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[Sarah J. Watzman](https://orcid.org/0000-0002-5244-2340), [Takashi Kikkawa](https://orcid.org/0000-0002-7789-604X), [Brian Skinner](https://orcid.org/0000-0003-0774-3563), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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Utilizing magnetization and spin in thermoelectric applicationsMRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletin               915Utilizing magnetization and spin in thermoelectric applicationsSarah J. Watzman,*   Takashi Kikkawa,   Brian Skinner,   and Ken‑ichi Uchida The combined use of heat, charge, and spin transport gives rise to new or deeply altered thermoelectric properties from those found in conventional, nonmagnetic thermoelectric transport; these phenomena include the magneto-Seebeck, Nernst, magnon drag, and spin Seebeck effects. Here, we explore both electron-driven and magnon-driven magneto-thermoelectric effects stemming from different origins depending on if the effect is longitudinal, where the electric field and thermal gradient are collinear, or transverse, where the electric field and thermal gradient are orthogonal. We consider both a Lorentz force acting on charge carriers in nonmagnetic conductors and the spin–orbit interaction acting on spin-polarized electrons in magnetic materials. Both intrinsic and extrinsic sources of skew forces on electrons or anomalous velocities offer promising avenues for generating new functionalities and applications in the burgeoning field of magneto-thermoelectrics and transverse thermoelectrics. Adding magnetism as a design degree of freedom offers more candidate classes of materials, such as topological, metallic, and amorphous materials, for consideration in the field of thermoelectrics.© The Author(s) 2025doi:10.1557/s43577-025-00941-8Introduction: Magneto‑thermoelectric phenomena and their originsThe field of thermoelectrics began with the initial discovery of the Seebeck effect by T.J. Seebeck in the early 1820s.1 Con-ventional thermoelectric devices require alternating pairs of n-type and p-type semiconductors connected electrically in series and thermally in parallel to generate an output volt-age from an input heat flux. Much research in the field has focused on increasing zT, the dimensionless figure of merit, although recent progress in the field has not brought significant enhancements to make conventional thermoelectric devices and materials competitive for consumer applications.2 How-ever, the first observation of the spin Seebeck effect (SSE) in 20083 and the experimental discovery of Weyl semimet-als (WSMs) in 20154–7 have brought resurgence in interest in using magnetization and spin in thermoelectric applications to enhance thermal-to-electrical energy conversion and offer geometrical freedom in device design. The Nernst effect, first discovered by Walther Nernst and Albert von Ettingshausen in elemental bismuth in 1886,8 employs a transverse geometry in which an applied heat flux and orthogonal external magnetic field generate a Lorentz force, accelerating charge carriers in a mutually perpendicular direction to generate a transverse electric field. Although a plethora of magneto-thermoelectric effects exist, here we focus on the magneto-Seebeck effect, magnon-drag thermopower, Nernst effect, and SSE-induced inverse spin Hall effect (ISHE), as these phenomena are repre-sentative of both electron-driven and magnon-driven longitu-dinal and transverse magneto-thermoelectric effects, as shown in Figure 1. We have chosen these four representative trans-port phenomena to demonstrate to readers both the geometri-cal opportunities (longitudinal and transverse) and the oppor-tunities in origin of transport phenomena (electron-driven and magnon-driven) offered by magneto-thermoelectrics, which are not found in the field of conventional thermoelectrics.Magneto‑thermoelectric transport phenomenaIn Figure 1, the thermoelectric effects discussed in this article are classified in terms of energy carriers and configurations. In both magnetic and nonmagnetic materials and their hybrid systems, a wide variety of transport phenomena occur, but in this article, we focus on the magneto-Seebeck effect, Nernst effect, magnon-drag (MD) thermopower, and SSE-induced ISHE. The magneto-thermoelectric transport phenomena are Sarah J. Watzman, Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, USA; watzmasj@ucmail.uc.eduTakashi Kikkawa, Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Japan; kikkawa.takashi@jaea.go.jpBrian Skinner, Department of Physics, The Ohio State University, Columbus, USA; skinner.352@osu.eduKen‑ichi Uchida, Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Tsukuba, Japan; Department of Advanced Materials Science,  The University of Tokyo, Kashiwa, Japan; UCHIDA.Kenichi@nims.go.jp*Corresponding authorhttp://orcid.org/0000-0002-5244-2340http://orcid.org/0000-0002-7789-604Xhttp://orcid.org/0000-0003-0774-3563http://orcid.org/0000-0001-7680-3051http://crossmark.crossref.org/dialog/?doi=10.1557/s43577-025-00941-8&domain=pdfUtilizing magnetization and spin in thermoelectric applications916         MRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletinthermoelectric effects that occur depending on the external magnetic field or the direction of spontaneous magnetization; they are categorized into