Paradoxical coexistence of superconductivity and magnetism, and explaining unexpected preferred domain orientations

Abstract The classical Ginzburg–Landau model has long provided the foundation for modeling superconductivity, yet it does not fully capture the rich diversity of unconventional superconducting phenomena observed experimentally. Examples include magnetic superconductors, re-entrant superconductivity, and the cuprates—materials whose behaviors are not adequately explained by traditional Ginzburg–Landau and/or BCS theories. In this work, we develop a thermodynamically consistent reformulation of th