Spin-phonon and lattice contributions to the ground-state splitting of Gd$^{3+}$ and Eu$^{2+}$ in scheelite crystals

The EPR spectra of Gd$^{3+}$ in CaWO$_4$ single crystals have been studied at temperatures $T$ = 1.8, 4.2, and 114–300 K, and the temperature dependence of the parameters $b_n^m(T)$ of the spin Hamiltonian has been found. The behavior of $b_2^0(T)$ has been analyzed. The spin-phonon and static lattice contributions $b_2^0(F)$ and b $b_2^0(L)$ to $b_2^0(T)$ have been revealed. For this purpose, the variation of $b_2^0(L)$ has been calculated taking into account the thermal shifts of oxygen ions in CaWO$_4$. Similar analysis has been carried out for CaWO$_4$: Eu$^{2+}$ based on the EPR data of other authors (Bronstein, Voterra and Harvey, Kiefte). It has been shown that at $b_2^0(F)>$ 0, the variation of $b_2^0(F)$ as a function of $T$ for these impurity centers is described well by the Pfister model and a sign change of $b_2^0(T)$ for Eu$^{2+}$ is determined by thermal expansion of the lattice.