Significance Peculiar materials properties, such as Invar anomalies, including low thermal expansion and anomalous temperature dependence of modulus of elasticity, had substantial academic and technical impact. Today both invariant effects are associated with the interplay between temperature and magnetic order and thus they are considered to be specific to magnetically ordered alloys. In this work, an invariant phenomenon manifesting in temperature-independent stacking fault energy is discovered in magnetically disordered Ni–Fe alloys. Based on our understanding of the atomic-level mechanisms behind this Invar anomaly, a similar invariant phenomenon is identified in other systems including nonmagnetic alloys. These findings advance the design of high-temperature alloys with exceptional plastic stability.