${\Gamma }_8^{\mathrm{}\left(3\right)\mathrm{}}$ resonance in ESR of $\left(\mathrm{Er}Y\right){\mathrm{Al}}_2$ single crystals

Angle-dependent ESR results are given for 500-, 2500-, and 5000-ppm Er-doped Y${\mathrm{Al}}_2$ single crystals. An almost perfect analysis of the $X$- and $Q$-band data is achieved if the admixture of the first excited state ${\Gamma }_8^{\mathrm{}\left(2\right)\mathrm{}}$ into the ground state ${\Gamma }_8^{\mathrm{}\left(3\right)\mathrm{}}$ via the Zeeman interaction is taken into consideration. This enables us to determine the crystal electric field (CEF) parameter $x=-0.322\mathrm{}\left(20\right)\mathrm{}$ and $W=-0.29\mathrm{}\left(2\right)\mathrm{}$ K. The $g$-value shift yields $N\left(E_F\right)J^{\Delta g}=+0.09\mathrm{}\left(5\right)\mathrm{}$ and the thermal broadening of the linewidth $\left|N\right(E_F\left)J^{\Delta H}\mathrm{}\right|=0.059\left(5\mathrm{}\right)\mathrm{}$. The precision of the experimental data allows, in principle, the determination of a hypothetical anisotropic exchange interaction. However, the fit yields an almost isotropic exchange interaction and upper limits for $\left|N\right(E_F\left)J_4\right|\lesssim 5\times {10}^{-5\mathrm{}}$ and $\left|N\right(E_F\left)J_6\right|\lesssim 6\times {10}^{-8\mathrm{}}$. This will be discussed in view of other results, i.e., $\mathrm{Dy}\mathrm{Pd}$. The effect of annealing of local defects on the CEF is discussed. In addition we observe and analyze for the first time the so-called cluster line in a ${\Gamma }_8$ resonance and for high Er concentration. Briefly, we will present similar results on $\left(\mathrm{Er}Sc\right){\mathrm{Al}}_2$ single crystals. In addition, we present a detailed theoretical calculation for impurity—conduction-electron and impurity-impurity relaxation for ${\Gamma }_8$ resonances.