---
title: Anomalous Nernst Effect (ANE) in Magnetic Materials
url: https://www.emergentmind.com/topics/anomalous-nernst-effect-ane
type: topic
---

# Anomalous Nernst Effect (ANE) in Magnetic Materials

The anomalous Nernst effect (ANE) is a transverse thermoelectric phenomenon observed in magnetic materials, in which the application of a temperature gradient (∇T) generates an electromotive force perpendicular to both the magnetization (M) and the gradient. While traditionally associated with ferromagnets, recent research has established the ANE as a generic probe of Berry curvature at the Fermi level, with large signals observed in noncollinear antiferromagnets, compensated ferrimagnets, magnetic Weyl semimetals, and even collinear altermagnets. The ANE is of central importance in spin caloritronics, energy harvesting, ultrafast spintronics, and nanoscale magnetic imaging due to its compatibility with planar device architectures, its sensitivity to band-topological features, and its ability to operate without external magnetic fields.

## 1. Theoretical Foundation and Formalism

The ANE is described phenomenologically by the relation
$$
\mathbf{E}_{\rm ANE} = S_{\rm ANE} (\nabla T \times \mathbf{M})
$$
where $\mathbf{E}_{\rm ANE}$ is the induced electric field, $S_{\rm ANE}$ the anomalous Nernst coefficient, $\nabla T$ the applied thermal gradient, and $\mathbf{M}$ the (local) magnetization. In tensor notation, the effect is encoded in the off-diagonal thermoelectric tensor components $\alpha_{xy}$, yielding a transverse current density under $\nabla_xT$ as $j_y = -\alpha_{yx} \nabla_xT$.

The microscopic mechanism, for the intrinsic contribution, is rooted in the Berry curvature $\Omega_n(\mathbf{k})$ of electronic bands,
$$
\alpha_{xy} = -\frac{1}{T} \sum_n \int_{\text{BZ}} \frac{d^3k}{(2\pi)^3} \Omega_n^z(\mathbf{k}) s\big(\varepsilon_n(\mathbf{k})\big)
$$
where $s(\varepsilon)$ is the entropy density per state and $n$ indexes bands. At low temperature, the Mott relation links the transverse thermoelectric to the energy derivative of the anomalous Hall conductivity:
$$
\alpha_{xy} \simeq -\frac{\pi^2 k_B^2 T}{3e} \left.\frac{\partial \sigma_{xy}}{\partial E}\right|_{E = E_F}
$$
This formalism undergirds the vast majority of recent quantitative theory and simulation of ANE in both topological and conventional magnetic materials [2109.09382, 1710.00062, 1811.03485, 1908.11183].

## 2. Material Classes and Symmetry Considerations

The ANE requires both time-reversal symmetry breaking and significant spin–orbit coupling (SOC), but does not necessarily require net magnetization. Material systems exhibiting large or tunable ANE include:

- **Ferromagnets and Ferrimagnets:** The conventional context, but recent work shows the ANE magnitude can far exceed predictions based on $S_{\rm ANE}\sim M$ scaling if Berry curvature is sharply peaked at the Fermi level (e.g., magnetic Weyl semimetals Co$_3$Sn$_2$S$_2$ [1811.03485], UCo$_{0.8}$Ru$_{0.2}$Al [2104.09060], Co$_2$MnAl$_{1-x}$Si$_x$ Heuslers [1807.02209]).
- **Noncollinear Antiferromagnets:** In Mn$_3$Sn [1710.00062] and Mn$_3$NiN [1908.11183], a chiral triangular spin structure enables a large zero-field ANE, circumventing the vanishing Berry curvature of conventional collinear compensated AFMs.
- **Canted and Collinear Antiferromagnets:** Canted structures (YbMnBi$_2$ [2109.09382]) or altermagnets (Mn$_5$Si$_3$ [2403.13427]) can support an ANE via symmetry-allowed Berry curvature even with vanishing net magnetization.
- **Compensated Ferrimagnets and Amorphous Alloys:** As demonstrated in Co$_x$Gd$_{1-x}$ [2211.15074], TbCo [2401.04445], and GdFe [2107.05215], a substantial ANE persists even at magnetic compensation; the sign is controlled by the dominant transition-metal sublattice and its associated Berry curvature.

A critical insight is the pivotal role of symmetry: noncollinear spin arrangements or altermagnetic band structures may induce finite Berry curvature and hence ANE even in the absence of macroscopic M [2403.13427, 1710.00062].

## 3. Microscopic Origins: Berry Curvature and Extrinsic Mechanisms

While the intrinsic ANE is dominated by Berry curvature at or near the Fermi surface, extrinsic mechanisms such as skew scattering and side-jump also contribute, especially in classic 3$d$ perovskite ferromagnets La$_{1-x}$Na$_x$MnO$_3$ [1811.02432]. The magnitude, sign, and temperature dependence of the ANE can thus be tailored via electronic structure engineering:

- **Weyl Nodes, Nodal Lines, and Flat Bands:** Materials with Fermi-energy–proximate Weyl points or topological nodal lines (e.g., Co$_3$Sn$_2$S$_2$, Mn$_3$NiN, Fe$_3$Ga) generate sharp Berry curvature hot spots, greatly enhancing the ANE [1811.03485, 1908.11183, 2303.12886].
- **Band Engineering:** Doping, strain, and alloying shift the Fermi level with respect to Berry curvature features, enabling sign and magnitude control of $\alpha_{xy}$ (e.g., Fe$_3$Ga under strain and doping, Mn$_5$Si$_3$ via Mn content) [2303.12886, 2403.13427].
- **Interfaces and Multilayers:** In Ni/Pt and Pt/Fe multilayers, interfacial electronic structure modification can boost $\alpha_{xy}$ and the ANE far above bulk values, independent of proximity magnetism [2009.11006, 1505.07183].

