# A unified description of collective magnetic excitations

## TL;DR

This paper introduces a comprehensive analytical framework for describing the dynamic magnetic response, resonance spectra, and magnon dispersion in ferromagnetic materials, applicable without saturation and useful alongside simulations.

## Contribution

It provides a unified analytic approach to characterize magnetic excitations, including susceptibility, resonance, and dispersion, expanding understanding beyond existing models.

## Key findings

- Analytic description of ferromagnetic susceptibility tensor
- Modeling of angular and frequency-dependent resonance spectra
- Description of magnon dispersion in reciprocal space

## Abstract

In this work, we define a set of analytic tools to describe the dynamic response of the magnetization to small perturbations, which can be used on its own or in combination with micromagnetic simulations and does not require saturation. We present a general analytic description of the ferromagnetic high frequency susceptibility tensor to describe angular as well as frequency dependent ferromagnetic resonance spectra and account for asymmetries in the line shape. Furthermore, we expand this model to reciprocal space and show how it describes the magnon dispersion. Finally we suggest a trajectory dependent solving tool to describe the equilibrium states of the magnetization.