Mössbauer Studies of Lattice Dynamics, Fine and Hyperfine Structure of DivalentFe57in FeF2

Mössbauer studies of the isomer shift, recoil-free fraction, and quadrupole splitting for ${\mathrm{Fe}}^{57}$ in Fe${\mathrm{F}}_2$ between 80 and 300°K are reported. The temperature dependence of the isomer shift and recoil-free fraction are well explained within the harmonic approximation. The ascertained sum of the microscopic force constants acting on the ${\mathrm{Fe}}^{++}$ ion is $K=(1.24\mathrm{}\pm 0.07)\times {10}^5$ dyn/cm. The weighted frequency average associated with the classical mean-square displacement of the ${\mathrm{Fe}}^{57}$ is ${〈\frac{1}{{\omega }^2}〉}^{-\frac{1}{2}}=(2.08\mathrm{}\pm 0.05)\times {10}^{13}$ ${\sec }^{-1\mathrm{}}$. Analysis of the quadrupole splitting, coupled with an analysis of the magnetic behavior by Lines, leads to a reassessment of the measurable effects of covalency upon the crystal-field, spin-orbit, and hyperfine interaction. The spin-orbit coupling parameter is estimated to be $\lambda =-85\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Using this value for the spin-orbit coupling parameter, the resulting crystal-field splitting of the ${}_{}{}^5{}_{}{}^{}T_2^{}{}_{}{}^{}$ orbital levels which describe the temperature dependence of the quadrupole splitting are ${\Delta }_1=780\mathrm{}\pm 40$ ${\mathrm{cm}}^{-1\mathrm{}}$ and ${\Delta }_2=930\mathrm{}\pm 70$ ${\mathrm{cm}}^{-1\mathrm{}}$. The ${〈r^{-3\mathrm{}}〉}_{\mathrm{eff}}=3.0\mathrm{}\pm 0.3{a_0}^{-3\mathrm{}}$ for the $d$ electrons and the contact contribution to the internal field at 4.2°K is $H_c=-518\mathrm{}\pm 25$ kOe.