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We present magnetization measurements in single crystals of the tetragonal$YNi_2B_2C$ compound, which exhibit the phenomenon of peak effect as well asthe second magnetization peak anomaly for H $>$ 0.5T (H $||$ c). At the lowerfield (50mT $<$ H $<$ 200mT), we have observed the presence of flux jumps,which seem to relate to a structural change in the local symmetry of the fluxline lattice (a first order re-orientation transition across a local field insome parts of the sample, in the range of 100mT to 150mT). These flux jumps arealso observed in a single crystal of $LuNi_2B_2C$ for H $||$ c in the fieldregion from 2 mT to 25 mT, which are compatible with the occurrence of are-orientation transition at a lower field in a cleaner crystal of thiscompound, as compared to those of $YNi_2B_2C$. Vortex phase diagrams drawn forH $||$ c in $LuNi_2B_2C$ and $YNi_2B_2C$ show that the ordered elastic glassphase spans a larger part of (H, T) space in the former as compared to latter,thereby, reaffirming the difference in the relative purity of the two samples.

Flux jumps, Second Magnetization Peak anomaly and the Peak Effect phenomenon in single crystals of $YNi_2B_2C$ and $LuNi_2B_2C$