# Grueneisen-Approach for the Experimental Determination of Transient Spin and Phonon Energies from Ultrafast X-ray Diffraction Data: Gadolinium

## TL;DR

This study uses ultrafast X-ray diffraction and a Grueneisen approach to analyze transient spin and phonon energies in gadolinium thin films, revealing non-equilibrium dynamics after femtosecond laser excitation.

## Contribution

It introduces a method to distinguish spin and phonon contributions to strain in ultrafast experiments using a simple Grueneisen model.

## Key findings

- Phonons and spins are driven out of thermal equilibrium for several nanoseconds.
- Ultrafast laser pulses induce measurable transient strain related to spin and phonon energies.
- The Grueneisen approach effectively decomposes strain into spin and phonon components.

## Abstract

We study gadolinium thin films as a model system for ferromagnets with negative thermal expansion. Ultrashort laser pulses heat up the electronic subsystem and we follow the transient strain via ultrafast X-ray diffraction. In terms of a simple Grueneisen approach the strain is decomposed into two contributions proportional to the thermal energy of spin and phonon subsystems. Our analysis reveals that upon femtosecond laser excitation phonons and spins can be driven out of thermal equilibrium for several nanoseconds.