Superconducting and Pauli Paramagnetic Anisotropies in TmNi$_2$B$_2$C

A direct measure of the intrinsic superconducting anisotropy ($\Gamma_{ac}$) is difficult to obtain in materials where multiple bands contribute to the superconductivity or where $H_{c2}$ is orbitally limited for one field direction and Pauli limited along another. We report on small-angle neutron scattering studies of the vortex lattice (VL) in TmNi$_2$B$_2$C with fields applied along the basal plane. This material orders antiferromagentically and the magnetic and superconducting states are known to strongly influence each other, even in the paramagnetic phase above $T_N$. Our measurements allowed an independent determination of $\Gamma_{ac}$ (through the VL anisotropy), and the magnetic-superconducting interaction anisotropy reflected in the Pauli paramagnetic effect (spin-polarization of unpaired quasiparticles in the vortex cores) on the VL scattered intensity (form factor).