Orbital Nernst Effect Overview

• The orbital Nernst effect is defined as a Hall-like thermal response that generates a transverse orbital current when a temperature gradient is applied.
• It leverages phenomena such as Berry curvature, interband hybridization, and scalar spin chirality in both electronic and magnonic systems, with sensitivity to Fermi level and magnetic field variations.
• Proposed detection strategies include measuring edge orbital accumulations via magnetoelectric conversion, MOKE imaging, and neutron scattering in materials like TMDCs, kagome, and honeycomb magnets.

The orbital Nernst effect (ONE) is the transverse generation of an orbital-angular-momentum or orbital-moment current by a longitudinal temperature gradient. In electronic systems it is formulated as the thermal analogue of the orbital Hall effect (OHE), while in magnonic systems it describes transverse transport of quantities such as topological orbital magnetization, magnon orbital angular momentum, or the orbital moment of a magnon wave packet. Across the current literature, the effect appears in nonmagnetic and ferromagnetic metals, transition-metal dichalcogenide monolayers, kagome and honeycomb magnets, zigzag Kitaev antiferromagnets, and noncollinear kagome antiferromagnets. The recurring theoretical ingredients are Berry curvature, orbital Berry curvature, scalar spin chirality, interband hybridization, and sensitivity either to the electronic Fermi level or to topological transitions in the magnon band structure (Zhang et al., 2019, Go et al., 2023, Salemi et al., 2022, Saha et al., 11 May 2026).

1. Conceptual definition and relation to neighboring effects

In its broadest usage, the ONE denotes a Hall-like thermally driven orbital transport channel. For electrons, a temperature gradient generates a transverse flow of orbital angular momentum in direct analogy with the relation between the spin Nernst effect and the spin Hall effect. For magnons, the literature uses closely related but not identical objects: the orbital angular momentum carried through scalar-spin-chirality coupling, the orbital moment associated with intersite circulating motion, and the self-rotation orbital moment of a magnon wave packet.

The effect is therefore adjacent to, but distinct from, several better-established responses. It is not the thermal Hall effect, because the transported quantity is orbital angular momentum or orbital moment rather than heat current. It is not the spin Nernst effect, because the transverse current need not be spin-polarized and in several platforms it survives even when the spin response is weak or symmetry-forbidden. In the 2019 kagome-ferromagnet proposal, the orbital current can overshadow the accompanying spin current because the orbital channel is generated by non-relativistic scalar chirality physics rather than by the spin-orbit-coupling bottlenecks that often limit spin transport (Zhang et al., 2019).

A second distinction concerns time-reversal symmetry. In bulk ferromagnets, the ordinary orbital Nernst effect is treated as the thermal analogue of the $\mathcal T$-even OHE, whereas the magnetic orbital Nernst effect is the $\mathcal T$-odd thermal analogue of the magnetic orbital Hall effect. The latter exists because ferromagnetism lowers symmetry and because spin-orbit coupling is present; it is not a separate orbital-current concept, but a symmetry-distinct branch of the same linear-response framework (Salemi et al., 2022).

2. Linear-response formulations

For electronic transport, the standard tensorial definition writes the orbital current density as

$$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$

with the orbital Nernst response contained in the transverse $\Lambda_{ij}^{L^k}$ components. In nonmagnetic metals and monolayer transition-metal dichalcogenides, the thermal coefficient is connected to the OHE through a Mott-type relation,

$$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$

or equivalently,

$$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$

This formalism makes the electronic ONE explicitly sensitive to the slope of the orbital Hall conductivity at the Fermi energy, which is why doping and band filling become central control parameters in monolayer $\mathrm{MoS_2}$, $\mathrm{NbS_2}$, and transition-metal series calculations (Salemi et al., 2022, Saha et al., 11 May 2026).

