate transverse charge and spin dc supercurrents in a ferromagnet coupled to a superconductor where the ferromagnet has inhomogeneous magnetic structure. These transverse supercurrents arise from nontrivial structure of the magnetization. The magnetic structure manifested in the transverse charge supercurrent is essentially different from that discussed in the context of anomalous Hall effect, reflecting the dissipationless nature of supercurrent. Possible candidates of magnetic structure to verify our prediction are also discussed.

Figure 1

Schematic illustration of the ferromagnet/ superconductor junction.

Figure 2

Diagrammatic representations of the current densities. Diagrams (a) describe first order contributions in $J$, (b) second-order contributions and (c) third-order contributions. The wavy lines denote the interaction with the local spin $\mathbf{n}$ and dotted lines represent the phase gradient $\mathbf{\nabla }\phi$. The last diagrams in (a), (b), and (c) correspond to the second terms in Eqs. (5) and (6).

Figure 3

(a) Magnetization vector $\mathbf{n}$. (b) Vortex spin structure. (c) Conical spin structure. The transverse supercurrents under the phase gradient arise in these spin structures.