First-Principles Approaches to Magnetoelectric Multiferroics

Magnetoelectric multiferroics, which display both ferroelectric and magnetic orders, are appealing because of their rich fundamental physics and promising technological applications. The revival of multiferroics since 2003 led to a comprehensive understanding of the mechanisms that facilitate the coexistence of electric and magnetic orders and conceptually new design strategies for device architectures, which brought us an important step closer to multiferroic-based technology. In the past thirty years, first-principles calculations based on the laws of quantum mechanics played a crucial role in understanding the electronic, magnetic, and structural properties of multiferroics and guided the design of new multiferroics with improved properties. In this review, we provide a comprehensive overview of first-principles approaches to magnetoelectric multiferroics, especially in low-dimensional forms. In particular, we discuss methods to build an effective Hamiltonian from first principles for magnets, ferroelectrics, and multiferroics. The recently developed machine learning potential approach for multiferroics is also outlined. Furthermore, we present the unified model for spin-induced ferroelectricity and methods for computing the linear magnetoelectric coupling tensor. Finally, recent progress in multiferroic systems and the applications of first-principles approaches to these systems are reviewed.Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 15 is March 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.