Magnetic Anisotropy Energy, Gap Anisotropy, and Enhanced Pauli Limits in Zr4Pd2O Superconductors

We investigate the magnetic anisotropy energy density, superconducting gap anisotropy, and Pauli paramagnetic limit enhancement in Zr$_4$Pd$_2$O superconductors through direction-dependent energy scale $E^*$. Using calculated anisotropy constants and crystallographic directions $[100]$, $[110]$, and $[111]$, we derive $E^*$ values, estimate spin-orbit coupling (SOC) strength, and predict directional upper critical fields $H_{c2}$. The results reveal significant anisotropy in gap magnitude and critical fields, highlighting the role of SOC in elevating the Pauli limit and influencing superconducting properties