# Fast Vortex Oscillations in a Ferrimagnetic Disk near the Angular Momentum Compensation Point

## TL;DR

This paper demonstrates that ferrimagnetic vortex disks near their angular momentum compensation point can support high-frequency oscillations, tunable via external fields or temperature, useful for fast magnetic devices.

## Contribution

It introduces the concept of ferrimagnetic vortex oscillations near the compensation point, showing their potential for high-frequency applications and detection of the compensation temperature.

## Key findings

- Vortex oscillation frequencies reach tens of GHz.
- Frequency can be tuned by external magnetic fields or temperature.
- Maximum eigenfrequency indicates the angular momentum compensation point.

## Abstract

We theoretically study the oscillatory dynamics of a vortex core in a ferrimagnetic disk near its angular momentum compensation point, where the spin density vanishes but the magnetization is finite. Due to the finite magnetostatic energy, a ferrimagnetic disk of suitable geometry can support a vortex as a ground state similar to a ferromagnetic disk. In the vicinity of the angular momentum compensation point, the dynamics of the vortex resemble those of an antiferromagnetic vortex, which is described by equations of motion analogous to Newton's second law for the motion of particles. Owing to the antiferromagnetic nature of the dynamics, the vortex oscillation frequency can be an order of magnitude larger than the frequency of a ferromagnetic vortex, amounting to tens of GHz in common transition-metal based alloys. We show that the frequency can be controlled either by applying an external field or by changing the temperature. In particular, the latter property allows us to detect the angular momentum compensation temperature, at which the lowest eigenfrequency attains its maximum, by performing FMR measurements on the vortex disk. Our work proposes a ferrimagnetic vortex disk as a tunable source of fast magnetic oscillations and a useful platform to study the properties of ferrimagnets.