Anomalous Hall antiferromagnets

Only in recent years has the Hall effect been predicted and observed in materials with antiferromagnetic order. This Review systematically organizes the current understanding of anomalous antiferromagnetic materials that generate a Hall effect, discussing these systems in the broad context of spintronics, topological condensed matter and multipole magnetism. The Hall effect, in which a current flows perpendicular to an electrical bias, has been prominent in the history of condensed matter physics. Appearing variously in classical, relativistic and quantum guises, the Hall effect has - among other roles - contributed to the establishment of the band theory of solids, to research on new phases of interacting electrons and to the phenomenology of topological condensed matter. The dissipationless Hall current requires time-reversal symmetry breaking. When this symmetry breaking is due to an externally applied magnetic field, the effect is referred to as the ordinary Hall effect; when it is due to a non-zero internal magnetization (ferromagnetism), it is referred to as the anomalous Hall effect. The Hall effect has not usually 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 goal of this Review is to systematically organize the present understanding of anomalous antiferromagnetic materials that generate a Hall effect - which we call anomalous Hall antiferromagnets - and to discuss this class of materials in a broader fundamental and applied research context. Our motivation is twofold: first, because 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 incarnation of the Hall effect has placed it again in the middle of an emerging field in physics, at the intersection of multipole magnetism, topological condensed matter and spintronics.