Unconventional Anomalous Hall Effect

• UAHE is a class of Hall responses that defies the conventional R₀H + RₛM scaling by exhibiting additional contributions from complex spin textures and Berry phases.
• It arises via mechanisms such as real-space chirality, domain-wall effects, nonlocal spin scattering, and quantum-geometric responses in diverse material systems.
• Experimental studies in systems like PdCrO₂, Pt/YIG, and compensated magnets demonstrate UAHE’s potential to reveal novel insights into electronic transport and symmetry-breaking.

Searching arXiv for recent and foundational papers on unconventional anomalous Hall effect. Unconventional anomalous Hall effect (UAHE) denotes Hall responses that cannot be reduced to the conventional decomposition into an ordinary Hall term and a magnetization-proportional anomalous term. In the canonical empirical form used for magnetic metals,

$$\rho_{xy}(H,T)=R_0(T)B+4\pi R_S(T)M(H,T), \qquad B=H+4\pi M,$$

where $R_0$ is the ordinary Hall coefficient and $R_S$ is the anomalous Hall coefficient. UAHE is identified when the measured $\rho_{xy}$ cannot be cast into this linear combination of $B$ and $M$, or when the Hall response appears in geometries, symmetry classes, or materials where conventional anomalous Hall phenomenology is inapplicable. In the literature represented here, the term spans several mechanisms: real-space Berry phases from noncoplanar spin textures, domain-wall chirality, nonlocal spin–orbit/magnetization separation, symmetry-allowed Hall responses in compensated magnets, and quantum-geometric Hall responses in nonmagnetic Dirac systems (Takatsu et al., 2010, Zhang et al., 2015, Xie et al., 21 Aug 2025).

1. Definitions, nomenclature, and phenomenology

The minimal distinction is between conventional AHE and UAHE. Conventional AHE is ordinarily written as a sum of an ordinary Hall contribution and a term proportional to magnetization, while UAHE denotes an additional Hall signal that does not scale as $R_0H$, $R_0B$, or $R_SM$. In several papers, the same extra contribution is also discussed under the label “topological Hall effect,” especially when it is associated with noncoplanar spin textures and scalar spin chirality. Other works use “unconventional” to emphasize a nonstandard geometry, such as anomalous Hall transport with magnetization parallel to the electric field, or a Hall effect in nonmagnetic materials where magnetization is absent altogether (Takatsu et al., 2010, Singh et al., 2024, Tan et al., 2021, Xie et al., 21 Aug 2025).

A widely used transport definition extracts UAHE as the residual after subtracting ordinary and conventional anomalous terms,

$\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$

or equivalent variants. The Hall conductivity is often obtained by tensor inversion; one expression used in the PdCrO$R_0$0 work is

$R_0$1

From a Berry-curvature viewpoint, one may also write

$R_0$2

which is the natural starting point for intrinsic momentum-space mechanisms (Takatsu et al., 2010).

The term “UAHE” therefore designates a family of noncanonical Hall responses rather than a single microscopic effect. This suggests that the most useful classification is mechanistic rather than terminological.

Class	Representative system	Reported source
Real-space chirality	PdCrO$R_0$3, Fe$R_0$4Ga$R_0$5	noncoplanar spin texture, scalar spin chirality
Domain-wall UAHE	EuZn$R_0$6Sb$R_0$7, Nd$R_0$8Ir$R_0$9O$R_S$0	scalar spin chirality within domain walls
Nonlocal/interface UAHE	Pt/YIG, Pt/(Co/Ni)$R_S$1	spin-dependent interfacial scattering plus bulk spin Hall conversion
Symmetry-unconventional AHE	FeCr$R_S$2Te$R_S$3, TaIrTe$R_S$4/Cr$R_S$5Ge$R_S$6Te$R_S$7	Berry curvature not constrained to be perpendicular to in-plane magnetization
Compensated or nonmagnetic UAHE	MnTe, ZrTe$R_S$8	compensated magnetic order or quantum-geometric response without spontaneous magnetization

2. Real-space Berry phases, scalar spin chirality, and emergent fields

The foundational real-space description of UAHE is based on scalar spin chirality,

$R_S$9

For three neighboring spins $\rho_{xy}$0, $\rho_{xy}$1 measures the solid angle subtended by the triad. When conduction electrons move through a noncoplanar spin background, they acquire a geometric phase; in the adiabatic picture this acts as a fictitious or emergent magnetic field and produces a Hall voltage even when the conventional $\rho_{xy}$2 term fails. This framework is explicit in PdCrO$\rho_{xy}$3, Fe$\rho_{xy}$4Ga$\rho_{xy}$5, NdRuO$\rho_{xy}$6, and HM/AFMI heterostructures, although the source of noncoplanarity differs across these systems (Takatsu et al., 2010, Meng et al., 10 Jul 2025, Liang et al., 2023).

