EN
The investigation of Gd^{3+}-doped LaF_3, La_{0.9}Ce_{0.1}F_3, CeF_3, La_{0.9}Nd_{0.1}F_3, LiYF_4, and LiY_{0.9}Yb_{0.1}F_4 single crystals at 4.2 K was carried out in order to study the Gd^{3+}-RE^{3+} exchange interactions (RE = Ce, Nd, Yb). The exchange interactions were estimated by the application of the molecular-field model at liquid-helium temperature, using the g shift from the isostructural diamagnetic hosts LaF_3 and LiYF_4 to the paramagnetic hosts. The lattice dynamics is studied by analysing spin-Hamiltonian parameters in the light of the superposition model and the rotational invariance theory for phonon-induced contributions to spin-Hamiltonian parameters. It is suggested from the rotational invariance mechanism for phonon-induced contributions to spin-Hamiltonian parameters that the rotational contributions influence the exchange interactions significantly. Further, the distortions caused by the La^{3+}/Ce^{3+}, La^{3+}/Nd^{3+}, and Y^{3+}/Yb^{3+} substitutions affect significantly the 4f^7 electron-phonon interactions, as well as the exchange interactions. The magnitude of the isotropic exchange interactions is larger for more symmetrical charge distribution of the 4f^7 shell.