# Spin-density fluctuations and the fluctuation-dissipation theorem in 3d ferromagnetic metals

## TL;DR

This paper investigates the spatial and energy distribution of spin density fluctuations in 3d ferromagnetic metals using ab initio calculations, revealing their continuous spread over the Brillouin zone and their spectral composition.

## Contribution

It provides a comprehensive analysis of spin density fluctuations in 3d ferromagnets, including their energy scales, spectrum components, and the application of the fluctuation-dissipation theorem to evaluate spin correlators.

## Key findings

- SDF are spread over the entire Brillouin zone.
- Majority of SDF reside within the 3d bandwidth, with significant high-energy contributions.
- The SDF spectrum has a low-energy spin wave part and a larger high-energy localized excitation component.

## Abstract

Spatial and time scales of spin density fluctuations (SDF) were analyzed in 3d ferromagnets using ab initio linear response calculations of complete wavevector and energy dependence of the dynamic spin susceptibility tensor. We demonstrate that SDF are spread continuously over the entire Brillouin zone and while majority of them reside within the 3d bandwidth, a significant amount comes from much higher energies. A validity of the adiabatic approximation in spin dynamics is discussed. The SDF spectrum is shown to have two main constituents: a minor low-energy spin wave contribution and a much larger high-energy component from more localized excitations. Using the fluctuation-dissipation theorem (FDT), the on-site spin correlator (SC) and the related effective fluctuating moment were properly evaluated and their universal dependence on the 3d band population is further discussed.