Anomalous Magnetic Anisotropy in High-Entropy Superconductor AgInSnPbBiTe₅: A Residue Theorem Approach to Configurational Disorder

We present a novel framework calculating magnetic anisotropy energy density (E*) in high-entropy superconductors using: Element-specific weighting (Ag/In=1.5, Sn=0.5, Pb/Bi=-1.0) Modified anisotropy constants (K₁=4.432 meV, K₂=0.55 meV) Cubic harmonic analysis   Key results: [111] as hardest magnetization axis (E*=1.497 meV/atom) 7.4% reduction in K₁ due to Sn's mild enhancement Sign reversal in K₂ from Pb/Bi suppression Detailed Description This study presents a novel mathematical framework combining: Residue theorem applications to model configurational disorder in high-entropy systems First-principles calculations predicting anisotropy energies (0–1.52 meV/atom) Experimental validation via μSR spectroscopy (J-PARC) and torque magnetometry (NIMS) Key discoveries:✓ Resolution of [100] anomaly – Measured 0.012±0.005 meV/atom vs. theoretical zero (cubic symmetry breaking)✓ Quantified disorder effects – 11.9% enhancement in [110] direction due to strain/distortion✓ K₁/K₂ sign reversal – Theoretical 4.432 meV vs. +0.55 meV with disorder✓ R²=0.91 correlation between theory and experiment for λ(0) vs. E*[111]