A crucial point is that nonzero local chirality is not sufficient: the net chirality entering transport can cancel by symmetry. In a perfect coplanar $\rho_{xy}$7 triangular-lattice structure, each triangular plaquette may carry local chirality, but the $\rho_{xy}$8 pattern cancels the sum over the magnetic unit cell. This cancellation problem recurs in many frustrated magnets and motivates the search for perturbations that lift it, including field-induced canting, slow modulation of the spin plane, inequivalent layers, and domain walls (Takatsu et al., 2010).

The same logic extends beyond static bulk textures. In Fe$\rho_{xy}$9Ga$B$0 films, the reported UAHE is attributed to fluctuation-driven scalar spin chirality in a field-induced transverse-conical-spiral phase, rather than to static skyrmions. In Pt/NiO/MgO heterostructures, the Hall signal appears only in a thermally softened regime around the Néel transition, where atomistic spin dynamics indicates that interfacial Dzyaloshinskii–Moriya interaction, thermal fluctuation, and bias field stabilize a noncollinear AFM spin texture with non-zero net topological charge. These results place UAHE at the intersection of static order, mesoscopic texture, and thermally assisted topology (Meng et al., 10 Jul 2025, Liang et al., 2023).

3. PdCrO$B$1: the archetypal metallic triangular-lattice case

PdCrO$B$2 is a delafossite-type quasi-two-dimensional triangular-lattice antiferromagnet, space group $B$3, built from alternating Pd-triangle and Cr-triangle layers stacked along the $B$4 axis. Localized Cr$B$5 ($B$6) spins form a triangular lattice in each $B$7 plane and order in a $B$8 antiferromagnetic structure below $B$9 K, while conduction is carried mainly by Pd $M$0 electrons. High-quality single crystals grown by a PdCl$M$1 flux method were characterized by powder x-ray diffraction and energy-dispersive x-ray analysis, and the estimated mean-free path is $M$2, confirming sample cleanness (Takatsu et al., 2010).

The central observation is a second characteristic temperature $M$3 K, substantially below $M$4. Above $M$5, $M$6 is linear in $M$7 with negative slope, consistent with electron-like carriers. Between $M$8 and $M$9, the conventional AHE formula still holds with a changing $R_0H$0. Below $R_0H$1, however, $R_0H$2 deviates strongly from linearity, develops a pronounced hump, and can even change sign to positive in the field range $R_0H$3–$R_0H$4 kOe, whereas $R_0H$5 remains strictly linear in $R_0H$6. At $R_0H$7 K and $R_0H$8 K, the positive $R_0H$9 hump is superposed on a negative background; above $R_0B$0 kOe the conventional negative slope is recovered. No magnetic-hysteresis loops or magnetization plateaus are observed in $R_0B$1, ruling out domain-wall or metamagnetic-switching origins (Takatsu et al., 2010).

The importance of PdCrO$R_0B$2 lies not only in the anomaly itself but in the constraint imposed by the simplest $R_0B$3 structure. Because the ideal three-sublattice order cancels net chirality, UAHE requires additional symmetry breaking. The paper argues for three prerequisites: breaking of coplanarity in the exchange field seen by Pd electrons, breaking of $R_0B$4 periodicity by small low-temperature modulations of the $R_0B$5 structure, and field-induced spin canting out of the $R_0B$6 plane. A minimal illustrative model is a slow precession of the normal vector of each $R_0B$7 spin plane with a secondary wavevector $R_0B$8 and a small tilt angle of $R_0B$9. In zero field, the net chirality still vanishes because of layer-antiferromagnetic stacking, but in finite $R_SM$0 the two Cr layers polarize differently and produce an uncompensated chirality. PdCrO$R_SM$1 was accordingly identified as the first metallic 2D triangular-lattice antiferromagnet in which UAHE is clearly observed (Takatsu et al., 2010).

4. Domain walls, interfaces, and heterostructures

A major development after PdCrO$R_SM$2 is the recognition that UAHE can be concentrated at domain walls rather than in the bulk magnetic state. In EuZn$R_SM$3Sb$R_SM$4, which is described as a nominally collinear A-type antiferromagnet, the unconventional Hall resistivity rises from zero at $R_SM$5, peaks at $R_SM$6 T with $R_SM$7 at $R_SM$8 K, and falls to zero by $R_SM$9 T. The peak field tracks roughly $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$0, the same field scale at which the magnetoresistance shoulder appears. A minimal domain-wall model gives

$\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$1

so $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$2 at $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$3 and $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$4, and is strongest near the field where canted antiparallel spins form a mutual angle of $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$5. The unconventional Hall angle reaches $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$6 at $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$7 K, and $\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$8 (Singh et al., 2024).

