Zero-Point Phonon Contribution to the Hyperfine Coupling of S -State Ions

The temperature-independent phonon zero-point motion is shown to decrease the hyperfine coupling constant A for Mn²⁺ ions in a cubic environment. A spherical approximation is made for the phonon vibrational modes appropriate to a rocksalt structure, enabling the inclusion of contributions from both the acoustic and optical branches. Numerical calculations are performed for vibrational parameters appropriate to both MgO and SrO. The temperature-dependent part of the decrease in A due to thermal phonon excitation is also evaluated for both hosts. Comparing the two calculations, the temperature can be determined at which the decrease in A due to thermal excitations equals the decrease due to zero-point excitations. These temperatures are 383^∘{}K for MgO and 133^∘{}K for SrO. Use is then made of the observed decrease in A with temperature to find the magnitude of the zero-point reduction in both hosts. We find ΔAZ.P. (MgO: Mn²⁺) {}-0.8×{}10^-4 cm^-1 and ΔAZ.P. (SrO:Mn²⁺)-1.4×10^-4 cm^-1. The change in A, ΔAZ.P.[ΔA(T=0)+ΔAZ.P.], due to phonon zero-point motion is therefore 0.97% for MgO:Mn²⁺ and 1.70% for SrO: Mn²⁺, and the $T=0$ "rigid-lattice" values are estimated to be -82.3×{}10^-4 cm^-1 for both hosts.