Small-angle neutron scattering study of the vortex lattice in PrOs$_4$Sb$_{12}$

We carried out a small angle neutron scattering study of the vortex lattice in the Pr based heavy Fermion superconductor PrSb$_4$Os$_{12}$ with H applied along the c-axis. With a critical temperature T$_c$ of 1.85 K and a H$_{c2}$ of 2.5T, PrOs$_4$Sb$_{12}$ is the first Pr based heavy fermion superconductor (SC). Although PrOs$_4$Sb$_{12}$ crystallizes in a filled Skutterudite structure with a cubic lattice, this structure has a tetrahedral point group symmetry. In consequence, with the application of a magnetic field along the $c$-direction, the $a$ and $b$-axis are no longer equivalent. Measurements of the angular dependence of the thermal conductivity in PrOs$_4$Sb$_{12}$ suggest a change of the superconducting order parameter deep inside the SC phase diagram from a two fold symmetry to a fourfold symmetry. Three ways of applying field were tested and wiggle field cooling was found to produce the highest intensity. We observed a twinned distorted hexagonal VL up to 1T of applied field which is consistent with $s$-wave superconductivity. We did not observe a field dependent phase transition associated with a change in symmetry of the VL. We found a rapidly decreasing form factor |F|$^2$ of the vortex lattice (VL) in PrOs$_4$Sb$_{12}$ with increasing field.