# Broadband spectroscopy of thermodynamic magnetization fluctuations through a ferromagnetic spin-reorientation transition

## TL;DR

This study uses broadband optical magnetometry to analyze magnetization fluctuations in a ferromagnetic film across a spin reorientation transition, revealing critical spectral behaviors and the influence of magnetic fields.

## Contribution

It demonstrates broadband spectral analysis of thermodynamic magnetization fluctuations through a controlled spin reorientation transition in a ferromagnetic film.

## Key findings

- Magnetization noise follows a ν^{-3/2} power law in perpendicular anisotropy regions.
- A critical frequency ν_0 emerges during the transition, indicating a low-frequency cutoff.
- Magnetization noise is strongly affected by applied magnetic fields, revealing local anisotropies.

## Abstract

We use scanning optical magnetometry to study the broadband frequency spectra of spontaneous magnetization fluctuations, or "magnetization noise", in an archetypal ferromagnetic film that can be smoothly tuned through a spin reorientation transition (SRT). The SRT is achieved by laterally varying the magnetic anisotropy across an ultrathin Pt/Co/Pt trilayer, from the perpendicular to in-plane direction, via graded Ar$^+$ irradiation. In regions exhibiting perpendicular anisotropy, the power spectrum of the magnetization noise, $S(\nu)$, exhibits a remarkably robust $\nu^{-3/2}$ power law over frequencies $\nu$ from 1~kHz to 1~MHz. As the SRT region is traversed, however, $S(\nu)$ spectra develop a steadily-increasing critical frequency, $\nu_0$, below which the noise power is spectrally flat, indicating an evolving low-frequency cutoff for magnetization fluctuations. The magnetization noise depends strongly on applied in- and out-of-plane magnetic fields, revealing local anisotropies and also a field-induced emergence of fluctuations in otherwise stable ferromagnetic films. Finally, we demonstrate that higher-order correlators can be computed from the noise. These results highlight broadband spectroscopy of thermodynamic fluctuations as a powerful tool to characterize the interplay between thermal and magnetic energy scales, and as a means of characterizing phase transitions in ferromagnets.