Critical current of a Josephson junction containing a conical magnet

TL;DR

This paper models the critical current in a superconductor/ferromagnetic/superconductor Josephson junction with a conical magnetic layer, revealing rapid oscillations due to triplet correlations superimposed on slower singlet oscillations.

Contribution

It provides an analytical and computational framework for understanding how conical magnetic structures affect the critical current in Josephson junctions.

Findings

Critical current exhibits rapid oscillations due to triplet correlations.

Both oscillations decay over the magnetic coherence length.

Analytical and numerical methods for critical current calculation are developed.

Abstract

We calculate the critical current of a superconductor/ferromagnetic/superconductor (S/FM/S) Josephson junction in which the FM layer has a conical magnetic structure composed of an in-plane rotating antiferromagnetic phase and an out-of-plane ferromagnetic component. In view of the realistic electronic properties and magnetic structures that can be formed when conical magnets such as Ho are grown with a polycrystalline structure in thin-film form by methods such as direct current sputtering and evaporation, we have modeled this situation in the dirty limit with a large magnetic coherence length ($\xi_f$). This means that the electron mean free path is much smaller than the normalized spiral length $\lambda/2\pi$ which in turn is much smaller than $\xi_f$ (with $\lambda$ as the length a complete spiral makes along the growth direction of the FM). In this physically reasonable limit we have employed the linearized Usadel equations: we find that the triplet correlations are short ranged and manifested in the critical current as a rapid oscillation on the scale of $\lambda/2\pi$. These rapid oscillations in the critical current are superimposed on a slower oscillation which is related to the singlet correlations. Both oscillations decay on the scale of $\xi_f$. We derive an analytical solution and also describe a computational method for obtaining the critical current as a function of the conical magnetic layer thickness.