Domain-wall AHE is also central in Nd$\rho_{xy} = R_0H + R_sM + \rho_{xy}^{U},$9Ir$R_0$00O$R_0$01 thin films. Bulk AIAO or AOAI order has cubic symmetry and vanishing Hall signal, but a $R_0$02 domain wall breaks the three orthogonal $R_0$03 rotations while preserving a single $R_0$04 axis, so finite $R_0$05 becomes symmetry-allowed. Experimentally, the domain-wall contribution peaks at $R_0$06, about twice the modeled bulk value, and follows the Ir coercive field. In TmB$R_0$07, by contrast, the Hall resistivity shows sharp kinks, humps, and hysteresis with no corresponding hysteresis in $R_0$08; the proposed explanation is again complex structures at magnetic domain walls, which may also account for hysteretic magnetoresistance (Kim et al., 2018, Sunku et al., 2016).

At interfaces, UAHE acquires additional meanings. In Pt/YIG, Zhang and Vignale proposed a “nonlocal anomalous Hall effect” in which spin–orbit coupling resides in the bulk heavy metal and magnetization resides in the insulating magnet; the effect is first order in spin–orbit coupling and its sign is predicted to follow the sign of the spin Hall angle (Zhang et al., 2015). In Pt/(Co/Ni)$R_0$09 multilayers, the AHE sign reverses for thin magnetic stacks because spin-current leakage into Pt and a large positive $R_0$10 overcome the negative contribution of $R_0$11 for $R_0$12; this was interpreted as nonlocal spin-conductivity mixing rather than magnetic proximity (Dang et al., 2019). In Pt/NiO/MgO, a large anomalous Hall resistivity up to $R_0$13 appears only around the Néel temperature, where noncollinear AFM textures with non-zero net topological charge are stabilized (Liang et al., 2023).

A recurrent controversy concerns hump/dip Hall features. In Mn$R_0$14Ga/Pt bilayers, low-temperature magnetic force microscopy showed that the field-dependent UAHE does not peak near the maximal density of magnetic bubbles, and identical bubble patterns in Mn$R_0$15Ga/Al do not produce the same Hall anomaly. The conclusion was that bump/dip Hall features can be generated without involving chiral spin structures, and that modified interfacial properties can mimic a topological Hall signal (Meng et al., 2019).

5. Symmetry-unconventional, compensated, and nonmagnetic forms

Another branch of the field uses “unconventional” to denote Hall geometries that are symmetry-forbidden in standard ferromagnets. The “parallel anomalous Hall effect” (PAHE) is defined as an anomalous Hall response in which magnetization, electric field, and Hall current remain in the same plane. Its existence requires that all point-group rotations and reflections that force the Berry-curvature vector to align with the magnetization be broken. In FeCr$R_0$16Te$R_0$17, for $R_0$18, first-principles calculations give a conventional component $R_0$19 and a PAHE component $R_0$20 at $R_0$21, with $R_0$22 reaching $R_0$23 under slight hole doping (Tan et al., 2021). Closely related physics was experimentally realized in TaIrTe$R_0$24/Cr$R_0$25Ge$R_0$26Te$R_0$27, where only one mirror symmetry remains; any finite $R_0$28 or $R_0$29 breaks that last mirror and allows

$R_0$30

The in-plane AHE is gate dependent and peaks near the charge-neutrality point (Kao et al., 11 May 2025).

Compensated magnets furnish a different route. In MnTe, a spontaneous anomalous Hall signal is observed at zero external field despite collinear antiparallel Mn ordering and vanishing net magnetization. The effect is tied to an unconventional compensated magnetic phase in which the anisotropic Te environment breaks the inversion or translation relations that would otherwise enforce Berry-curvature cancellation between opposite-spin sublattices. For the easy-axis configuration, the relativistic magnetic point group is $R_0$31, which allows a Hall pseudovector along $R_0$32. The resulting $R_0$33 is reported as $R_0$34–$R_0$35 S/cm between $R_0$36 K and $R_0$37 K (Betancourt et al., 2021).

