  A first-principles-based method for computing phonons of magnetic random
solid solutions including thermal magnetic fluctuations is developed. The
method takes fluctuations of force constants (FCs) due to magnetic excitations
as well as due to chemical disorder into account. The developed approach
correctly predicts the experimentally observed unusual phonon hardening of a
transverse acoustic mode in Fe-Pd an Fe-Pt Invar alloys with increasing
temperature. This peculiar behavior, which cannot be explained within a
conventional, harmonic picture, turns out to be a consequence of thermal
magnetic fluctuations.