For magnons, the notation differs by model but the transport structure is analogous. In the honeycomb antiferromagnet,

$$(J_z^L)_y=-\alpha_z^L\,\partial_x T,\qquad \alpha_{z,n}^L=\frac{2k_B}{\hbar V}\sum_{\mathbf k} c_1(\rho_n)\,\Omega_n^L(\mathbf k),$$

where $c_1(\rho)=(1+\rho)\ln(1+\rho)-\rho\ln\rho$, $\mathcal T$0, and $\mathcal T$1 is the orbital Berry curvature (Go et al., 2023). In the kagome-ferromagnet scalar-chirality formulation, the orbital Nernst current is written as

$\mathcal T$2

and the crucial feature is that $\mathcal T$3 depends on the product of the magnon Berry curvature and the local topological orbital magnetization, rather than on Berry curvature alone (Zhang et al., 2019).

A common magnonic object across several later papers is the orbital-moment operator

$\mathcal T$4

or its equivalent orbital-moment notation $\mathcal T$5. In these formulations, the ONE is controlled by an orbital-current operator and an orbital Berry curvature or orbital-moment Berry curvature, rather than by the ordinary magnon Berry curvature alone (Go et al., 2023, An et al., 2024, Debnath et al., 5 Jan 2026).

3. Microscopic mechanisms in magnon systems

The first magnonic formulation tied the ONE to scalar spin chirality,

$\mathcal T$6

in a two-dimensional kagome ferromagnet with Heisenberg exchange, Dzyaloshinskii-Moriya interaction (DMI), external field, and a field coupling to the orbital moment induced by scalar spin chirality. Under linear spin-wave theory, the chirality becomes bilinear in magnon operators, showing explicitly that magnons carry chirality fluctuations. Thermally excited magnons then generate topological orbital magnetization (TOM), and a temperature gradient drives its transverse transport. In this picture, magnons “drag” orbital angular momentum through the coupling between spin-texture chirality and the electronic bath (Zhang et al., 2019).

A distinct intrinsic mechanism appears in the honeycomb antiferromagnet. There, the magnon has both a spin character and an orbital moment associated with intersite circulating motion. The Hamiltonian contains only antiferromagnetic exchange, easy-axis anisotropy, and magnetic field; there is no DMI. Because the honeycomb lattice and exchange network alone generate a finite orbital Berry curvature, the resulting magnon orbital Hall and Nernst effects are intrinsic and do not require spin-orbit coupling. The ordinary magnon Berry curvature is odd in momentum and integrates to zero for Hall transport, but the orbital Berry curvature is even in momentum and remains finite after Brillouin-zone integration (Go et al., 2023).

Later magnon literature broadened the microscopic landscape. In a zigzag-ordered honeycomb Kitaev antiferromagnet with DMI, extended Kitaev interactions, and field, the decisive ingredient is hybridization between opposite spin sectors, which opens topological bulk gaps and produces large orbital moments and orbital Berry curvature near avoided crossings; the resulting orbital Nernst conductivity can remain finite even at zero magnetic field (Debnath et al., 5 Jan 2026). In noncollinear kagome antiferromagnets modeled on potassium iron jarosite, the external field changes the canting angle and thereby tunes DMI-induced hybridization, acting as an effective control knob for topological phase transitions and for large peaks in the magnon orbital Nernst conductivity (To et al., 22 Feb 2025). In honeycomb ferromagnets with Heisenberg, DMI, Kitaev, and Zeeman interactions, the focus shifts to a magnon orbital moment Nernst conductivity (MOMNC) whose driving geometric object is the orbital-moment Berry curvature and whose field dependence is especially pronounced in Kitaev materials such as $\mathcal T$7 (An et al., 2024).

4. Symmetry, topology, and sign structure

A central theme is that orbital Nernst transport is topological, but not reducible to Chern number alone. In the kagome-ferromagnet TOM formulation, the response is governed by the product $\mathcal T$8, so both band topology and chirality-induced orbital magnetism are essential (Zhang et al., 2019). In the honeycomb antiferromagnet, the combined $\mathcal T$9 symmetry forces $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$0 and makes the ordinary Berry curvature odd in $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$1, eliminating the conventional Hall response, while the orbital Berry curvature remains even and nonzero (Go et al., 2023).

