Magnetic domains in 2D moir\'e lattices with square and hexagonal symmetry

TL;DR

This study demonstrates the persistence of magnetic domains in moiré patterns with square and hexagonal symmetries using ultracold atom simulations, revealing angle-dependent structures and stable magnetic states.

Contribution

It introduces a dynamical model showing magnetic domain stability in moiré lattices with different symmetries and identifies associated lattice parameters for specific twisting angles.

Findings

Magnetic domains persist for twist angles >10° in both lattice types.

Initial magnetic domains are preserved over time in the studied moiré patterns.

Lattice parameters for moiré crystals are identified within specific angle intervals.

Abstract

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.