longitudinal effects, in which an elec-tric field is generated in a direction parallel to an input tem-perature gradient, and transverse effects, in which an electric field is generated in a direction perpendicular to the tempera-ture gradient.The most fundamental phenomenon of the electron-driven longitudinal magneto-thermoelectric effects is the magneto-Seebeck effect. This is a phenomenon in which the Seebeck coefficient changes depending on the magnetic field, and the behavior differs depending on whether the magnetic field is parallel or perpendicular to the temperature gradient (Figure 1, and Figure 2a).9–11 In magnetic materi-als with spontaneous magnetization, the Seebeck coefficient changes anisotropically with respect to the magnetization direction; this phenomenon is thus called the anisotropic magneto-Seebeck effect. In contrast, the electron-driven transverse magneto-thermoelectric effect is called the Nernst effect. Its popularity has increased in condensed-matter physics in recent years, following the development of topological materials science and spin caloritronics. In the ordinary (anomalous) Nernst effect, when an external magnetic field (spontaneous magnetization) is oriented in the z-direction, an electric field is generated in the y-direction when a temperature gradient is applied in the x-direction (Figures 1 and 2b).12–15However, the magneto-thermoelectric effects are caused not only by the transport of conduction electrons/holes but also by the transport of quasiparticles such as magnons (i.e., collective excitations of localized magnetic moments). The phenomenon in which the Seebeck coefficient changes as electrons or holes receive momentum from phonons is known as phonon drag, and a similar phenomenon occurring with magnons is called magnon drag.17–19 The magnon drag is classified as a longitudinal magneto-thermoelectric effect because it modulates the Seebeck coefficient through mag-non transport (Figure 1). SSE-induced ISHE is classified as a magnon-driven transverse magneto-thermoelectric effect in this article. This is because, while ISHE is a phenomenon in which a conduction-electron spin current is converted into an electric field in a nonmagnetic conductor, SSE generates a magnon spin current in a magnetic material. The symme-try of the thermoelectric conversion by SSE-induced ISHE is similar to that by the Nernst effect, but SSE-induced ISHE works only when the magnetization direction of the magnetic material is oriented within the junction interface between the magnetic material and nonmagnetic conductor (Figures 1 and 2c).16,20–22Magnetic and spin origins of magneto‑thermoelectric effectsThe origins of the electron-driven magneto-thermoelec-tric effects are the Lorentz force acting on charge carriers in Figure 1.   Definition of the thermopower for the magneto-thermoelectric effects discussed in this article, characterized by (quasi-)particle driving them and geometrical relationship between an applied temperature gradient ∇xT  along the x-direction and induced electric field. Ex (Ey) denotes the electric field in the x- (y-) direction for the longitudinal (transverse) thermoelectric effects. Hx (Hz) denotes the magnetic field in the x- (z-) direction. MD, SSE, and ISHE represent the magnon drag, spin Seebeck, and inverse spin Hall effect, respectively.a b cFigure 2.   Schematics of the (a) magneto-Seebeck effect, (b) Nernst effect, and (c) spin Seebeck effect (SSE)-induced inverse spin Hall effect (ISHE). Note that the direction of the generated electric fields Ex and Ey depends on the sign of the magneto-Seebeck thermopow-ers Sxxx and Sxxz for (a), the Nernst thermopower Sxyz for (b), and the SSE thermopower SSSE (which is determined by the sign of the mag-non polarization of the magnetic layer and the spin-Hall angle of the metallic layer16) for (c). The external magnetic field (Hx or Hz) orients the magnetization M in the magnetic layers parallel to the field direction.Utilizing magnetization and spin in thermoelectric applicationsMRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletin               917nonmagnetic conductors and the spin–orbit interaction acting on spin-polarized electrons in magnetic materials. When the applied temperature gradient and external magnetic field are orthogonal, the Lorentz force bends the trajectory of charge carriers driven by the temperature gradient, resulting in the ordinary Nernst effect in nonmagnetic conductors. As a second-order effect of the magnetic field, the longitudinal transport properties also change, resulting in the magneto-Seebeck effect, which is a thermoelectric analogue of the magnetoresistance. In magnetic materials, the spin–orbit interaction anisotropically changes the hybridization of the electronic bands, resulting in the anisotropic magneto-Seebeck effect.11 The origin of the anomalous Nernst effect (ANE) is also the spin–orbit interaction, but, in a similar manner to the anomalous Hall effect, it can be classified into an intrinsic mechanism that originates in the electronic band structure and an extrinsic mechanism that originates in spin-dependent impurity scattering. The recent trend is to search for materials that exhibit large ANE due to intrinsic mechanisms; in various topological materials, large anomalous Nernst coef-ficients and transverse thermoelectric conductivities have been observed because of the