Comprehensive approach to the zero-field splitting of S6-state ions: Mn2+ and Fe3+ in fluoroperovskites

Abstract

The zero-field splitting of ${\mathrm{S}}^6$-state ions is studied in the intermediate-field coupling scheme by taking the crystal-field and the electrostatic interactions as the unperturbed Hamiltonian and the spin-orbit interaction as a perturbation. This perturbation process shows a very good convergence and provides a comprehensive approach to the derivation of both the rank-2 ${\mathrm{b}}_2^{\mathrm{q}}$ and the rank-4 ${\mathrm{b}}_4^{\mathrm{q}}$ zero-field splitting parameters, which are shown to come predominantly from the first nonzero peturbation terms. Cubic and tetragonal symmetries are considered and the zero-field splitting parameters D (∼${\mathrm{b}}_2^0$), a (∼${\mathrm{b}}_4^4$), and F (∼${\mathrm{b}}_4^0$) are investigated in detail as functions of the cubic Dq and the tetragonal crystal-field (CF) parameters ${\mathrm{B}}_{20}$ and ${\mathrm{B}}_{40}^{\prime }$. It is found that the tetragonal CF components ${\mathrm{B}}_{20}$ and ${\mathrm{B}}_{40}^{\prime }$ contribute, to the cubic zero-field splitting parameter a, a value ${\mathrm{a}}_{\mathrm{t}}$, which is non-negligible. The ratio ${\mathrm{a}}_{\mathrm{t}}$/F is found to be insensitive to CF parameters and to lie in the range -0.2 to -0.5. Both parameters ${\mathrm{a}}_{\mathrm{t}}$ and F depend mainly on ${\mathrm{B}}_{20}$, whereas D depends mainly on ${\mathrm{B}}_{40}^{\prime }$. The results of earlier perturbation procedures are also calculated and compared with the present ones. The present theory deals with the zero-field splitting parameters ${\mathrm{b}}_4^{\mathrm{q}}$ (k=2 and 4) by regarding the crystal-field parameters ${\mathrm{B}}_{\mathrm{kq}}$ (k=2 and 4) as freely adjustable phenomenological parameters, thus avoiding problems arising from the application of a specific crystal-model to the evaluation of ${\mathrm{B}}_{\mathrm{bq}}$. Following this idea, numerical calculations are carried out for the parameters a, D, and F for ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ ions in cubic and tetragonal fluoroperovskites. The results are in good agreement with experimental data. This work presents examples where the crystal-field theory allows a successful interpretation of the zero-field splitting of ${\mathrm{S}}^6$-state ions.