Unconventional Superconductivity in η-Carbide-Type Zr₄Pd₂O: Role of Spin-Orbit Coupling and Magnetic Anisotropy

We present a theoretical analysis of the superconducting properties of η-carbide-type Zr₄Pd₂O, focusing on its anomalous upper critical field (H_c2) that violates the Pauli limit. Through calculations of magnetic anisotropic energy density (E) and critical field parameter (B₅₀), we demonstrate how strong spin-orbit coupling (SOC) from Pd-4d electrons leads to unconventional superconductivity. The positive E (11.657 kJ/m³) indicates significant energy costs to maintain superconductivity against SOC effects, while the negative B₅₀ (-1.256) suggests non-BCS behavior. These results explain the material's enhanced H_c2(0) = 6.72 T beyond the Pauli limit (5.29 T).