Anisotropy in spatial order-disorder transformations and the vortex lattice symmetry transition in $YNi_2B_2C$ and $LuNi_2B_2C$

Explorations of the order-disorder transformation in vortex matter in single crystals of tetragonal structured (c/a $\sim$3) borocarbide superconductors, $YNi_2B_2C$ and $LuNi_2B_2C$, reveal that vortex arrays experience different effective pinning in different crystallographic directions. We surmise that correlation exists between the large anisotropy in effective pinning/disorder and the differences in the (local) symmetry transition from rhombohedral to (quasi) square vortex lattice(VL). For field along high symmetry directions, like, c-axis and ab-basal plane, the VL symmetry is close to square and the ordered state spans a large field interval. When the field is turned away from the c-axis towards ab-plane, at intermediate angles, the region of ordered state shrinks, in response to enhancement in effective pinning. At such intermediate angles the symmetry of the VL would be far from ideal triangular or square.