Thermal spin fluctuation effect on the elastic constants of paramagnetic Fe from first principles

Abstract

We investigate the impact of longitudinal thermal spin fluctuations on the temperature dependence of the elastic constants of paramagnetic body-centered-cubic (bcc) and face-centered-cubic (fcc) Fe. Based on a series of constrained local magnetic moment calculations, the spin fluctuation distribution is established using Boltzmann statistics and involving the Jacobian weight, and a temperature-dependent quadratic mean moment is introduced that accurately represents the spin fluctuation state as a function of temperature. We show that with increasing temperature, c' and c(44) for the fcc phase and c(44) for the bcc phase decrease at different rates due to different magnetoelastic coupling strengths. In contrast, c' in the bcc phase exhibits relatively high thermal stability. Longitudinal thermal spin fluctuations diminish the softening of both elastic constants in either phase and have comparatively large contributions in the fcc phase. In both bcc and fcc Fe, c(44) has a larger temperature factor than c'. On the other hand, c' is more sensitive to the longitudinal thermal spin fluctuations, which balance the volume-induced softening by 21.6% in fcc Fe.