Microscopic Anisotropy Energy and Uniaxial Negative Thermal Expansion in Superconducting CoZr₃: A Combined Theoretical and Experimental Study

This investigation establishes a fundamental connection between microscopic anisotropy energy (E₁*) and macroscopic superconducting/thermal properties in orthorhombic CoZr₃ (Tc = 4.3 K). Through integrated first-principles calculations and synchrotron X-ray diffraction, we demonstrate: A quantitative anisotropy energy model (E₁* = 0.69) arising from low-dimensional Co-Zr bonding networks, validated by temperature-dependent lattice parameter measurements (90-800 K) Uniaxial negative thermal expansion (αc = -8.2 μK-1) originating from phonon mode softening along the c-axis, coexisting with superconductivity Composition-dependent scaling laws linking E₁* to critical current density (Jc ≈ 0.12 MA/cm2) and upper critical field (Bc2 = 2.9 T) These findings provide a design framework for thermal-expansion-tuned superconductors with applications in cryogenic engineering and quantum technologies.