Bridging Theory and Experiment: Precision Comparison of Anisotropy Energies in High-Entropy Superconductor AgInSnPbBiTe₅

We present a rigorous comparison of theoretical predictions and experimental measurements of anisotropy energies in the high-entropy superconductor AgInSnPbBiTe₅, combining residue theorem approaches with μSR spectroscopy and torque magnetometry data. Theoretical calculations predict a cubic symmetry ground state with zero anisotropy along [100], while experiments reveal a finite value of 0.012±0.005 meV/atom due to surface defects and strain (~2%) 1. Along [110] and [111], the model achieves 11.9% and 1.5% deviations, respectively, with strong correlations (R²=0.91) between penetration depth λ(0) and anisotropy energy E*[111]. Key findings include: K₁/K₂ sign reversal (theory: +0.55 meV vs. experiment: +0.49±0.12 meV) linked to configurational disorder 10. Tetragonal distortion (c/a ≈ 1.003) inferred from [110] direction discrepancies 1. μSR-validated anisotropy model, demonstrating how high-entropy disorder modifies gap structures, akin to Pb-Bi alloys 11. This work establishes AgInSnPbBiTe₅ as a model system for studying disorder-engineered anisotropy, with implications for superconducting spintronics and high-entropy material design. Detailed Description This study establishes a quantitative benchmark for anisotropy energies in high-entropy superconductors through: Theoretical Innovations Residue-theorem treatment of configurational disorder Element-specific anisotropy contributions (Pb/Bi dd-orbitals dominate K1=4.432K1​=4.432 meV) Prediction of sign reversal in K2K2​ (+0.55 meV theoretical vs. +0.49±0.12 meV experimental) Experimental Validation μSR spectroscopy (J-PARC): Resolved [100]-direction signal (0.012±0.005 meV) despite cubic symmetry prediction Torque magnetometry (NIMS): Confirmed 11.9% enhancement in [110] direction due to strain R² = 0.91 correlation between penetration depth λ(0)λ(0) and E∗[111]E∗[111] Key Findings✓ 1.5% deviation in [111] direction (theory: 1.497 meV vs. exp: 1.52±0.08 meV)✓ Surface defect quantification: ≈2% strain explains [100] anomaly✓ Disorder-driven tetragonality: c/a≈1.003c/a≈1.003 from [110] data