Field and Temperature Dependence of the Superconducting Anisotropy in Sr$_2$RuO$_4$

The superconductor Sr$_2$RuO$_4$ (SRO) has been well-studied for triplet pairing of electrons and an odd, p-wave order parameter symmetry. However, because of its complexity, questions remain about the superconducting state. To study this we measured the superconducting anisotropy ($\Gamma_{ac}$). Direct imaging of the vortex lattice (VL) anisotropy in SRO is possible with small-angle neutron scattering (SANS), with $H$ applied close to the basal plane. The VL anisotropy reflects the intrinsic anisotropy of $\Gamma_{ac}$, and may differ significantly from the $H_{c2}$ anisotropy ($\Gamma_{H_{c2}}$) as recently seen for intermediate fields [C. Rastovski $et$ $al.$, Phys. Rev. Lett. {\bf 111}, 087003 (2013)]. For $H \rightarrow H_{c2}$, the VL anisotropy is found to exceed earlier results at intermediate fields. Our data, combined with new low field measurements, indicate a field dependent superconducting anisotropy in SRO, increasing as $H$ approaches $H_{c2}$. This suggests a varying contribution of the different Fermi Surface bands on the $\Gamma_{ac}$. In contrast, the VL anisotropy is found to remain constant as the temperature is increased toward $T_{c2}$, while the $\Gamma_{H_{c2}}$ increases with increasing temperature.