Temperature-Dependent Spin-Hamiltonian Parameters ofMn2+in Trigonal Sites of CaCO3

The spin-Hamiltonian parameters of divalent manganese in CaC${\mathrm{O}}_3$ have been measured over the temperature range 4.2-850 °K using electron-spin-resonance-absorption techniques. Eigenvalues to the spin-Hamiltonian and best-fit parameters were obtained using perturbation calculations, where the off-diagonal component in the hyperfine interaction is treated as the major perturbation. The crystalline-field parameters and the hyperfine-coupling constant $A$ were found to decrease in magnitude with increasing temperature, although there was no measurable variation of the $g$ value over this temperature range. Variation in the parameters with temperature is discussed in terms of implicit (thermal-expansion) and explicit (lattice-vibration) effects. Contributions from implicit effects were evaluated using previously reported isothermal pressure-dependent data. After correcting the experimental data for the implicit effect, a large residual-temperature variation is found for the crystalline-field parameters $D$ and $a_0$. This residual-temperature variation is attributed to lattice vibrations which couple into the crystalline-field splitting energy. Temperature variations in the axial crystalline-field-splitting energy can be explained, in part, by resonant vibrations which couple to the impurity ion via a relativistic second-order correction proposed by Wybourne. Temperature variations in the hyperfine-coupling constant $A$ are also due primarily to explicit effects. A detailed theoretical analysis of the temperature dependence of $A$ for ${\mathrm{Mn}}^{2+}$ in a non-cubic environment has not been carried out. However, it is possible to qualitatively interpret this temperature variation if it assumed that a large-amplitude local-mode vibration couples strongly to the hyperfine-coupling parameter.