Temperature-hyperfine coupling constant of Mn2+ in MgO

Abstract

The Van Vleck orbit-lattice interaction associated with an ${XY}_{6}$ cubic molecular cluster is used to calculate the phonon-induced hyperfine coupling constant of $M{n}^{2+}$ in $MgO$. Within the Debye approximation, the phonon-induced hyperfine fields is found to be proportional to the Debye-Waller factor. By introducing a "modified Debye temperature" which would calculate one would calculate on the assumption that only acoustic phonons were involved, we are able to compute the contributions attributed to acoustic and optical phonons separately. The agreement between experiment and theory is good. From the fitted curve, we find that the zero-point phonon contribution to the hyperfine coupling constant is 1.1 per cent and hence the hyperfine coupling constant in the "rigid lattice" at $T=\mathit{0}\ifmmode^\circ\else\textdegree\fi{}K$ is $\ensuremath{-}\mathit{82.4}\ifmmode\times\else\texttimes\fi{}{\mathit{10}}^{\ensuremath{-}4}\phantom{\rule{0.25em}{0ex}}{cm}^{\ensuremath{-}1}$.