Theoretical investigations of the temperature dependence of zero-field splitting for in crystals

Abstract

In this paper, we carry out a detailed theoretical investigation of the temperature dependence of zero-field splitting (characterized by of crystals by taking into account both the static contributions due to the thermal expansion of crystal and the vibrational contributions due to the electron - phonon interaction. The static contributions are calculated from the spin - orbit coupling mechanism, the relativistic mechanism, the covalency and overlap mechanism and the spin - spin interaction mechanism. Similar to the studies on the specific heat of crystals, the vibrational contribution of phonons of acoustic branches is given using the long-wavelength approximation and that of phonons of optical branches is calculated using a single-frequency model. The calculated results show that the contribution coming from the coupling with optical phonons is comparable with that due to the thermal expansion and that, to reach good fits between the theoretical and experimental , all the contributions from the thermal expansion and the electron - phonon (including the optical and acoustic phonons) interaction should be taken into account.