We report the persistence of magnetic domains lying in moir\'e patterns with square and hexagonal symmetries. Our investigation is based on the dynamical description of two magnetic domains represented by a two species bosonic mixture of $^{ 87}$Rb ultracold atoms, being each specie initially localized in the left and right halves of a moir\'e lattice defined by a specific angle $\theta$. To demonstrate the persistence of such initial domains, we follow the time evolution of the superfluid spin texture, and in particular, the magnetization on each halve. The two-component superfluid, confined in the moir\'e pattern plus a harmonic trap, was described through the time dependent Gross-Pitaevskii coupled equations for moir\'e lattices having $90 \times 90$ sites. Results showed the existence of rotation-angle-dependent structures for which the initial magnetic domain is preserved for both, square and hexagonal moir\'e patterns; above $\theta >10^\circ$ the initial magnetic domain is never destroyed. Stationary magnetic states for a single component Bose condensate allowed us to identify the lattice parameter associated with moir\'e crystals that emerge for twisting angles belonging to the intervals $\theta \in \left(0^\circ ,30^\circ \right)$ and $\theta \in \left(0^\circ ,45^\circ \right)$ for hexagonal and square geometries respectively.
Categories: cond-mat.quant-gas quant-ph
