Phase diagram of magnetic shape memory alloy Ni50Mn 50 − x In x , 0 < x < 25 from first principles, via spin cluster expansion and phonon vibrational entropies

The metamagnetic shape memory Heusler alloy Ni 50 Mn 50 − x In x exhibits a rich phase diagram featuring competing magnetic states, coupled magnetic–structural phase transitions, and strong compositional sensitivity. Existing first-principles approaches struggle to capture the intertwined chemical, magnetic, and vibrational effects in these alloys, necessitating a more integrated modeling framework. We develop a spin cluster expansion (spin-CE) framework augmented by a quasi-harmonic phonon model to capture both configurational (chemical and magnetic) and vibrational contributions to the free energy of Ni 50 Mn 50 − x In x over the full compositional range 0 ≤ x ≤ 25 . The spin-CE includes both chemical clusters and composition-dependent Ising spin interactions, with parameters fit to a first-principles density functional theory (DFT) dataset. Using this approach, we predict the complete magnetostructural phase diagram and transformation temperatures of Ni 50 Mn 50 − x In x across the composition space. We find that vibrational entropy alone is insufficient to reproduce the martensitic transformation in the magnetic shape memory alloy regime, highlighting the essential role of magnetism. Incorporating both magnetic and vibrational contributions allows us to reproduce all experimentally known phases, including the disappearance of the stable martensite phase at a critical In concentration and the Curie temperature of the austenite phase. The method also captures the transition with increasing In in martensite from antiferromagnetic to ferromagnetic order and predicts re-entrant ferromagnetism, though the latter occurs at higher In content than reported experimentally. We discuss possible sources of this discrepancy and highlight the broader applicability of the method to other magnetostructurally complex materials, where it may offer mechanistic insight and predictive design capabilities.