large Berry curvature near the Fermi energy owing to the specific band structures, including Weyl points, nodal lines, webs, and planes.12–15 The same is true for the Onsager reciprocal of the previously discussed phenomena.The origins of the magnon-driven magneto-thermoelectric effects are fundamentally different from those of the electron-driven effects. Magnons do not carry a charge, but they modulate the thermoelectric conversion properties of electrons via elec-tron–magnon scattering and a spin-motive force, which is an electric field induced by the energy transfer between conduction-electron spins and magnetic moments; this is the magnon-drag thermopower.17 Magnon-drag thermopower can persist even in a paramagnetic state as short-range spin fluctuations.18,19 On the other hand, SSE is a phenomenon that directly generates a magnon spin current from a temperature gradient in a magnetic material. The transverse thermopower induced by SSE is gener-ated through three key steps: (1) an applied temperature gradient in the magnetic layer induces a flow of magnons (i.e., a magnon spin current), which (2) at the interface with the metallic con-tact is converted into a conduction-electron spin current via the interfacial exchange interaction and (3) is subsequently detected as a transverse voltage via ISHE.16,20–22Review of material advances in magneto‑thermoelectricsAnomalous Nernst effect (ANE)Topological materialsTopological materials have attracted significant attention in the field of solid-state physics since their first experimental confirmation4–7 and are of particular interest in magneto-ther-moelectrics due to the ultrahigh mobility found in their Dirac bands.23,24 In particular, the unique features of WSMs, such as bulk Weyl nodes23,24 and surface Fermi arcs,25 were expected to have signatures in magneto-thermoelectric transport beyond those from classical electronic contributions. Specifically, Berry curvature was expected to contribute to an ANE even in the absence of ferromagnetism.26,27 The first topological material in which this was observed was Cd3As2, a Dirac semimetal, where the anomalous Nernst signal increases sig-nificantly above ~50 K; here, the ANE is linked to topologi-cal protection as the transport relaxation time increases in the same temperature range.28 Berry curvature was determined as the source of the large ANE.28 due to the external mag-netic field breaking time-reversal symmetry and thus lifting the degeneracy of the Dirac nodes, splitting them into Weyl nodes. NbP is the first WSM in which ANE was observed, with ANE exceeding the ordinary Nernst effect in fields of magnitude less than ~2 T and an unsaturating transverse ther-mopower Sxyz up to 9 T with a maximum observed value of ~800 μV K−1 at 109 K.29 Both the Seebeck coefficient and Sxyz were observed to have maximum values in similar temperature ranges, and this behavior was attributed to the temperature-dependent motion of the chemical potential that got pinned at the energy of the Weyl points due to the charge neutrality condition arising from a zero density of states at the energy of the Weyl points when no trivial pockets contribute to trans-port.29 Although no magneto-Seebeck effect was observed in single-crystalline NbP,29 a large magneto-Seebeck effect was observed in polycrystalline NbP over a broad tempera-ture range; Sxxz was also observed to maximize over a similar temperature range as Sxyz,30,31 which is unique to this class of materials. The differences in magneto-thermoelectric transport data among these samples of NbP was later attributed to the sensitivity of WSMs to slight changes in composition, sug-gesting that doping could be used as a tuning mechanism for magneto-thermoelectric effects in not only NbP but topologi-cal materials in general.31 Interestingly, both Sxxz and Sxyz being maintained near their maximal values over broad temperature ranges are currently theoretically predicted to be a trait spe-cific to compensated or nearly compensated Type I WSMs, where their Dirac bands are symmetric about an energy axis in k-space.32 Recent work in WTe2, a Type II WSM whose Dirac bands are tilted in k-space, supports this claim as its Sxyz is near 8000 μV K−1 at 9 T near ~10–15 K but quickly drops near zero by ~30 K.33Although exciting, reported values of ANE in the afore-mentioned materials required large, externally applied mag-netic fields, making these materials potentially incompatible with conventional thermal energy-conversion applications. However, WSMs that break time-reversal symmetry are expected to have a net Berry curvature, which can act like a magnetic field while being intrinsic to a material’s band structure.24,26 Recent work in ferromagnetic WSMs, such as Co2MnGa, indicates that Berry curvature can indeed lead to a giant ANE, beyond that expected from intrinsic magnetiza-tion alone.12,13 ANE was also observed in Co3Sn2S2, a hard ferromagnet, at zero-field,34,35 and the Nernst conductivity’s scaling relation with the material’s magnetization determined that Berry curvature was the dominant mechanism behind the Utilizing magnetization and spin in thermoelectric applications918         MRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletinlarge ANE.35,36 Recent attention has turned to antiferromag-netic WSMs, which offer further potential in device applica-tions as they do not have the stray