Search

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 "hidden orders" since they are insensitive to common experimental probes. Theoretically, it is also difficult to predict multipolar orders via 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 metastable magnetic octupolar states in monolayer α-RuCl_{3}, which is confirmed by self-consistent unrestricted Hartree-Fock calculations. We then demonstrate that these octupolar states can be stabilized in monolayer α-RuI_{3}, one of which becomes the octupolar ground state. Furthermore, we also predict a fingerprint of an orthogonal magnetization pattern produced by the octupole moment that can be easily detected by experiment. The method and the example presented in this Letter serve as a guide for searching multipolar order parameters in other correlated materials.

With angle-resolved photoemission spectroscopy, gap opening is resolved at up to room temperature in the Dirac surface states of molecular beam epitaxy grown Cr-doped Bi2Se3 topological insulator films, which, however, show no long-range ferromagnetic order down to 1.5 K. The gap size is found decreasing with increasing electron-doping level. Scanning tunneling microscopy and first-principles calculations demonstrate that substitutional Cr atoms aggregate into superparamagnetic multimers in the Bi2Se3 matrix, which contribute to the observed chemical-potential-dependent gap opening in the Dirac surface states without long-range ferromagnetic order.