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 Zr₄Pd₂O 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 Hc2. 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