magnetic fields associated with ferromagnetic materials.37 YbMnBi2 is a time-reversal symmetry breaking Type II WSM, and it is a canted antiferro-magnet.38 In YbMnBi2, the ANE is highly anisotropic, in part due to the highly anisotropic band structure and in part due to the directionality associated with spin canting. The sign of the Berry curvature, and therefore the sign of the anomalous Hall conductivity, is determined by the direction of the spin cant-ing, which can be toggled by a weak external magnetic field applied in the canting direction. YbMnBi2 thus offers promise as a switchable transverse thermoelectric.39Permanent magnetsThe appearance of giant ANE is not an exclusive feature of topological materials. In 2019, SmCo5-type permanent mag-nets were discovered, which are mass-produced and used in practical applications, and they exhibit large ANE.40 The anomalous Nernst thermopower, SANE (a subset of Sxyz from Figure 1 corresponding specifically to the ANE) of SmCo5 exceeds 3.5 μV K–1 at room temperature, monotonically increases with increasing temperature, and reaches >5.5 μV K–1 at T > 550 K.41 Although these values are smaller than SANE of Co2MnGa, the ratio of the electrical conductivity σ to the thermal conductivity κ of the SmCo5-type magnets is larger than that of Co2MnGa. Thus, the figure of merit for ANE in these materials is comparable. The transverse thermoelectric conductivity of the SmCo5-type magnet at room temperature (4.6 A K–1 m–1) was estimated to be much larger than that of Co2MnGa (2.4–3.0 A K–1 m–1). The SmCo5-type magnets are known as permanent magnets with excellent temperature stability. Their coercive force is extremely large, and the rema-nent magnetization remains finite up to T > 700 K. Therefore, the SmCo5-type magnets enable the zero-field operation of large ANE and can be regarded as top-class ANE materials. Interestingly, Nd2Fe14B-type magnets, which have the largest maximum energy product (BH)max and are the most widely used permanent magnets in society, show negative SANE, although |SANE| is small.40 It has been demonstrated that by alternately stacking the SmCo5-type magnets with SANE > 0 and the Nd2Fe14B-type magnets with SANE < 0 and connecting them in series, it is possible to construct an anomalous Nernst thermopile module that operates in the absence of a magnetic field, in which all the magnets contribute to the total output power.42 This was demonstrated in the magnetic-field-free ANE-driven power generation up to 177 μW around room temperature at a temperature difference of 75 K, leading to the record-high power density of 65 μW cm–2 due to ANE.ANE in permanent magnets has been investigated mainly using bulk materials. However, magnetic materials having large coercivity and remanent magnetization are useful also for ANE-based thin-film devices, which are developed toward future applications as heat flux sensors.43 An ANE-based heat flux sensor has a thermopile structure comprising two different thin wire-shaped materials arranged alternately and connected in series, where the temperature gradient is in the thickness direction and the magnetization is in the width direction of the wires. This configuration enables the construction of heat flux sensors with low thermal resistance. Due to the large demag-netization field in the thin wires, the magnetization has to be aligned in the hard axis.44,45 Thus, materials development is also being carried out to overcome this issue, and promising materials such as Co3Sn2S2-based alloys46 and amorphous Sm-Co-based alloys,47 described next have been reported. Note that the performance of heat flux sensors is determined by the open-circuit voltage per unit heat flux, and the figure of merit is not a good indicator for this application.Amorphous materialsWhile most of the ANE studies to date have been conducted using crystalline materials, amorphous magnetic materials are also promising for applications of ANE because they can be mass-produced inexpensively and have mechanical flex-ibility. The amorphous structure is also effective in reducing lattice thermal conductivity. In 2022, amorphous Sm-Co-based alloy thin films were developed that can be deposited on any substrate, including flexible polymers and glass, and that exhibit large in-plane coercivity and remanent magnetiza-tion.47 These amorphous alloy films can be used to construct flexible, ultrathin ANE devices that operate without magnetic fields, which are suitable for heat-flux sensing applications. However, SANE of the amorphous Sm-Co-based alloys remains small: SANE ~1–1.5 μV K–1. To overcome this situation, Gau-tam et al. have demonstrated that by applying nanostructure engineering to Fe-based amorphous alloys called Nanomet, the SANE and ANE power factor are increased by 70% and 200%, respectively, while maintaining the mechanical flex-ibility and average composition of the alloys.48 This is exem-plified in Figure 3b.49–53 SANE of the nanostructure-engineered Nanomet ribbon, as shown in Figure 3a, was estimated to be 3.7 μV K–1 at room temperature, which is comparable to the values for single-crystalline and polycrystalline topological magnets. It has been shown that the increase in SANE is due to Cu nanoclustering in the Fe-based amorphous alloys, but the microscopic origin is still unclear. Nevertheless, this study clearly shows that, in addition to the electronic