Anomalous Hall Effect in Geometrically Frustrated Magnets

Geometrically frustrated conducting magnets display extraordinarily large anomalous Hall effects (AHEs) that could be used to realise materials required for the emerging field of spintronics. While the intrinsic Berry phase developed in collinear ferromagnets is well explained through the effects of spin-orbit interactions within the Karplus and Luttinger model, its origins in frustrated magnets are not. The directspace mechanism based on spin chirality that was originally applied to the pyrochlore Nd2Mo2O7 appears unsatisfactory. Recently, an orbital description based on the Aharonov-Bohm effect has been proposed and applied to both the ferromagnetic pyrochlores Nd2Mo2O7 and Pr2Ir2O7; the first of which features long-ranged magnetic order while the latter is a chiral spin liquid. Two further examples of geometrically frustrated conducting magnets are presented in this paper—the kagome-like Fe3Sn2 and the triangular PdCrO2. These possess very different electronic structures to the 3-dimensional heavy-metal pyrochlores and provide new opportunities to explore the different origins of the AHE. This paper summarises the experimental findings in these materials in an attempt to unite the conflicting theoretical arguments