The sign behavior is correspondingly subtle. In the kagome-ferromagnet model, the sign of $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$2 is the same in phases whose Chern-number sets differ by an overall sign, because the Berry-curvature factor and the local TOM both reverse sign, leaving their product invariant (Zhang et al., 2019). In the honeycomb-ferromagnet MOMNC study, opposite-Chern parameter sets produce Berry curvatures of opposite sign near $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$3 and $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$4, but the orbital-moment Berry curvatures have similar shapes and generate orbital-moment Nernst currents in the same transverse direction; the authors therefore conclude that the orbital-moment Berry curvature is largely insensitive to the sign of the band Chern number (An et al., 2024). By contrast, the zigzag Kitaev antiferromagnet study finds that the orbital Nernst conductivity distinguishes topological phases more lucidly than the thermal Hall conductivity, particularly across gap-closing and reopening transitions (Debnath et al., 5 Jan 2026). Taken together, these results show that ONC sign, Chern sign, and thermal Hall sign are not universally interchangeable indicators.

Field-driven phase transitions provide the clearest explicit examples. In jarosite-like kagome antiferromagnets, the zero-field Chern numbers are

$$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$5

and vary under out-of-plane field as

$$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$6

with gap closings and reopenings at approximately $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$7 for $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$8 and $$J_i^{L^k}=\sigma_{ij}^{L^k}E_j-\Lambda_{ij}^{L^k}\frac{\partial T}{\partial r_j},$$9 for $\Lambda_{ij}^{L^k}$0 (To et al., 22 Feb 2025). In the zigzag Kitaev antiferromagnet, the lower two bands and upper two bands can carry combined Chern numbers $\Lambda_{ij}^{L^k}$1, and these flip across topological transitions induced by varying $\Lambda_{ij}^{L^k}$2 or $\Lambda_{ij}^{L^k}$3 (Debnath et al., 5 Jan 2026).

Another persistent misconception is that a transverse orbital response should vanish whenever the net spin moment vanishes. Several magnon papers reject that identification explicitly. In the zigzag Kitaev antiferromagnet, a finite magnon orbital moment contributes to the Nernst response even when the net spin moment vanishes, owing to the fundamental independence of spin and orbital magnetizations; correspondingly, the orbital Nernst conductivity may remain finite at $\Lambda_{ij}^{L^k}$4, whereas the thermal Hall conductivity vanishes there (Debnath et al., 5 Jan 2026).

5. Material realizations and reported scales

Reported magnitudes depend strongly on whether the platform is electronic or magnonic, on whether the response is ordinary or magnetic, and on whether the relevant control parameter is the Fermi level, magnetic field, or temperature.

System	Reported orbital Nernst result	Note
Kagome ferromagnet magnons	$\Lambda_{ij}^{L^k}$5 can reach the order of $\Lambda_{ij}^{L^k}$6	Orbital current can dominate accompanying spin current (Zhang et al., 2019)
Honeycomb antiferromagnet magnons	$\Lambda_{ij}^{L^k}$7 and about $\Lambda_{ij}^{L^k}$8 times larger than the predicted magnon spin Nernst conductivity	Drift-diffusion estimate gives $\Lambda_{ij}^{L^k}$9 (Go et al., 2023)
Bulk ferromagnets at $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$0 K	ONC: Fe $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$1, Co $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$2, Ni $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$3$$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$4 for $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$5	Ni is much larger than Fe and Co (Salemi et al., 2022)
40 monoatomic metals	ONE is significantly larger ($$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$6) than the SNE	Maximum values occur for Ni, Pd, and Pt; OHC reaches $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$7 (Salemi et al., 2022)
Jarosite kagome antiferromagnet	ONC can be about five times larger than its zero-field value near $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$8	Enhancement occurs near topological transition points (To et al., 22 Feb 2025)
Monolayer TMDCs	In hole-doped valley theory, $$\Lambda_{ij}^{L^k}= \frac{\pi^2 k_B^2 T}{-3e}\left(\frac{d}{dE}\sigma_{ij}^{L^k}\right)_{E=E_F},$$9	$$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$0 requires doping; metallic $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$1 hosts intrinsic ONE and sign reversal with Fermi-level shift (Saha et al., 11 May 2026)

