Abstract

We consider a Josephson junction between a bulk superconductor and a thin ferromagnetic layer placed on the superconductor's surface. For the ferromagnet, the lowest energy state corresponds to uniform magnetization. At the same time, Cooper pairs from the superconductor can efficiently diffuse into the ferromagnetic layer provided its magnetization is changing in space. The interplay of these two effects can lead to a phase transition between uniform and nonuniform magnetic order.

We consider the problem in the framework of the 2D Usadel equation assuming the ferromagnetic layer is sufficiently narrow and a tunnel interface between the superconductor and ferromagnet. We derive an effective Landau functional expanding the free energy of the system in powers of the magnetization gradients. We demonstrate the possibility of the second order phase transition between uniform and helical magnetic order. In particular, we observe a quite unexpected "resonance": when the exchange energy of the ferromagnet equals the proximity induced superconducting order parameter, transition to the helical state occurs irrespective of the value of magnetic stiffness. Our theory also allows to analyze proximity induced magnetic structure far from the phase transition and find the helical state wave vector as a function of all system's parameters.