## 4. Experimental Observation and Quantification

Experimental quantification of ANE requires precise control and measurement of temperature gradients and detection of transverse voltages:

| Methodology                | Key Features                                                              | Representative Systems                |
|----------------------------|---------------------------------------------------------------------------|---------------------------------------|
| Heater-based gradients     | Steady-state, macroscale $\nabla T$; broad applicability                  | Co, Ni/Pt, Heuslers                   |
| Laser/AFM-induced gradients| Localized, intense, fast-modulated $\nabla T$; micro/nanoscale, time-resolved| Co thin films, near-field imaging      |
| Strain tuning              | Control of magnetic phase and Berry curvature via epitaxy or piezoactuators| Mn$_3$SnN, Fe$_3$Ga, Mn$_3$NiN         |
| Terahertz emission         | Ultrafast detection of ANE-driven currents (sub-ps) via THz radiation     | Fe, Co films [2302.11134]             |

Finite-element modeling is essential for extracting accurate $S_{\rm ANE}$ values under inhomogeneous or nanoscale temperature profiles [2501.17045, 2407.13028]. ANE-based imaging achieves sub-100 nm spatial resolution using near-field laser excitation [2407.13028].

## 5. Quantitative Trends and Optimization Principles

The magnitude of ANE in notable systems spans several orders:

| Material/System                                    | Reported $S_{\rm ANE}$ ($\mu$V/K) | $\alpha_{xy}$ (A/K·m)        | Remarks                                               |
|----------------------------------------------------|------------------------------------|-----------------------------|-------------------------------------------------------|
| UCo$_{0.8}$Ru$_{0.2}$Al [2104.09060]               | 23                                 | 21                          | Colossal ANE, 5f systems, $\geq$10$^2$ Weyl nodes      |
| Co$_2$MnAl$_{1-x}$Si$_x$ [1807.02209]              | 6.2                                | —                           | Giant ANE in B2/L2$_1$-Heuslers, Berry curvature peak |
| Co$_3$Sn$_2$S$_2$ [1811.03485]                     | 5                                  | 10                          | Weyl semimetal, large $\partial \sigma_{xy}/\partial E$|
| YbMnBi$_2$ [2109.09382]                            | 6                                  | 10                          | Canted AFM, extremely low M                           |
| Mn$_3$NiN (AFM) [1908.11183]                       | 0.5 (in films)                     | 1.8                         | Largest in AFMs; symmetry-protected                   |
| Amorphous Tb$_{11}$(Fe$_{50}$Co$_{50}$)$_{89}$ [2512.17223]| 1.8                       | 0.8                         | Combinatorial maximum via direct + indirect ANE terms |
| Gd$_{33}$Fe$_{67}$ glass [2107.05215]              | 2.13                               | —                           | Flexible, amorphous, near-compensation                |
| Co$_x$Gd$_{1-x}$ films [2211.15074]                | 0.13–0.15 (near compensation)      | —                           | ANE polarity governed by Co sublattice                |
| Classic 3d FM (bulk Ni)                            | 0.2–0.6                            | 0.1–1                       | Reference for enhancement                             |

Strategies for maximizing ANE focus on maximizing the derivative $\partial \sigma_{xy}/\partial E$ at $E_F$ (steep Berry curvature slopes) and optimizing phase, band filling, and disorder to maintain transport.

## 6. Nanoscale and Ultrafast Applications

The ANE serves as a detection principle in several advanced device architectures:

- **Planar Thermopiles:** The transverse geometry enables modules with laterally arranged elements, offering full heat-source coverage and higher packing density without the need for stray-field mitigation, particularly using antiferromagnetic or compensated materials [1710.00062, 1908.11183].
- **Heat-Flux Sensors/Harvesters:** Zero-field operation and large coercive force in materials such as amorphous TbCo and GdFe films facilitate robust, self-powered devices [2401.04445, 2107.05215].
- **Near-field Magnetothermal Imaging:** Laser-induced ANE voltages provide quantitative, spatially-resolved detection of magnetic textures in both ferromagnets and antiferromagnets, with sub-100 nm spatial resolution [2407.13028].
- **Ultrafast Spin Caloritronics:** Femtosecond laser pulses drive picosecond ANE currents, emitting terahertz radiation and enabling interrogation of ultrafast magnetization dynamics [2302.11134].

## 7. Future Directions and Open Questions

Ongoing and future research is focused on:

- **Altermagnets and Compensated Systems:** Confirming and optimizing ANE in collinear, compensated systems where symmetry breaking is exclusively encoded in band topology, as recently shown in Mn$_5$Si$_3$ [2403.13427].
- **Fermi Level and Band Structure Engineering:** Systematic control of doping, strain, and interface design to position Berry curvature hotspots at $E_F$, maximize $\alpha_{xy}$, and realize giant or sign-reversible ANE [2303.12886, 2512.17223].
- **Disorder and Amorphous Effects:** Determining the extent to which short-range order and transition-metal content in amorphous alloys determines Berry curvature and ANE, as exemplified by compositional engineering in Tb-Fe-Co [2512.17223].
- **Scalability and Device Integration:** Implementing robust, substrate-flexible, and zero-field devices with high $ZT_{\rm ANE}$ for thermoelectric and spintronic applications, including integration with complementary effects (e.g., spin Seebeck).

The ANE is thus a canonical example of macroscopic observable directly determined by quantum topological properties and is increasingly central in the design of next-generation thermoelectric, spintronic, and magneto-optical technologies.

Source: https://www.emergentmind.com/topics/anomalous-nernst-effect-ane