Anomalous Hall antiferromagnets (2107.03321v1)

Abstract: The Hall effect, in which current flows perpendicular to an applied electrical bias, has played a prominent role in modern condensed matter physics over much of the subject's history. Appearing variously in classical, relativistic and quantum guises, it has among other roles contributed to establishing the band theory of solids, to research on new phases of strongly interacting electrons, and to the phenomenology of topological condensed matter. The dissipationless Hall current requires time-reversal symmetry breaking. For over a century it has either been ascribed to externally applied magnetic field and referred to as the ordinary Hall effect, or ascribed to spontaneous non-zero total internal magnetization (ferromagnetism) and referred to as the anomalous Hall effect. It has not commonly been associated with antiferromagnetic order. More recently, however, theoretical predictions and experimental observations have identified large Hall effects in some compensated magnetic crystals, governed by neither of the global magnetic-dipole symmetry breaking mechanisms mentioned above. The goals of this article are to systematically organize the present understanding of anomalous antiferromagnetic materials that generate a non-zero Hall effect, which we will call anomalous Hall antiferromagnets, and to discuss this class of materials in a broader fundamental and applied research context. Our motivation in drawing attention to anomalous Hall antiferromagnets is two-fold. First, since Hall effects that are not governed by magnetic dipole symmetry breaking are at odds with the traditional understanding of the phenomenon, the topic deserves attention on its own. Second, this new reincarnation has again placed the Hall effect in the middle of an emerging field of physics at the intersection of multipole magnetism, topological condensed matter, and spintronics.

Anomalous Hall Antiferromagnets: A Comprehensive Overview

The paper entitled "Anomalous Hall Antiferromagnets" explores the intricate phenomenon of the Hall effect, focusing particularly on its manifestations in antiferromagnetic materials. Historically, the Hall effect—a key phenomenon in condensed matter physics—has been associated predominantly with ferromagnetic systems. The prevailing understanding was that the Hall effect necessitates time-reversal symmetry breaking, typically attributed to either an external magnetic field or internal magnetization as found in ferromagnets. However, this paper challenges this traditional view by investigating the emergence of a Hall effect in antiferromagnets, where total magnetization is ostensibly zero.

Key Concepts and Findings

The paper systematically organizes the current understanding of anomalous Hall effects in antiferromagnetic materials, referred to as "anomalous Hall antiferromagnets." This phenomenon is remarkable because it persists even without the conventional mechanisms of global magnetic dipole symmetry breaking. Notably, the recent theoretical predictions and experimental discoveries of large Hall effects in certain classes of these antiferromagnets underscore the limitations of the traditional models and call for a reevaluation of the Hall effect's underlying principles.

The authors explore the symmetry aspects that permit the existence of a Hall current in antiferromagnets, emphasizing the critical role of crystal and magnetic symmetries. They introduce the concept of the N\'eel vector, which describes the arrangement of magnetic moments in antiferromagnetic materials. The interplay between this vector and spin-orbit coupling emerges as pivotal in facilitating a non-zero Hall effect despite the absence of net magnetization.

Numerous examples of such phenomena in specific antiferromagnetic compounds are investigated, demonstrating significant Berry curvature contributions, a concept borrowed from quantum Hall physics. The paper meticulously discusses how the Berry curvature relates to the anomalous Hall conductivity in these systems, unveiling the potential robustness of this mechanism compared to its ferromagnetic analogs.

Numerical Results and Speculations

Key numerical results illustrate the scale of anomalous Hall effects achievable in these materials, comparable to those in ferromagnets. For instance, in non-collinear antiferromagnets like Mn₃Sn and Mn₃Ge, the presence of a nontrivial Berry curvature arising from their Weyl semimetallic characteristics is highlighted. This results in a substantial anomalous Hall conductivity even at room temperature, indicating promising applications.

From a theoretical perspective, the paper signifies a paradigm shift in understanding quantum phases and transport phenomena in magnetic systems. It highlights the potential for zero-field quantum Hall effects at high temperatures if such systems could be realized as insulators or semimetals with appropriate band filling and symmetry protection.

Implications and Future Directions

The implications of this research are far-reaching, impacting both fundamental theory and potential applications in spintronics—particularly in designing novel devices that leverage the low-damping and high-speed characteristics of antiferromagnetic materials alongside the sizable Hall effects. This could lead to cutting-edge developments in high-density data storage and processing technologies. Additionally, the findings inspire further exploration of the potential for novel quantum phases and topological materials with exotic transport properties.

Future research directions may involve detailed exploration of these effects in other antiferromagnetic compounds, theoretical models that adequately capture the phenomenology of anomalous Hall effects without net magnetization, and experimental approaches to engineer materials with enhanced or tunable properties for practical applications. This work significantly broadens the horizon for spin-based electronics and the paper of quantum materials, suggesting a rich vein of scientific inquiry into the complex landscape of antiferromagnetic spintronics.