Crystalline Electric Field Effect in Ho$_{1-x}$Dy$_{x}$Ni$_{2}$B$_{2}$C System.

We have measured magnetization curves of Ho$_{1-x}$Dy$_{x}$Ni$_{2}$B$_{2}$C (x $=$ 0.0, 0.1, 0.3, 0.6, 1.0) single crystals at various temperatures with the applied magnetic fields up to 20 kG where Neel and superconducting temperatures (T$_{N}$, T$_{C})$ ratio, T$_{N}$/T$_{C,\, }$varies from 0.73 to 1.66 for x$=$ 0.0 and 1.0. All measurements show some not linear behaviors in magnetization versus applied magnetic fields at low temperature regions. From the theoretical analysis of I4/mmm group symmetry in structure with the energy level pictures of CEF (crystalline electric field) effect of magnetization isotherms anisotropy at various temperatures, we have obtained ground state energy states in D$_{4h}$ singlet $\Gamma_{4}$ and first excited doublet state $\Gamma_{5}$ in addition to excited $\Gamma _{1.}$ Current CEF energy level analysis shows some qualitative agreement between theoretical calculation and experiments only at high magnetic fields regime, which means the interplay between magnetism and superconductivity may be considered.