Effect of the lattice and spin-phonon contributions on the temperature behavior of the ground state splitting of Gd$^{3+}$ in SrMoO$_{4}$

The temperature behavior of the EPR spectra of the Gd$^{3+}$ impurity center in single crystals of SrMoO$_{4}$ in the temperature range $T$ = 99–375 K is studied. The analysis of the temperature dependences of the spin Hamiltonian $b_{2}^{0}(T)=b_{2}(F)+b_{2}(L)$ and $P_{2}^{0}(T)=P_{2}(F)+P_{2}(L)$ (for Gd$^{157}$) describing the EPR spectrum and contributing to the Gd$^{3+}$ ground state splitting $\Delta E$ is carried out. In terms of the Newman model, the values of $b_{2}(L)$ and $P_{2}(L)$ depending on the thermal expansion of the static lattice are estimated; the $b_{2}(F)$ and $P_{2}(F)$ spin-phonon contributions determined by the lattice ion oscillations are separated. The analysis of $b_{2}^{0}(T)$ and $P_{2}^{0}(T)$ is evidence of the positive contribution of the spin-phonon interaction; the model of the local oscillations of the impurity cluster with close frequencies $\omega$ describes well the temperature behavior of $b_{2}(F)$ and $P_{2}(F)$.