Grueneisen-approach for the experimental determination of transient spin and phonon energies from ultrafast x-ray diffraction data: gadolinium

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.