EN
The X-band EPR study of Gd^{3+}-doped LaF_3, La_{0.9}Ce_{0.1}F_3, La_{0.9}Nd_{0.1}F_ 3, LiYF_4 and LiY_{0.9}Yb_{0.1}F_4 single crystals in the temperature range 4.2-295 K was carried out in order to investigate the Gd^{3+} spin-phonon interactions. Spin-Hamiltonian parameters are analysed in the light of the superposition model and the rotational invariance theory for phonon-induced contributions to spin-Hamiltonian parameters. The 4f^7 electron-phonon interactions can be described by the Debye model. It is suggested, from the rotational invariance mechanism for phonon-induced contributions to spin-Hamiltonian parameters, that the rotational contributions are much smaller than those from the strain. Temperature-induced distortions of the crystal field, as well as these distortions caused by the La^{3+}/Nd^{3+} and Y^{3+}/Yb^{3+} substitutions, influence significantly the 4f^7 electron-phonon interactions. The coupling constant K_2 of 4f^7 electrons to the whole phonon spectrum of the crystal lattice is stronger in the LaF_3, La_{0.9}Ce_{0.1}F_3, La_{0.9}Nd_{0.1}F_3 with larger temperature-induced distortion of the Gd^{3+} site symmetry than in LiYF_4, LiY_{0.9}Yb_{0.1}F_4. Our results are compared with those for Gd^{3+}-doped RbCdF_3 and PbF_2 single crystals.