# Hierarchy of critical temperatures in four-layered ferromagnet/superconductor nanostructures and control devices

## TL;DR

This paper investigates a four-layered ferromagnet/superconductor nanostructure, revealing complex phase behaviors and proposing a control device based on its multiple critical temperature states for potential magnetic and superconducting applications.

## Contribution

It introduces a detailed theoretical analysis of four-layered F/S/F'/S' structures, highlighting their unique phase states and potential for multi-state control devices.

## Key findings

- Multiple critical temperatures for different layers are identified.
- Distinct 0 and π phase superconducting states are characterized.
- A conceptual multi-state control device scheme is proposed.

## Abstract

The four-layered F/S/F$'$/S$'$ nanostructure consisting of rather dirty superconducting (S) and ferromagnetic (F) metals is studied within the theory of the proximity effect taking detailed account of the boundary conditions. The F/S structures with four F and S layers are shown to have considerably richer physics than the F/S/F trilayer (due to the interplay between the 0 and $\pi$ phase superconductivity and the 0 and $\pi$ phase magnetism) and even the F/S superlattices. The extra $\pi $ phase superconducting states obtained for the four-layered F/S/F$^{\prime }$/S$^{\prime }$ system are found to be different from the known "superlattice" states. The dependence of the critical temperatures versus the F layers thicknesses is investigated. An optimal set of parameters is determined, for which the difference between the critical temperatures for different states becomes significant, and the corresponding phase diagrams are plotted. It is proven that this system can have different critical temperatures for different S and S$'$ layers. A conceptual scheme of a control device with superconducting and magnetic recording channels that can be controlled separately using a weak external magnetic field is proposed on the basis of the F/S/F$'$/S$'$ nanostructure. The devices with four, five, six, and seven different states are explored.