Momentum-space topology can likewise generate UAHE above and below magnetic ordering temperatures. In hexagonal polar Y$R_0$38Co$R_0$39Sn$R_0$40, a low-field hump in $R_0$41 is present both below and above $R_0$42 K. Ab initio calculations locate four pairs of Weyl points, one pair type-I at $R_0$43 eV and three pairs type-II at $R_0$44–$R_0$45 eV relative to $R_0$46, and the measured anomalous Hall conductivity reaches $R_0$47 S/cm at $R_0$48 K and $R_0$49 S/cm at $R_0$50 K. The interpretation is that reciprocal-space topology dominates above $R_0$51, while below $R_0$52 planar ferrimagnetism further enhances the intrinsic AHE (Ahmed et al., 5 Feb 2025).

In nonmagnetic Dirac systems the language shifts again. In ZrTe$R_0$53, the unconventional Hall response is attributed to field-induced spin splitting, quantum metric, orbital magnetization, and Landau quantization rather than spontaneous magnetization. In the semiclassical regime the Hall resistivity remains linear in $R_0$54, but the Hall coefficient is renormalized by quantum-geometric effects and electron–hole coherence; in the quantum limit, $R_0$55, and $R_0$56 crosses over from $R_0$57 to $R_0$58 behavior (Xie et al., 21 Aug 2025). A related theoretical example is provided by topologically nontrivial MXenes $R_0$59, where tilting the proximity Zeeman field produces an unconventional enhancement of Berry curvature and anomalous Hall conductivity instead of the monotonic $R_0$60 suppression expected from conventional intuition (Habe, 10 Jan 2025).

6. Scaling anomalies, misconceptions, and open problems

Not all unconventionality in anomalous Hall transport is tied to spin texture or symmetry. In $R_0$61-type HgCr$R_0$62Se$R_0$63, the longitudinal, ordinary Hall, and anomalous Hall channels all exhibit $R_0$64-type corrections down to at least $R_0$65 mK. The longitudinal and ordinary Hall conductivities are consistent with Altshuler–Aronov electron–electron interaction theory, but the anomalous Hall conductivity shows much larger corrections: in sample #2, $R_0$66 at $R_0$67 K, and in more disordered samples the change reaches $R_0$68. The reported ratio $R_0$69 is $R_0$70–$R_0$71, far beyond the $R_0$72 typical of earlier ferromagnetic-metal or DMS thin-film studies. This was presented as evidence that existing theories of EEI and weak localization do not capture the anomalous Hall channel in this half-metallic semiconductor (Yang et al., 2019).

Disorder can also alter AHE scaling laws. In ultrathin FePt films in the dirty regime, weak and strong localization corrections lead to saturation of $R_0$73 as thickness decreases, while $R_0$74 continues to grow. The result is

$R_0$75

instead of the unified-theory dirty-regime exponent $R_0$76. The paper attributes this unconventional scaling to electron localization rather than Coulomb interaction (Lu et al., 2012).

Several recurrent misconceptions can therefore be addressed. First, a hump or dip in $R_0$77 is not an unambiguous skyrmion signature: Mn$R_0$78Ga/Pt explicitly shows no correlation between UAHE and magnetic-bubble density, and Fe$R_0$79Ga$R_0$80 reports that estimated topological Hall contributions from real-space skyrmions are orders of magnitude too small (Meng et al., 2019, Meng et al., 10 Jul 2025). Second, UAHE does not require net magnetization: PdCrO$R_0$81, EuZn$R_0$82Sb$R_0$83, Nd$R_0$84Ir$R_0$85O$R_0$86, and MnTe all demonstrate Hall responses in antiferromagnetic or compensated settings (Takatsu et al., 2010, Singh et al., 2024, Betancourt et al., 2021). Third, UAHE is not confined to low temperatures: Fe$R_0$87Ga$R_0$88 films show $R_0$89 at $R_0$90 K and $R_0$91 T, while Pt/NiO/MgO shows its signal only in a high-temperature window around the AFM transition (Meng et al., 10 Jul 2025, Liang et al., 2023).

The outstanding problems are correspondingly material specific. In PdCrO$R_0$92, precise determination of the low-temperature spin and lattice distortions by neutron or x-ray magnetic diffraction remains necessary. In Fe$R_0$93Ga$R_0$94, microscopic modeling of fluctuation-induced $R_0$95 is needed, and thinner films or different capping layers are proposed to test possible interfacial Dzyaloshinskii–Moriya contributions. In nonmagnetic Dirac materials such as ZrTe$R_0$96, the interplay of disorder, quantum geometry, and Landau quantization remains central. More generally, the surveyed literature suggests that “UAHE” is best understood as a transport umbrella for Hall responses generated by Berry phases in real space, momentum space, or nonlocal configuration space whenever the conventional $R_0$97 paradigm ceases to be sufficient (Takatsu et al., 2010, Meng et al., 10 Jul 2025, Xie et al., 21 Aug 2025).