Superluminal Propagation of Composite Collective Modes in Superconductor-Ferromagnet Heterostructures

TL;DR

This paper investigates the collective modes in superconductor-ferromagnet heterostructures, revealing conditions under which these modes exhibit superluminal group velocities and identifying experimental signatures of these phenomena.

Contribution

It introduces the analysis of composite collective modes considering the interplay between demagnetization and anisotropy fields, revealing new spectral behaviors and superluminal propagation conditions.

Findings

Spectrum of collective modes depends on the ratio of demagnetization to anisotropy fields.

Superluminal group velocities occur at inflection points in the spectrum.

Differences in spectra can be experimentally observed via Fiske measurements.

Abstract

Superconductor/ferromagnet/superconductor Josephson junctions are paradigmatic systems for studying the delicate interplay of superconductivity and magnetism via proximity effects as well as their composite excitations. Here, we analyse the collective modes (CM) in such a heterostructure by taking into account the interplay between the de-magnetisation field $H_{dem}$ and the field caused by the anisotropy of the ferromagnet $H_{an}$, which was previously neglected. It turns out that the spectrum of composite collective modes, $\omega(k)$, has a qualitatively different form in the case of $H_{dem}<H_{an}$ and of $H_{dem}>H_{an}$. In the first case, the dependence $\omega(k)$ has the same form as in previous studies, whereas in the second case, the spectrum looks completely different. In particular, for moderate or weak anisotropy in ferromagnet the group velocity of collective modes demonstrates inflection point where the group velocity become infinite and is superluminal. Furthermore, this point separates purely real and complex-conjugate solutions for the collective modes and is also {\it exception point}. We show that the difference of the CMs spectra can be revealed by Fiske experiment, i.\,e.\,by measuring the $I-V$ characteristics in the presence of magnetic field and voltage.