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Ferromagnets generate an anomalous Hall effect even without the presence of amagnetic field, something that conventional antiferromagnets cannot replicatebut noncollinear antiferromagnets can. The anomalous Hall effect governed bythe resistivity tensor plays a crucial role in determining the presence of timereversal symmetry and the topology present in the system. In this work wereveal the complex origin of the anomalous Hall effect arising in noncollinearantiferromagnets by performing Hall measurements with fields applied inselected directions in space with respect to the crystalline axes. Our coplanarmagnetic field geometry goes beyond the conventional perpendicular fieldgeometry used for ferromagnets and allows us to suppress any magnetic dipolecontribution. It allows us to map the in-plane anomalous Hall contribution andwe demonstrate a 120$^\circ$ symmetry which we find to be governed by theoctupole moment at high fields. At low fields we subsequently discover asurprising topological Hall-like signature and, from a combination oftheoretical techniques, we show that the spins can be recast into dipole,emergent octupole and noncoplanar effective magnetic moments. These co-existingorders enable magnetization dynamics unachievable in either ferromagnetic orconventional collinear antiferromagnetic materials.

Revealing the higher-order spin nature of the Hall effect in non-collinear antiferromagnet $\mathrm{Mn_3Ni_{0.35}Cu_{0.65}N}$