structure and composition of materials, nanostructure engineering is impor-tant for improving the thermoelectric performance of ANE. It is also possible to create amorphous magnetic metal ribbons with finite coercivity and remanent magnetization through nanostructure engineering; the zero-field operation of ANE has been demonstrated using such materials.54ANE in amorphous materials is interesting from the view-points of not only applications but also physics. The Berry curvature contribution to the transverse transport phenom-ena, which has been confirmed through research on ANE in topological materials, cannot be defined exactly in amor-phous alloys that do not have long-range crystalline order. However, experiments using amorphous Fe-Sn alloys show Utilizing magnetization and spin in thermoelectric applicationsMRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletin               919that the short-range crystalline order of Kagome-lattice frag-ments can induce the Berry curvature contribution to ANE and the anomalous Hall effect.55 As exemplified by this work, the studies on the transport phenomena in amorphous alloys and topological materials are related to each other. It is thus expected that the synergistic effect of these materials will lead to further progress in ANE research.SSE‑induced ISHEThe SSE refers to the generation of a spin current, Js, as a result of a temperature gradient, ∇T, in a magnetic material with a metallic contact (Figure 4).16,20–22 Thus, SSE is often classified as a thermospin effect, not a magneto-thermoelectric effect.56 However, SSE functions as a thermoelectric conver-tor when combined with the ISHE, where the spin current in a magnetic material is injected into a nonmagnetic conductor and converted to an electrical current via ISHE,16,20–22 so here we classify it as one of the magneto-thermoelectric effects. The effect was first discovered in a ferromagnetic metal per-malloy in 20083 and later has been observed in a wide range of magnetic materials, including magnetic semiconductors, elec-trically insulating ferro-, ferri-, and antiferro-magnets, as well as two-dimensional (2D) magnetic materials.16,20–22 The SSE voltage arises when ∇T is applied in a magnetic material, gen-erating a magnon spin current (Figure 4a), which, at the inter-face with a metal, is converted into a conduction-electron spin current via the interfacial exchange interaction (Figure 4b) and is subsequently detected as a transverse voltage via the ISHE (Figure 4a).16,20–22From a materials perspective, the ferrimagnetic insulator yttrium-iron-garnet (YIG, Y3Fe5O12) has been central in SSE research due to its exceptionally low magnetic damping, high electrical resistivity, and high Curie temperature (~560 K). These prop-erties make YIG an ideal platform for studying magnon spin currents and understanding their role in SSE. Extensive SSE studies using YIG-based heterostructures, especially with Pt contacts exhibiting strong ISHE, have provided key insights into the SSE mechanisms.20,21A distinctive aspect of SSE is its involvement of thermally excited mag-nons with relatively high frequencies in the sub-THz to THz range, ena-bling studies of magnon spin currents induced by gapped antiferromagnetic a bFigure 3.   (a) Schematic of anomalous Nernst effect (ANE) in an amorphous magnetic material with nanoprecipitates/cluster and elemental maps of Fe (blue), P (red), B (green), and Cu (orange) for the Nanomet ribbon post-annealed at 653 K, measured by atom probe tomography. (b) Comparison of the absolute values of the ANE thermopower, SANE, at room temperature for various amorphous magnetic alloys. This figure is reconstructed from Reference 48 licensed under a Creative Commons Attribution 4.0 International License. The data for other materials in (b) are obtained from References 47, 49–53, 55.a bFigure 4.   Schematic illustrations of (a) spin Seebeck effect in a magnet/metal junction sys-tem and (b) the interfacial magnon–electron-spin scattering due to interfacial spin-exchange interaction. Js, σ↑(↓) , EISHE, ∇T, and Hz denote the spatial direction of the spin current, the up (down) electron spin, the electric field induced by inverse spin Hall effect, the tempera-ture gradient, and the external magnetic field, respectively.Utilizing magnetization and spin in thermoelectric applications920         MRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletinmagnon modes. For instance, References 57–60 report the observation of antiferromagnetic SSEs in easy-axis antifer-romagnets Cr2O3, MnF2, and α-Fe2O3, which host two degen-erated antiferromagnetic magnon modes with opposite spin polarization above ~0.1 THz at zero magnetic field. An exter-nal magnetic field lifts this degeneracy, creating an imbalance between the two modes, which in turn generates a net mag-non spin current. The SSE voltages in these systems exhibit characteristic features reflecting the magnetic-field response of the magnon branches.57–60 However, their voltage sign remains debated and has been suggested to depend on inter-facial details.60–62 Resolving this issue is a key SSE research challenge.SSEs in 2D van der Waals magnets represent another prom-ising direction. These materials exhibit spin correlations that differ between in-plane and out-of-plane directions. SSE sig-nals linked to such anisotropies have been studied in Cr2Si2Te6 