Temperature dependence of phonons in Pd_3Fe through the Curie temperature

Iron phonon partial densities of states of Pd_3^(57)Fe were measured from room temperature through the Curie transition at 500 K using nuclear resonant inelastic x-ray scattering. The experimental results were compared to ab initio spin-polarized calculations that model the finite-temperature thermodynamic properties of L1_2-ordered Pd_3Fe with stochastically generated atomic displacements, coupled with magnetic special quasirandom structures of noncollinear magnetic moments. The scattering measurements and first-principles calculations show that the Fe partial vibrational entropy is close to what is predicted by the quasiharmonic approximation owing to a cancellation of effects. Anharmonicity and a magnon-phonon interaction approximately cancel a ferromagnetic optical phonon stiffening.