Moir\'e magnetism in a bilayer Ising model

TL;DR

This paper investigates how moiré patterns in magnetic bilayers lead to spatially modulated interlayer interactions, resulting in diverse magnetic textures, without altering the fundamental phase transition characteristics.

Contribution

It introduces a minimal classical bilayer Ising model with moiré-modulated coupling and shows the transition remains in the 2D Ising universality class despite domain textures.

Findings

Transition remains in 2D Ising universality class

Smooth crossover between uniform and domain-textured states

No layer symmetry breaking in twisted bilayers

Abstract

Moir\'e patterns in magnetic bilayers generate spatially modulated interlayer exchange interactions that can give rise to nonuniform magnetic textures. We study a minimal classical bilayer Ising model with a moir\'e-modulated interlayer coupling, generated either by relative twist or differential strain between the layers. Using large-scale classical Monte Carlo simulations, we show that the ordering transition remains in the conventional two-dimensional Ising universality class, even when the low-temperature state is domain-textured. At low temperatures, we find a smooth crossover between a uniform ferromagnet and domain-textured state, in which the spins locally follow the sign of the interlayer exchange. We demonstrate that there is no breaking of layer symmetry for twisted bilayers. The location of the crossover is determined by a simple geometric energy balance between bulk interlayer exchange and intralayer domain-wall costs. Our results provide a minimal framework for understanding how moir\'e-modulated magnetic textures can emerge from geometric energetics without requiring a thermodynamic phase transition.