A simple electron-counting rule to determine the interlayer magnetic coupling of the van der Waals materials
Published 2020-03-22Version 1
In layered magnetic materials, the magnetic coupling between neighboring van der Waals layers is challenging to understand and anticipate, although the exchange interaction inside a layer can be well rationalized for example by the superexchange mechanism. In this work, we propose a simple electron-counting rule to determine the interlayer magnetic order between van der Waals layers. This method is based on counting the $d$-orbital occupation ($d^n$, where $n$ is the number of $d$-electrons at the magnetic cation), as a generalization of the Goodenough-Kanamori superexchange rules to the interlayer exchange coupling. With this rule, we classify magnetic monolayers into two groups, type-I ($n<5$) and type-II ($n\geq5$), and derive three types of interlayer magnetic coupling for both insulators and metals. The coupling between two type-II layers prefers the antiferromagnetic (AFM) way, that between the type-I and type-II favors the ferromagnetic (FM) way, while that between two type-I layers displays a competition among the FM and AFM orders. Additionally, the exchange coupling between metallic layers requires a minor correction by the itinerant carriers. This rule provides a simple guidance to design van der Waals junctions with the desired magnetic order.