Efficient Method for Prediction of Meta-stable/Ground Multipolar Ordered States and its Application in Monolayer $\alpha$-\ce{RuX3} (X=Cl,I)

Exotic high-rank multipolar order parameters have been found to be unexpectedly active in more and more correlated materials in recent years. Such multipoles are usually dubbed as "Hidden Orders" since they are insensitive to common experimental probes. Theoretically, it is also difficult to predict multipolar orders via \textit{ab initio} calculations in real materials. Here, we present an efficient method to predict possible multipoles in materials based on linear response theory under random phase approximation. Using this method, we successfully predict two pure meta-stable magnetic octupolar states in monolayer $\alpha$-\ce{RuCl3}, which is confirmed by self-consistent unrestricted Hartree-Fock calculations. We then demonstrate that these octupolar states can be stabilized in monolayer $\alpha$-\ce{RuI3}, one of which becomes the octupolar ground state. Furthermore, we also predict a fingerprint of orthogonal magnetization pattern produced by the octupole moment, which can be easily detected by experiment. The method and the example presented in this work serve as a guidance for searching multipolar order parameters in other correlated materials.
Comment: 15 pages,8 figures