Bonding Transition Mechanism in Invar Alloy Induced by Noncollinear Magnetic Disorder: DFT+<i>U</i> Insights

The Fe–Ni Invar alloy is extensively utilized in industry due to its nearly zero thermal expansion coefficient at room temperature. Concurrently, the origin of the Invar effect has been a subject of continuous investigation for over a century. There is currently increasing interest in the connection between noncollinear magnetism and the Invar effect, but the underlying physical mechanism remains unclear. In this work, systematic DFT+U calculations confirm that the spontaneous magnetostriction of Invar alloy can be well evaluated with a suitable Hubbard U correction. Constrained DFT combined with atomic spin dynamics is employed to verify the longitudinal spin attenuation behavior (i.e., the reduction of moment magnitude) induced by the magnetic disorder in the noncollinear magnetic structure model. These extraordinary phenomena related to the Invar effect can be attributed to the transition mechanism of atomic bonding characteristics, primarily manifested by the transformation of the localized antibonding states to the nonbonding states in the Fe atom pairs by crystal orbital Hamilton population analysis. Furthermore, the electronic structure calculations indicate that with the enhancement of noncollinear orientation disorder, there is electron transfer from antibonding states to nonbonding states near the Fermi level. The bonding transition mechanism provides a simple and effective pattern for understanding the Invar effect.