Critical states of superconductivity and their crossover in multilayer superconductor/ferromagnet structures

In order to calculate the critical temperature of multilayer S/F structures (where S is a superconductor and F is a ferromagnet), a matrix method for solving linearized Usadel equations has been proposed. The spectrum of critical temperatures $T^{(k)}$ for the F/$N_{bl}$(S/F) structure has been obtained in the single-mode approximation. Eigenfunctions describing the spatial distribution of superconducting correlations in the direction perpendicular to the S-F interfaces have been calculated for each $T^{(k)}$ value. It has been found that dependences of $T^{(k)}$ on the thickness of F layers have a jump near the transition from 0 to $\pi$-state; any of the calculated $T^{(k)}$ values can be implemented in the region of jumps. It has been shown that the crossover of eigenstates is characterized by the suppression of superconductivity in outer S layers and by induced countercurrents in F layers. The possibility of the experimental implementation of a state corresponding to a given value from the spectrum of $T^{(k)}$ has been discussed.