Several robust trends recur across these platforms. Orbital responses are frequently much larger than spin responses. In bulk Fe, Co, and Ni, the OHE-like orbital conductivities are several times to one order of magnitude larger than the SHE-like spin conductivities and are nearly isotropic. In the monoatomic-metal survey, the ONE is about one order of magnitude larger than the SNE and peaks in group 10 elements. In TMDC monolayers, orbital Berry curvatures are generally much larger than spin Berry curvatures, so orbital responses dominate over spin responses. In magnonics, the same hierarchy appears in a different language: orbital transport can exceed spin Nernst transport in kagome ferromagnets and honeycomb antiferromagnets.

The role of the Fermi level is especially explicit in electronic materials. In monolayer $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$2, the OHC is nonzero even in the gap, but the ONE vanishes at the intrinsic Fermi level because the OHC is flat there; electron or hole doping makes the ONC finite. In metallic $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$3, the Fermi level already cuts bands with finite Berry curvature, so the ONE exists without doping. In ferromagnetic Ni, the large ordinary and magnetic orbital Nernst coefficients are attributed to the steep energy dependence of the underlying orbital conductivities at $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$4, exactly the situation emphasized by the Mott relation (Salemi et al., 2022, Saha et al., 11 May 2026).

6. Detection strategies and device relevance

Detection proposals fall into three main categories. The honeycomb-antiferromagnet work proposes a magnetoelectric route: orbital Hall accumulation of magnons induces polarization via

$$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$5

so edge orbital accumulation can be converted into a local voltage signal. Because spin-up and spin-down magnons cancel in zero field, a field-induced spin polarization of the magnon orbital current is introduced to obtain a nonzero electric response, yielding the estimate $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$6 for a $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$7 sample (Go et al., 2023).

In monolayer TMDCs, the proposed setup is a Hall bar with local heaters. The temperature gradient generates transverse orbital and spin accumulations at the edges, to be detected by magneto-optic Kerr effect (MOKE). Reversing the temperature gradient should reverse the Kerr signal, and an in-plane field should reduce the out-of-plane moment through Larmor precession. The same work also emphasizes the need to separate thermal Nernst signals from electrically driven OHE or SHE signals generated through the Seebeck effect (Saha et al., 11 May 2026).

Magnonic device implications are broader than detection alone. The kagome-ferromagnet proposal points to magnonic orbital torques, orbital accumulation in magnetic heterostructures, and the use of orbital transport as a probe of topological magnon band structure (Zhang et al., 2019). The field-tunable jarosite theory suggests experimental access through MOKE, induced electric polarization, transverse voltages from spin-orbital interplay, and neutron-scattering signatures of anticrossing gaps and band topology (To et al., 22 Feb 2025). The honeycomb-ferromagnet MOMNC study similarly identifies edge orbital-moment accumulation and polarization induced by magnon orbital moment as promising routes, with $$\sigma^{\gamma,\mathrm{ONE}}_{\alpha\beta}= \frac{\pi^2 k_B^2 T}{-3e}\left.\frac{d}{d\epsilon}\sigma^{\gamma,\mathrm{OHE}}_{\alpha\beta}\right|_{\epsilon=\epsilon_F}.$$8 highlighted as a concrete candidate platform (An et al., 2024).

The present theoretical record therefore portrays the orbital Nernst effect as a broad transport phenomenon rather than a single mechanism. In metals it is the thermal derivative of the OHE and is often strongest where the orbital Hall conductivity varies sharply at the Fermi level. In magnonic matter it can arise from scalar spin chirality, intersite circulating motion, or wave-packet self-rotation, and it is frequently amplified by topological gaps, spin-sector hybridization, and field-tuned band inversions. Across both electronic and magnonic settings, the literature converges on the same conclusion: orbital transport constitutes an independent transverse thermothermal channel with its own symmetry content, geometric response functions, and experimental signatures.