and Cr2Ge2Te6.63 Moreover, SSEs in 2D van der Waals mag-nets have recently been actively studied in nonlocal configura-tions,16 as demonstrated in MnPS3,64,65 CrPS4,66 and CrBr3.67 Another exciting avenue is tuning SSE via stacking order and combinations of 2D materials (e.g., References 68 and 69), which may open new research opportunities.Magnon‑drag effects in metalsWhile magnon-driven, SSE-induced ISHE requires an inter-face between a magnetic material and a metallic contact, fer-romagnetic metals exhibit magnon transport without the need for an interface. Early work in elemental iron suggested that its Seebeck coefficient was larger than theoretically predicted by diffusion alone and potentially dominated by magnon drag,70 an advective transport mechanism. Magnons are quasiparticles stemming from the collective excitation of magnetization that carry both linear and spin angular momentum; in the presence of a temperature gradient, heat is transferred to magnons from phonons, and electrons can be pulled through solid materials as the magnon moves through them, as shown in Figure 5.71,72Magnon drag was shown to dominate the thermopower of elemental iron and cobalt and contribute to the thermopower of elemental nickel, all of which are transition-metal ferro-magnets.17 A hydrodynamic theory,73 in which magnons and electrons are treated as interpenetrating fluids, suggests that the magnon drag contribution to thermopower scales with the magnon specific heat, which scales with T3/2; electronic dif-fusion thermopower scales linearly with T,74 and the sum of the two thermopowers amounts to the total measured thermo-power.17 Interestingly, a microscopic theory based on spin-motive forces75 gives the same result for magnon-drag ther-mopower when a Berry phase correction is applied.76Magnon drag is also expected to contribute to the ANE and was experimentally shown to do so in elemental iron.17 A spin-mixing model was considered, in which independent spin-up and spin-down conduction electron channels exist; each chan-nel was treated separately, as is done for two-carrier transport in semimetals and semiconductors.77 When the thermopower contribution to the Nernst coefficient was dominated by mag-non-drag thermopower, the anomalous Nernst coefficient was also found to scale with the magnon-drag thermopower, which scales with T3/2.17 More recent work in MnBi suggests that extrinsic contributions from magnons can actually dominate the ANE, where the presence of large spin–orbit coupling leads to an additional spin polarization of conduction electrons in the presence of a thermal gradient, enhancing the transverse voltage (Figure 5).72Nonlinear effects driven by Berry curvature dipoleIn the absence of time-reversal symmetry breaking, either by an external magnetic field or by internal magnetic order, transverse linear responses such as the Hall and Nernst effects are forbid-den by symmetry. Materials with time-reversal symmetry can still possess finite Berry curvature at different points in momen-tum space, but the net Berry curvature integrated over the vol-ume of filled electron states must be zero so that the Berry curvature provides no net effect in transverse linear responses.However, the same constraint does not apply to nonlinear effects, in which a current flows that is proportional to two pow-ers of an applied field. For example, a transverse electrical cur-rent can appear in materials possessing time-reversal symmetry so long as this current is proportional to the square of the lon-gitudinal electric field. This effect is dubbed the nonlinear Hall effect,78 and it has received a number of experimental confirma-tions in recent years (e.g., References 79 and 80). The idea of the nonlinear Hall effect is that under the influence of an electric field, the volume of filled states shifts in momentum space. If the Berry curvature has a finite dipole moment in the direction of the field, then the shifted Fermi volume has a net Berry curvature even though the equilibrium Fermi volume does not, such that a transverse response is generated under the influence of the electric field.Figure 5.   Schematic of magnon drag contributions to thermo-power (SMD) and ANE (SANE). Heat flux is transferred from phonons to magnons in ferromagnets. Magnons carry linear angular moment ( −→p  ), which creates SMD when transferred to electrons; magnons also carry spin angular momentum ( −→S  ), which creates SANE when transferred to electrons in materials with large spin–orbit coupling. Figure reproduced from Reference 72 under the terms of the Creative Commons CC-BY license.Utilizing magnetization and spin in thermoelectric applicationsMRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletin               921A similar shift of the Fermi surface can be accomplished by a temperature gradient, which allows for a nonlinear ANE, in which a transverse voltage appears that is proportional to the square of the longitudinal temperature difference.81–84 The magnitude of the effect is directly proportional to the Berry curvature dipole in the direction of the temperature gradient. Related effects that can be driven by the Berry curvature dipole include an anomalous nonlinear thermal Hall effect, in which a transverse heat current is proportional to the squared longi-tudinal temperature difference, and an anomalous nonlinear thermoelectric Hall