# Devil's Staircases in SFS Josephson Junctions

## TL;DR

This paper investigates how magnetization dynamics influence the electrical characteristics of SFS Josephson junctions under circularly polarized magnetic fields, revealing devil's staircase structures in their IV curves.

## Contribution

It introduces a coupled RCSJ and Landau-Lifshitz-Gilbert model to explain fractional steps in IV characteristics, linking magnetization dynamics to phase differences.

## Key findings

- Demonstrates ferromagnetic resonance effects on critical current density
- Reveals devil's staircase structures in IV curves following continued fraction patterns
- Provides analytical justification for fractional steps in the junctions

## Abstract

We study the effect of coupling between the superconducting current and magnetization in the superconductor/ferromagnet/superconductor Josephson junction under an applied circularly polarized magnetic field. Manifestation of ferromagnetic resonance in the frequency dependence of the amplitude of the magnetization and the average critical current density is demonstrated numerically. The IV-characteristics show subharmonic steps that form devil's staircases, following a continued fraction algorithm. The origin of the found steps is related to the effect of the magnetization dynamics on the phase difference in the Josephson junction. The dynamics of our system is described by a generalized RCSJ model coupled to the Landau-Lifshitz-Gilbert equation. In the suplement we justify analytically the appearance of the fractional steps in IV-characteristics of the superconductor/ferromagnet/superconductor Josephson junction.