Complete mapping of the spin-wave spectrum in vortex state nano-disk

TL;DR

This study comprehensively maps the spin-wave spectrum in vortex state nano-disks and reveals how the modes evolve during a phase transition to a saturated magnetic state, highlighting the continuous transformation of the gyrotropic mode.

Contribution

It provides the first complete mapping of spin-wave modes in vortex nano-disks and details their evolution during magnetization transition.

Findings

Gyrotropic mode softens and vanishes at saturation field.

Spin-wave modes are bijectively related between vortex and saturated states.

Level anti-crossing alters the character of non-gyrotropic modes.

Abstract

We report a study on the complete spin-wave spectrum inside a vortex state nano-disk. Transformation of this spectrum is continuously monitored as the nano-disk becomes gradually magnetized by a perpendicular magnetic field and encouters a second order phase transition to the uniformly magnetized state. This reveals the bijective relationship that exists between the eigen-modes in the vortex state with the ones in the saturated state. It is found that the gyrotropic mode can be continuously viewed as a uniform phase precession, which uniquely softens (its frequency vanishes) at the saturation field to transform above into the Kittel mode. By contrast the other spin-wave modes remain finite as a function of the applied field while their character is altered by level anti-crossing.