Relaxation of the environment of Gd$^{3+}$ and Eu$^{2+}$ impurity ions in the Y$_{3}$Al$_{5}$O$_{12}$ garnet

The second-rank spin Hamiltonian parameters of Gd$^{3+}$ and Eu$^{2+}$ orthorhombic centers in crystals of the yttrium aluminum garnet Y$_{3}$Al$_{5}$O$_{12}$ have been analyzed within the framework of the superposition model for the zero-field splitting of the ground state. It has been shown that the description of the experimental data in this model is possible only under the assumption of relaxation of the ligand environment of the paramagnetic impurity.