Critical ultrasonic propagation in magnetic fields

Effect of an external magnetic field on the critical sound attenuation and velocity of the longitudinal wave is studied in ferromagnets. We derive a parametric model that incorporates a crossover from the asymptotic critical behavior to the Landau-Ginzburg regular behavior far away from the critical point. The dynamics is based on the time dependent Ginzburg-Landau model with non conserved order parameter (model A). The variations of the sound attenuation coefficient and velocity have been obtained for arbitrary values of the magnetic field and reduced temperature. The scaling functions are given within the renormalization group formalism at one-loop order. Using MnP as an example, we show that such parametric crossover model yields an accurate description of ultrasonic data in a large region of temperatures and magnetic fields around the critical point.