Element-resolved thermodynamics of magnetocaloric LaFe_{13-x}Si_x

By combination of two independent approaches, nuclear resonant inelastic X-ray scattering and first-principles calculations in the framework of density functional theory, we determine the element-resolved vibrational density of states in the ferromagnetic low temperature and paramagnetic high temperature phase of LaFe$_{13-x}$Si$_x$. This allows us to derive the lattice and electronic contribution to the entropy change at the first-order phase transformation, which are both of considerable magnitude. The change in lattice entropy is dominated by magneto-elastic softening, which originates from the itinerant electron metamagnetism associated with Fe. This counteracts the large volume change at the transition and leads to an unexpected, cooperative behavior of magnetic, vibrational and electronic entropy change, which is responsible for the large magneto- and barocaloric effect observed for this material.