# Competitive 0 and {\pi} states in S/F multilayers: multimode approach

## TL;DR

This paper investigates the critical temperature oscillations in superconductor/ferromagnet multilayers using a self-consistent multimode approach, providing insights into 0 and π state conditions and comparing with single-mode approximations.

## Contribution

It introduces an exact multimode method for calculating critical temperature in S/F multilayers and clarifies the applicability of simpler single-mode models.

## Key findings

- Critical temperature exhibits damped oscillations with ferromagnetic layer thickness.
- Conditions for 0 and π state realization are derived.
- Limits of single-mode approximation are established.

## Abstract

We have investigated the critical temperature behavior in periodic superconductor/ ferromagnet (S/F) multilayers as a function of the ferromagnetic layer thickness $d_f$ and the interface transparency. The critical temperature $T_c(d_f)$ exhibits a damped oscillatory behavior in these systems due to an exchange field in the ferromagnetic material. In this work we have performed $T_c$ calculations using the self-consistent multimode approach, which is considered to be exact solving method. Using this approach we have derived the conditions of 0 or $\pi$ state realization in periodic S/F multilayers. Moreover, we have presented the comparison between the single-mode and multimode approaches and established the limits of applicability of the single-mode approximation, frequently used by experimentalists.