Higher-order Hall response arises from octupole order and scalar spin chirality in a noncollinear antiferromagnet

TL;DR

This work shows that a noncollinear antiferromagnet can host multiple, coexisting order parameters that shape Hall transport: an octupole-driven AHE and a low-field, scalar chirality–driven signal. By applying magnetic fields in selected in-plane directions and combining symmetry analysis with first-principles calculations and magnetotransport, the authors disentangle dipole, octupole, and chirality contributions in Mn3NiCuN. The key findings are a 120° in-plane angular dependence of the octupole-driven AHE and a THE-like component at low fields from noncoplanar spin textures, highlighting three distinct orders that coexist and dominate in different field regimes. This framework paves the way for identifying and controlling complex magnetic orders in NC-AFM for spintronic applications, expanding beyond conventional magnetization-based descriptions.

Abstract

Noncollinear antiferromagnets can generate a transverse electrical response known as the anomalous Hall effect, even though they possess almost no net magnetization. The microscopic origin of this behaviour, however, has remained unclear because conventional measurement geometries mix different contributions to the measured response. Here, we show that applying magnetic fields in selected in-plane directions allows us to disentangle the mechanisms underlying the Hall effect in a representative noncollinear antiferromagnet. By suppressing any dipole-related signal, we isolate a purely octupole-driven Hall response that exhibits a characteristic three-fold angular symmetry. At low magnetic fields, we further observe an additional Hall-like contribution that arises from the scalar spin chirality associated with noncoplanar spin textures. Combining symmetry analysis, first-principles calculations, and transport measurements, we reveal that octupole order, dipole moments, and chirality coexist and contribute in distinct field regimes. These findings establish a framework for identifying and controlling complex magnetic order parameters for spintronic applications.

Figures (2)

• Figure 1: Octupole structure and field-induced spin configurations in a noncollinear antiferromagnet. (a) Crystal structure showing Mn atoms (orange), Ni/Cu atoms (blue), and N atoms (off-white). Blue arrows denote the coplanar 120° spin arrangement in the (111) kagome plane. (b) Schematic representation of the eight symmetry-allowed octupole components, including the two out-of-plane projections labelled $\Upsilon_{0}$ and $\overline{\Upsilon}_{0}$, aligned with the [111] and $[\overline{1}\,\overline{1}\,\overline{1}]$ axes, respectively. (c) Spin configurations and corresponding octupole vectors when magnetic fields are applied along selected crystallographic directions within the (111) plane. Each labelled direction matches an in-plane projection of an octupole component. The central configuration illustrates the case of an out-of-plane field probing the dominant octupole component. (d) Calculated evolution of the octupole vector $\vec{Q}_{T_{1g}}$ in spherical coordinates as the in-plane magnetic field is rotated. The out-of-plane projection displays a 120$^\circ$ periodicity, which determines the expected angular dependence of the AHE.
• Figure 2: Angular evolution of octupole-driven and chirality-driven Hall responses. (a–c) Transverse Hall resistance measured as a function of magnetic field applied (a) out of the kagome plane and (b–c) within the plane at two representative in-plane field angles. Black symbols show experimental data; green curves are fits to the combined model in Equation (2), consisting of an octupole-driven term (red curves) and a scalar-chirality-driven term (blue curves). Small arrows indicate the direction of hysteresis loop shift. (d–f) Schematics of the magnetic-field directions corresponding to the measurements in (a–c). (g) Device geometry used for magnetotransport measurements, indicating crystallographic axes and the orientation of current and voltage lines. (h) Extracted amplitudes of the octupole-driven contribution $R^{\mathrm{Oct}}_{xy}$ (red) and the scalar-chirality contribution $R^{\mathrm{SSC}}_{xy}$ (black) as functions of in-plane angle. Both show an approximate 120° periodicity. Error bars represent the standard deviation of five repeated measurements. (i) Symmetry-based theoretical calculation of scalar spin chirality, displaying the same 120° periodicity but with an opposite sign compared to the octupole contribution.