Orbital moir\'e and quadrupolar triple-q physics in a triangular lattice
Abstract
We numerically study orders of planer type (xy,x2-y2) quadrupoles on a triangular lattice with nearest-neighbor isotropic J and anisotropic K interactions. This type of quadrupoles possesses unique single-ion anisotropy proportional to a third order of the quadrupole moments. This provides an unconventional mechanism of triple-q orders which does not exist for the degrees of freedom with odd parity under time-reversal operation such as magnetic dipoles. In addition to several single-q orders, we find various orders including incommensurate triple-q quasi-long-range orders with orbital moir\'e and a four-sublattice triple-q partial order. Our Monte-Carlo simulations demonstrate that the phase transition to the latter triple-q state belongs to the universality class of the critical line of the Ashkin-Teller model in two dimensions close to the four-state Potts class. These results indicate a possibility of realizing unique quadrupole textures in simple triangular systems.
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