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

Abstract

This investigation establishes a fundamental connection between microscopic anisotropy energy (E₁*) and macroscopic superconducting/thermal properties in orthorhombic CoZr₃ (T_c = 4.3 K). Through integrated first-principles calculations and synchrotron X-ray diffraction, we demonstrate:

1. 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)

2. Uniaxial negative thermal expansion (α_c = -8.2 μK^-1) originating from phonon mode softening along the c-axis, coexisting with superconductivity

3. Composition-dependent scaling laws linking E₁* to critical current density (J_c ≈ 0.12 MA/cm²) and upper critical field (B_c2 = 2.9 T)

These findings provide a design framework for thermal-expansion-tuned superconductors with applications in cryogenic engineering and quantum technologies.