A theoretical study on the temperature dependence of zero-field splitting for the tetragonal Cr3+ center in MgO crystal

This paper reports a detailed theoretical calculation of the temperature dependence of zero-field splitting D (characterized by ΔD(T)=D(T)-D(0)) for the tetragonal Cr3+ center in MgO crystal by considering both the static contribution due to the thermal expansion of Cr3+ center and the vibrational contribution caused by electron-phonon (including the acoustic and optical phonons) interaction. The vibrational contribution due to the acoustic phonon is calculated using the long-wave approximation similar to the study on the specific heat of crystals and that due to optical phonon is estimated using the single-phonon model. The calculated results are in reasonable agreement with the experimental values. From the calculation, it is found that the static contribution ΔDstat(T) (which is often regarded as very small and is neglected in the previous papers) is larger than the vibrational contribution ΔDvib(T) and so the reasonable studies of temperature dependence of zero-field splitting should take both the static and the vibrational contributions into account.