conductivity, in which a transverse voltage arises that is proportional to the product of a longitudinal volt-age and a longitudinal temperature difference.81–84To date, there are no published experimental works demon-strating a nonlinear thermoelectric effect driven by the Berry curvature dipole. Yet theoretical work has pointed to a number of candidate materials in which this effect may be detectable, including layered compounds such as bilayer WTe2,85 MoS2,82 and other transition-metal dichalcogenides;86 bulk WSMs such as TaAs and MoTe2;87,88 and the antiferromagnetic semicon-ductor CuMnAs.89 Because the magnitude of the Berry curva-ture dipole can vary sensitively with the chemical potential,87 achieving precise control over chemical doping or electrical gating may be key for realizing and exploiting these effects. We note that a nonlinear ANE has recently been observed in a superconductor/magnet junction system with broken time-reversal symmetry,90 and the lock-in-based technique can also be applied to measure nonlinear ANEs arising from the Berry curvature dipole.Applications for magneto‑thermoelectricsMagneto‑thermoelectric figure of meritThe efficiency of conventional thermoelectric conversion increases with the dimensionless figure of merit, zT:where S is the Seebeck coefficient and T is the absolute tem-perature. A dimensionless figure of merit can similarly be defined for thermomagnetic materials based on the magneto-Seebeck (Equations 2 and 3) and Nernst (Equation 4) effects as:where (zT)xxx, (zT)xxz, and (zT)xyz are now functions of both tem-perature and magnetic field. For the magneto-thermoelectric (1)zT =S2σκT ,(2)(zT )xxx=S2xxxσxxxκxxxT(3)(zT )xxz=S2xxzσxxzκxxzT(4)(zT )xyz=S2xyzσyyzκxxzT ,effects, the electrical conductivity must be taken in the same direction as the induced electric field and the thermal conduc-tivity must be taken in the same direction as the applied heat flux, both in the presence of a magnetic field or magnetiza-tion. This implies that in order to fully characterize the figure of merit for a magneto-thermoelectric material, the magneto-electrical conductivity and magneto-thermal conductivity must also be measured in addition to the magneto-thermoelectric effect itself. Ideally, these would be measured simultane-ously as to capture their values at the same temperatures and externally applied magnetic fields, making the determination of zT for magneto-thermoelectric phenomena increasingly challenging.While zT values based on the Seebeck effect have been experimentally reported near 191–93 at room temperature and exceeding 294,95 at higher temperatures, (zT)xxx, (zT)xxz, and (zT)xyz are consistently at least an order of magnitude lower with maximal values observed below room temperature.31,39,96 However, experimental work in magneto-thermoelectric mate-rials majorly excludes reporting values of (zT)xxx, (zT)xxz, and (zT)xyz, which are necessary within the community to deter-mine the potential for device applications.Device advantages and disadvantages of magneto‑thermoelectricsAn advantage of the transverse thermoelectric conversion in conductors under magnetic fields and in magnetic materi-als with spontaneous magnetization is that it can occur in a wide variety of materials, without requiring special sin-gle crystals or hybrid structures. This versatility has led to a diversity of materials development for applications. The introduction of topological and layered materials has also led to new developments in condensed-matter physics. Because some materials that exhibit excellent transverse thermoelec-tric conversion properties require the application of a large external magnetic field, it is essential to develop transverse thermoelectric materials that exhibit large coercivity and remanent magnetization. Depending on target applications, the stray magnetic field generated by ferromagnetic materi-als may have a negative impact. With these points in mind, exploring new materials based on electronic structures97 is necessary but not sufficient in developing transverse ther-moelectric materials and devices using magnetic effects—nanostructure engineering to control magnetic properties is also important. The biggest issue in transverse thermoelec-trics based on the magnetic effects is that its output power is still insufficient for thermal energy harvesting and elec-tronic cooling applications. Thus, efforts are being made to solve this issue, for example, by hybridizing the transverse thermoelectric conversion phenomena based on the magnetic effects with those based on nonmagnetic effects, such as the off-diagonal Seebeck effect.98,99 To bridge the gap between practical thermoelectric devices and magneto-thermoelec-trics, it is necessary to optimize not only a thermopower Utilizing magnetization and spin in thermoelectric applications922         MRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletinbut also electrical and thermal conductivities. Based on the orthogonal relationship between charge and heat currents, anisotropic materials are suitable for optimizing the figure of merit for transverse thermoelectrics.100ConclusionAlthough the field of thermoelectrics has existed for over two centuries, recent discoveries in materials science have brought a resurgence of interest in magneto-thermoelectric effects. External magnetic fields can serve as the source of a skew force to