In the ordinary Hall effect, it is the magnetic field that tells which way the electric currents driven by a voltage bias should be deflected, simply through the Lorentz force. In a ferromagnetic conductor, it is the direction of the magnetization that determines that of the transverse anomalous Hall current flow, despite the more complicated microscopic mechanisms. However, for antiferromagnets when the magnetization vanishes but the anomalous Hall effect does not, how can the electrons know which way they should be deflected? In this work we answered this question by introducing a new quantity named as electronic chiralization (EC), that is determined by the spatial gradients of the microscopic magnetization rather than its mean. EC transforms in exactly the same way as the anomalous Hall vector under all space group operations, including continuous translation, and is free from the difficulties of defining multipole moments of infinite systems. Moreover, EC provides intuitive guidance for the search of new unconventional magnetic systems hosting the AHE as it suggests what types of spin and charge textures are necessary for the AHE. To demonstrate this we provided two novel, experimentally relevant examples: charge-ordered kagome spin ice, and 2D Dirac electrons skew-scattered by a magnetic charge texture. The former may solve the puzzle of the experimentally observed AHE in certain frustrated spin systems that lack long-range magnetic dipole order, while the latter demonstrates another paradigm of noncollinear magnetic textures, magnetic charge or monopole, that can give rise to the AHE, in contrast to the well-known scalar spin chirality and skyrmions.
Electronic chiralization as an indicator of the anomalous Hall effect in unconventional magnetic systems
Hua Chen, Phys. Rev. B 106, 024421 (2022).
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