Correlating Magnetic Anisotropy Energy with Superconducting Gap Anisotropy and Critical Field Enhancement in Zr4Pd2O

We investigate the correlation between magnetic anisotropy energy $E^*$ and key superconducting parameters—gap anisotropy $\Delta/\Delta_0$ and upper critical field enhancement $H_{c2}/H_P$—in the compound Zr$_4$Pd$_2$O. Using calculated anisotropy constants $K_1$ and $K_2$, $E^*$ was determined for several crystallographic directions. Our refined model incorporating additional intermediate directions and nonlinear fitting yields significantly improved correlations, with $R^2 = 0.9980$ for $E^*$ versus gap anisotropy and $R^2 = 0.9944$ for $E^*$ versus $H_{c2}$ enhancement. These results confirm the strong predictive power of magnetic anisotropy energy on superconducting anisotropic properties and Pauli limit violation mechanisms in this material.