Orbital moir and quadrupolar triple-q physics in a triangular lattice

Hattori, Kazumasa*; Ishitobi, Takayuki; Tsunetsugu, Hirokazu*

We numerically study orders of planer type quadrupoles on a triangular lattice with nearest-neighbor isotropic and anisotropic 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- 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- orders, we find various orders including incommensurate triple- quasi-long-range orders with orbital moire and a four-sublattice triple- partial order. Our Monte-Carlo simulations demonstrate that the phase transition to the latter triple- 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.