enhance both longitudinal and transverse thermoelectric effects via the magneto-Seebeck and Nernst effects, respectively, while magnon excitations contribute to a longitudinal magnon-drag thermopower and a transverse SSE-induced ISHE. While magneto-thermoelectrics offer the opportunity to decouple the electric field and heat flux, presenting many advantages in device design, the figure of merit of magneto-thermoelectric materials still remains sig-nificantly lower than that of conventional thermoelectrics. Thus, effort in the field should further explore hybrid and nanostructures to bring magneto-thermoelectrics closer to device realization.Acknowledgments S.J.W. acknowledges support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences Early Career Research Program (Award No. DE-SC0020154). T.K. acknowledges support from the Grant-in-Aid for Scien-tific Research (Grant No. JP24 K01326) from JSPS KAK-ENHI. B.S. acknowledges support from the Center for Emer-gent Materials, an NSF-funded MRSEC, under Grant No. DMR-2011876. K.U. was supported by JST ERATO “Mag-netic Thermal Management Materials” (JPMJER2201) and the Grant-in-Aid for Scientific Research (S) (22H04965) from JSPS KAKENHI.Author contributions S.J.W.: Conceptualization (equal); visualization (equal); supervision (equal); writing—original draft (equal); writing—reviewing and editing (equal). T.K.: Writing—original draft (equal); writing—reviewing and editing (supporting). B.S.: Writing—original draft (equal); writing—reviewing and edit-ing (supporting). K.U.: Conceptualization (equal); visualiza-tion (equal); writing—original draft (equal); writing—review-ing and editing (supporting).Funding Basic Energy Sciences, DE-SC0020154, S.W., JSPS KAK-ENHI, JP24K01326, T.K., Division of Materials Research, DMR-2011876, B.S., JST ERATO, JPMJER2201, K.U., JSPS KAKENHI, JP22H04965, K.U.Conflict of interest The authors declare no conflicts of interest.Open AccessThis article is licensed under a Creative Commons Attribu-tion 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Com-mons licence, and indicate if changes were made. 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Res. 2(9), 2300015 (2023)98.  K. Uchida, T. Hirai, F. Ando, H. Sepehri-Amin, Adv. Energy Mater. 14, 2302375 (2024)99.  T. Hirai, F. Ando, H. Sepehri-Amin, K. Uchida, Nat. Commun. 15, 9643 (2024)100.  K. Uchida, Nat. Mater. 21, 136 (2022)� ⃞Publisher’s note  Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Sarah J. Watzman  is an associate professor in the Department of Mechanical and Materials Engineering at the University of Cincinnati. She received her PhD degree at The Ohio State University in 2018. Her research focuses on understanding the interplay of thermal, electri-cal, and magnetic transport as a way to inform design of more energy-efficient solid-state devices, with a particular interest in topological materials. Watzman can be reached by email at  watzmasj@ucmail.uc.edu.Takashi Kikkawa  has been a team leader at the Advanced Science Research Center, Japan Atomic Energy Agency, since 2024. Previously, he was an assistant professor at Tohoku Univer-sity and The University of Tokyo, Japan, from 2018 to 2024. He received his PhD degree  from Tohoku University, Japan, in 2018.  His research interests include spin(calori)tronics, condensed-matter physics, and energy conver-sion. Kikkawa can be reached by email at  kikkawa.takashi@jaea.go.jp.http://arxiv.org/abs/2412.08853http://arxiv.org/abs/2412.08853https://arxiv.org/pdf/2505.00086http://arxiv.org/abs/2409.11108Utilizing magnetization and spin in thermoelectric applications924         MRS BULLETIN  •  VOLUME 50  •  August 2025  •  mrs.org/bulletinBrian Skinner  is an associate professor of physics at The Ohio State University. He received his PhD degree from the University of Minnesota in 2011. He held postdoctoral positions at Argonne National Laboratory and the Massachu-setts Institute of Technology before joining the faculty at Ohio State in 2020. He has wide-spread interests relating to dynamical and transport phenomena in many-body quantum systems. Skinner can be reached by email at skinner.352@osu.edu.Ken‑ichi Uchida  has been a Distinguished Group Leader of the Research Center for Mag-netic and Spintronic Materials at the National Institute for Materials Science (NIMS), Japan, since 2023 and professor of the Gradu-ate School of Frontier Science at The University of Tokyo, Japan, since 2024. Previously, he was an assistant/associate professor from 2012 to 2016 at Tohoku University, Japan, and group leader at NIMS. He has been leading the JST ERATO project and working mainly on spintron-ics and thermoelectrics. Uchida can be reached by email at UCHIDA.Kenichi@nims.go.jp. Utilizing magnetization and spin in thermoelectric applications Anchor 2 Introduction: Magneto-thermoelectric phenomena and their origins Magneto-thermoelectric transport phenomena Magnetic and spin origins of magneto-thermoelectric effects Review of material advances in magneto-thermoelectrics Anomalous Nernst effect (ANE) Topological materials Permanent magnets Amorphous materials SSE-induced ISHE Magnon-drag effects in metals Nonlinear effects driven by Berry curvature dipole Applications for magneto-thermoelectrics Magneto-thermoelectric figure of merit Device advantages and disadvantages of magneto-thermoelectrics Conclusion Acknowledgments  References