EPR of ${\mathrm{Gd}}^{3+}$-doped single crystals of ${\mathrm{LiYF}}_4$ and ${\mathrm{LiYbF}}_4$: ${\mathrm{Gd}}^{3+}$-${\mathrm{Yb}}^{3+}$ exchange constant

X-band EPR measurements on ${\mathrm{Gd}}^{3+}$-doped single crystals of ${\mathrm{LiYF}}_4$ and ${\mathrm{LiYbF}}_4$ are performed at room and low temperatures. The spin-Hamiltonian parameters are estimated with the use of a rigorous least-squares-fitting computer technique. The behavior of the linewidths and the spin-Hamiltonian parameters, as a function of temperature, are studied. The total exchange interaction of ${\mathrm{Gd}}^{3+}$ with its nearest and next-nearest paramagnetic ${\mathrm{Yb}}^{3+}$ neighbors in the ${\mathrm{LiYbF}}_4$ host crystal is estimated with the use of the g-value shift of ${\mathrm{Gd}}^{3+}$ in the paramagnetic lattice of ${\mathrm{LiYbF}}_4$, from the interaction in the isostructural diamagnetic lattice of ${\mathrm{LiYF}}_4$.