Room-temperature third-order nonlinear anomalous Hall effect in ferromagnetic metal Fe3GaTe2

Abstract: Berry curvature, as the imaginary component of quantum geometry, plays a crucial role in condensed matter physics. The spatial distribution of Berry curvature can be characterized by its dipole and multipole moments, which can induce the nonlinear anomalous Hall effect (NLAHE). To date, the NLAHE has been demonstrated in various materials, yet reports on room-temperature NLAHE are still limited. In this work, we report the observation of the third-order NLAHE in ferromagnetic metal Fe3GaTe2. The third-order NLAHE shows hysteretic behavior with the variation of magnetic field, where the coercive field is the same as that of the anomalous Hall effect, and the third-order NLAHE remains observable up to the Curie temperature (~350 K). The scaling analysis suggests that the third-order NLAHE may be attributed to the Berry curvature quadrupole. Our work not only provides an approach to study magnetic materials through nonlinear electric transports, but also opens up possibilities for the future development of room-temperature third-order nonlinear electronic devices.

• The paper demonstrates the first room-temperature third-order nonlinear anomalous Hall effect in Fe3GaTe2 using Berry curvature quadrupoles.
• High-quality exfoliated flakes and multi-probe measurements reveal a cubic current scaling and robust hysteresis up to the Curie temperature of 350 K.
• Results confirm intrinsic quantum geometric effects dominate over extrinsic contributions, paving the way for advanced nonlinear nanoelectronic applications.

Observation of Room-Temperature Third-Order Nonlinear Anomalous Hall Effect in Fe₃GaTe₂

Introduction

The study establishes the first experimental realization of the third-order nonlinear anomalous Hall effect (NLAHE) at room temperature in a ferromagnetic van der Waals (vdW) metal, Fe₃GaTe₂. This effect, arising predominantly from an intrinsic Berry curvature quadrupole, is discerned via current-driven Hall voltage measurements, with negligible second-harmonic response. The research bridges a critical gap in Hall effect and Berry curvature multipole studies by demonstrating a robust higher-order topological transport in a system with high Curie temperature and strong perpendicular magnetic anisotropy.

Background and Theoretical Position

The interplay between Berry curvature and transport phenomena underpins the understanding of anomalous Hall effects in quantum materials. While the conventional anomalous Hall effect (AHE) derives from the net Berry curvature integrated over the Brillouin zone, the nonlinear Hall effect emerges under broken inversion symmetry or higher Berry curvature moments, allowing transverse voltage generation under time-reversal invariant or ferromagnetic systems.

Second-order NLAHEs, linked to the Berry curvature dipole and quantum metric dipole, are now well-established, including at room temperature in Weyl semimetals and van der Waals systems. Third-order NLAHEs, associated more deeply with Berry curvature quadrupoles or the Berry connection polarization tensor, have only recently been explored, with most experimental confirmations in nonmagnetic or antiferromagnetic systems. Realization in a ferromagnet above room temperature has been a significant open question.

Experimental Methodology

High-quality Fe₃GaTe₂ flakes were fabricated by exfoliation onto SiO₂/Si substrates, incorporating hexagonal BN capping layers to mitigate air-induced degradation. Multi-probe Au contacts enabled longitudinal and transverse resistance measurements. Transport experiments spanning 2 K to 360 K and magnetic fields up to 14 T were conducted with lock-in techniques, ensuring sensitivity to both linear and higher-harmonic Hall voltages.

Crystal structure analysis confirmed a P6₃/mmc symmetry, and transport data established a Curie temperature of 350 K, aligning Fe₃GaTe₂ as an ideal vdW ferromagnet for nonlinear Hall studies.

Key Results

• Third-Order Nonlinear Hall Response:

Fe₃GaTe₂ devices exhibited measurable third-harmonic Hall voltage at room temperature, with negligible second-harmonic signal. The cubic scaling between applied current and third-harmonic voltage is quantitatively confirmed, in line with higher-order NLAHE predictions and inconsistent with lower-order or extrinsic thermal effects.

• Field and Temperature Dependence:

The third-order NLAHE signal exhibited magnetic hysteresis synchronized with conventional AHE coercivity, and robust magnitude up to the Curie temperature. Unlike AHE, the third-order response displayed non-monotonic temperature dependence, showing characteristic transitions near 60 K and a pronounced maximum at 330 K before quenching near $T_c$.

• Dominant Berry Curvature Quadrupole Contribution:
  • The anomalous Hall resistivity is quadratic in longitudinal resistivity, confirming its dominant Berry curvature origin.
  • The third-order NLAHE scale is primarily determined by the Berry curvature quadrupole for $T < 330$ K, with extrinsic contributions (e.g., skew scattering) subdominant and further suppressed at higher temperatures.
  • Near $T_c$, a rapid suppression of the third-order signal is attributed to increased scattering, consistent with theoretical models.

Numerical outcomes explicitly support the dominance of intrinsic mechanisms:

At 300 K, the Berry curvature quadrupole contribution exceeds the extrinsic scattering term by over an order of magnitude.

Implications and Theoretical Significance

The detection of a robust, room-temperature third-order NLAHE rooted in Berry curvature quadrupoles marks a pivotal advance. It positions Fe₃GaTe₂ as an archetype for studying the interplay of magnetism, topology, and quantum geometry in nonlinear transport regimes. The identification of clear cubic current dependence, hysteretic magnetic response, and a clean temperature evolution excludes most extrinsic mechanisms, reinforcing the relevance of quantum geometric multipoles.

These results provide a pathway to probe phase transitions, intrinsic symmetry properties, and topological multipoles in itinerant ferromagnets, extending prior third-order NLAHE studies into functional temperature regimes relevant for devices.

Prospects for Applications and Further Research

The room-temperature persistence and simple device integration (vdW stacking, capping layer compatibility) suggest immediate potential for developing nonlinear nanoelectronic elements and high-sensitivity sensors leveraging third-order NLAHE. The cubic dependence on input current may be exploited for on-chip harmonic detection, frequency conversion, or logic in next-generation device architectures.

From a theoretical perspective, this work compels further quantitative modeling of Berry curvature quadrupoles in correlated metallic systems and motivates exploration of tunability via gating, alloying, dimensional reduction, or heterostructuring. Extending these methods to other high-$T_c$ vdW ferromagnets or heterointerfaces may reveal novel nonlinear transport phenomena with technological relevance.

Conclusion

The work establishes Fe₃GaTe₂ as the first room-temperature ferromagnet hosting a third-order NLAHE governed by Berry curvature quadrupoles. The combination of experiment and scaling analysis unambiguously attributes the observed phenomenon to intrinsic quantum geometric effects, with extrinsic contributions suppressed at elevated temperatures. This research both enriches the fundamental understanding of higher-order topological responses and lays the groundwork for future nonlinear electronic applications utilizing quantum geometry in ferromagnetic systems.

For further details, see "Room-temperature third-order nonlinear anomalous Hall effect in ferromagnetic metal Fe3GaTe2" (2604.21285).