Origin of the magneto-volume effect in icosahedral Fe12X (X = Ti, Fe, Co, Ni) clusters

The magneto-volume effect in Fe-based clusters, as a microscopic manifestation of the Invar effect in Fe–Ni alloys, has recently attracted increasing attention. However, a deeper understanding of the physical mechanism underlying the magneto-volume effect remains lacking. Here we employed first-principles calculations to investigate the ground-state properties and thermal expansion behaviors of icosahedral Fe₁₂X (X = Ti, Fe, Co, Ni) clusters. The spin arrangement of Fe₁₂X clusters is determined by the magnetic exchange interaction between atomic pairs. During thermal expansion, Fe₁₂X clusters exhibit different volume and magnetic moment behaviors. The magnetic moment attenuation induced by thermal excitation is a prerequisite for the emergence of the magneto-volume effect in Fe₁₂X clusters, consistent with the Invar anomaly observed in Fe–Ni alloys. The bonding characteristic analysis reveals that there are two competing bonding transitions in the process of the moment attenuation. The strengthening of the bonding state of the surface Fe–Fe bonds significantly exceeds the weakening of the bonding state of the Fe–X bonds, resulting in a contraction of the cluster volume, which is considered to be the explanation of the magneto-volume effect at the electronic structure level. Understanding the origin of the magneto-volume effect in magnetic metal clusters not only deepens the insight into the Invar effect but also provides theoretical guidance for its practical application.