Understanding change in the sound wave frequency in a ferromagnet under magnetic field influence (Simon effect) in the low-field regime

Studies of coupled magnetic and elastic effects have a long history, however, these effects still hold the scientific interest of researchers. In particular, in recent years, there has been an increased interest in research on the interaction of surface acoustic waves with spin waves in ferromagnetic films . In turn, this calls for better understanding of low field regime of Simon effect (the effect is related to the influence of the applied magnetic field on the sound wave velocity in a ferromagnetic crystal). In our work, based on the example of bcc Fe, we propose a refined formula to describe the Simon effect, which contains terms related to dispersion effects associated with exchange stiffness. We compare our analytical solutions with other alternative computational approaches and show that dispersion effects can be significant for the Simon effect and cannot be neglected in the low field regime. As a result, we propose a more accurate analytical formula, which, due to its relative simplicity, can become a convenient tool to estimate the magnitude of the expected magnetic field effect on the sound wave speed propagation in a cubic ferromagnetic crystal, as well as it explains observed deviations from analytically expected results in Simon effect at low magnetic field.