Computational Frameworks for Patterned Two-Dimensional Magnetism

TL;DR

This paper reviews computational methods for understanding and designing patterned two-dimensional magnetic nanostructures, highlighting how geometry influences magnetic phases, textures, and stability for spintronic applications.

Contribution

It synthesizes theoretical and numerical frameworks for modeling patterned 2D magnetism, integrating classical spin models, stochastic dynamics, and multiscale approaches informed by first-principles calculations.

Findings

Geometry acts as an effective thermodynamic control parameter.

Computational models enable phase diagram construction and stability analysis.

Emerging directions include nonequilibrium modeling and data-centric workflows.

Abstract

Patterned two-dimensional (2D) magnetic nanostructures constitute geometry-engineered spin systems in which exchange, anisotropy, dipolar coupling, and finite-size effects operate on comparable energy scales. Spatial modulation of continuous magnetic films produces confinement-driven critical behavior, compensation phenomena, metastable switching pathways, and topologically non-trivial textures such as vortices and skyrmions. Computational modeling plays a central role in resolving this complexity, enabling quantitative construction of thermodynamic phase diagrams and analysis of geometry-dependent stability regimes. This review synthesizes theoretical and numerical frameworks for patterned 2D magnetism, including classical spin models, stochastic spin dynamics, rare-event methods, and multiscale parameterization informed by first-principles calculations. Representative systems-nanodot and antidot arrays, artificial spin-ice lattices, exchange-modulated heterostructures, and patterned van der Waals magnets- illustrate how geometry functions as an effective thermodynamic control parameter. Emerging directions in nonequilibrium modeling, multiphysics coupling, and scalable data-centric workflows are discussed in the context of predictive phase mapping. Patterned 2D magnetism thus exemplifies the convergence of geometry-controlled materials engineering and computational statistical physics, with phase stability and controlled spin textures at the core of next-generation spintronic architectures.