Calculation of the paramagnetic host spin-lattice relaxation time from impurity-ion EPR linewidth

An expression, appropriate to calculate the spin-lattice relaxation time (SLRT) of the host paramagnetic ions, using the EPR linewidths of the impurity ion, is derived by use of the second moment for crystals consisting of two different kinds of spins. Estimations have been made of the SLRT of the ${\mathrm{Yb}}^{3+}$ ion in ${\mathrm{Gd}}^{3+}$-doped Yb${\mathrm{Cl}}_3$·6${\mathrm{H}}_2$O and LiYb${\mathrm{F}}_4$ single crystals, as well as that of the ${\mathrm{Co}}^{2+}$ ion in a ${\mathrm{Mn}}^{2+}$-doped ${\mathrm{Cs}}_2$Co${\left(\mathrm{S}\mathrm{e}{\mathrm{O}}_4\right)}_2$·6${\mathrm{H}}_2$O single crystal. Significant differences are found in the values of SLRT as calculated using the presently derived expression from those calculated using the commonly used expression.