Thermodynamic origin of the pressure-induced Invar effect: General criterion and experimental study of Fe 68 Pd 32
Synchrotron X-ray diffraction measurements were performed on 57 Fe 68 Pd 32 at multiple pressures and two temperatures in a diamond-anvil cell. Between 4 and 11GPa, the thermal expansion was zero or slightly negative. This pressure-induced Invar effect was studied further with 57 Fe nuclear forward scattering and nuclear resonant inelastic X-ray scattering to obtain information on the pressure-induced changes in both the magnetization and the phonon density of states. Magnetic entropy and phonon entropy were obtained from these results, the latter with additional measurements from inelastic neutron scattering to account for the contributions from Pd atoms. The dependencies of these entropies on pressure gave the magnetic and phonon contributions to thermal expansion. These canceled in the region of pressure-induced Invar behavior, even though they individually increased by more than a factor of 2 below the Curie pressure. The behavior of phonons gives evidence for spin-phonon interactions in Fe 68 Pd 32 . A general explanation of the pressure-induced Invar effect is presented, showing that Invar behavior is typically expected at a pressure P* below a magnetic transition at pressure PC. The difference in pressure P C − P* scales with the fractional reduction in magnetic exchange interaction divided by the average Gr¨uneisen parameter.