Invar Effect of the Fe₁₃ Cluster

The Invar effect, which refers to magnetic alloys having an anomalously small thermal expansion, has been under extensive investigations over the past century. However, study on the thermal expansion of clusters and their Invar effect is still lacking. In this letter, we calculate the thermal expansion properties of Fe 13– n Ni n ( n = 0, 3, 6, 9, 12, 13) clusters and find that the Fe 13 cluster has an abnormally small thermal expansion, which is due to its remarkable magneto-volume effect. It is also revealed that the strong magneto-volume effect of the Fe 13 cluster is highly related with the two magnetic states, the same as the interpretation for the Invar effect of a bulk alloy. The anomalously small thermal expansion of the Fe 13 cluster is the manifestation of the Invar effect at the cluster scale.