  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.
