Josephson current in a superconductor-ferromagnet junction with two noncollinear magnetic domains

Abstract

We study the Josephson effect in a superconductor-ferromagnet-superconductor (SFS) junction with ferromagnetic domains of noncollinear magnetization. As a model for our study we consider a diffusive junction with two ferromagnetic domains along the junction. The superconductor is assumed to be close to the critical temperature ${T}_{c}$, and the linearized Usadel equations predict a sinusoidal current-phase relation. We find analytically the critical current as a function of domain lengths and of the angle between the orientations of their magnetizations. As a function of those parameters, the junction may undergo transitions between $0$ and $\ensuremath{\pi}$ phases. We find that the presence of domains reduces the range of junction lengths at which the $\ensuremath{\pi}$ phase is observed. For the junction with two domains of the same length, the $\ensuremath{\pi}$ phase totally disappears as soon as the misorientation angle exceeds $\frac{\ensuremath{\pi}}{2}$. We further comment on the possible implication of our results for experimentally observable $0$-$\ensuremath{\pi}$ transitions in SFS junctions.