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 Delta D(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 Delta D-stat(T) (which is often regarded as very small and is neglected in the previous papers) is larger than the vibrational contribution Delta D-vib(T) and so the reasonable studies of temperature dependence of zero-field splitting should take both the static and the vibrational contributions into account. (C) 2010 Elsevier B.V. All rights reserved.