Iron-based binary ferromagnets for transverse thermoelectric conversion

Spin caloritronics in metallic superlattices

Spin caloritronics, a research field studying on the interconversion between a charge current (Jc) and a heat current (Jq) mediated by a spin current (Js) and/or magnetization (M), has attracted much attention not only for academic interest but also for practical applications. Newly discovered spin-caloritronic phenomena such as the spin Seebeck effect (SSE) have stimulated the renewed interest in the thermoelectric phenomena of a magnet, which have been known for a long time, e.g. the anomalous Nernst effect (ANE). These spin-caloritronic phenomena involving the SSE and the ANE have provided with a new direction for thermoelectric conversion exploitingJsand/orM. Importantly, the symmetry of ANE allows the thermoelectric conversion in the transverse configuration betweenJqandJc. Although the transverse configuration is totally different from the conventional longitudinal configuration based on the Seebeck effect and has many advantages, we are still facing several issues that need to be solved before developing practical applications. The primal issue is the improvement of conversion efficiency. In the case of ANE-based applications, a material with a large anomalous Nernst coefficient (SANE) is the key for solving the issue. This review article introduces the increase ofSANEcan be achieved by forming superlattice structures, which has been demonstrated for several kinds of materials combinations. The overall picture of studies on spin caloritronics is first surveyed. Then, we mention the pioneering work on the transverse thermoelectric conversion in superlattice structures, which was performed using Fe-based metallic superlattices, and show the recent studies for the Ni-based metallic superlattices and the ordered alloy-based metallic superlattices.

Large transverse thermoelectric effect induced by the mixed-dimensionality of Fermi surfaces

Transverse thermoelectric effect, the conversion of longitudinal heat current into transverse electric current, or vice versa, offers a promising energy harvesting technology. Materials with axis-dependent conduction polarity, known as p × n-type conductors or goniopolar materials, are potential candidate, because the non-zero transverse elements of thermopower tensor appear under rotational operation, though the availability is highly limited. Here, we report that a ternary metal LaPt2B with unique crystal structure exhibits axis-dependent thermopower polarity, which is driven by mixed-dimensional Fermi surfaces consisting of quasi-one-dimensional hole sheet with out-of-plane velocity and quasi-two-dimensional electron sheets with in-plane velocity. The ideal mixed-dimensional conductor LaPt2B exhibits an extremely large transverse Peltier conductivity up to ∣αyx∣ = 130 A K-1 m-1, and its transverse thermoelectric performance surpasses those of topological magnets utilizing the anomalous Nernst effect. These results thus manifest the mixed-dimensionality as a key property for efficient transverse thermoelectric conversion.

Direct-Contact Seebeck-Driven Transverse Magneto-Thermoelectric Generation in Magnetic/Thermoelectric Bilayers

Transverse thermoelectric generation converts temperature gradient in one direction into an electric field perpendicular to that direction and is expected to be a promising alternative in creating simple-structured thermoelectric modules that can avoid the challenging problems facing traditional Seebeck-effect-based modules. Recently, large transverse thermopower has been observed in closed circuits consisting of magnetic and thermoelectric materials, called the Seebeck-driven transverse magneto-thermoelectric generation (STTG). However, the closed-circuit structure complicates its broad applications. Here, STTG is realized in the simplest way to combine magnetic and thermoelectric materials, namely, by stacking a magnetic layer and a thermoelectric layer together to form a bilayer. The transverse thermopower is predicted to vary with changing layer thicknesses and peaks at a much larger value under an optimal thickness ratio. This behavior is verified in the experiment, through a series of samples prepared by depositing Fe-Ga alloy thin films of various thicknesses onto n-type Si substrates. The measured transverse thermopower reaches 15.2 ± 0.4 µV K-1, which is a fivefold increase from that of Fe-Ga alloy and much larger than the current room temperature record observed in Weyl semimetal Co2MnGa. The findings highlight the potential of combining magnetic and thermoelectric materials for transverse thermoelectric applications.

Measurement setup for Nernst and Seebeck effect at high temperatures and magnetic fields tested on elemental bismuth and full-Heusler compounds

In this work, a measurement setup to study the Seebeck and Nernst effect at high temperatures and high magnetic fields is introduced and discussed. The measurement system allows for simultaneous measurements of both thermoelectric effects up to 700 K and magnetic fields up to 12 T. Based on theoretical concepts, measurement equations are derived that counteract constant spurious offset voltages and, therefore, inhibit systematic errors in the measurement setup. The functionality is demonstrated on polycrystalline samples of elemental bismuth as well as various full-Heusler materials, exhibiting an anomalous Nernst effect. In all samples, the measured Seebeck and Nernst coefficients align excellently with the reported values. This allows future research to substantially extend the measured temperature and field intervals, commonly limited to temperatures below room temperature. For the first time, the thermoelectric and thermomagnetic properties of these materials are reported up to temperatures of 560 K.

Efficient Thermo-Spin Conversion in van der Waals Ferromagnet FeGaTe

Recent discovery of 2D van der Waals magnetic materials has spurred progress in developing advanced spintronic devices. A central challenge lies in enhancing the spin-conversion efficiency for building spin-logic or spin-memory devices. Here, the anomalous Hall and Nernst effects are systematically investigated to uncover significant spin-conversion effects in above-room-temperature van der Waals ferromagnet FeGaTe with perpendicular magnetic anisotropy. The anomalous Hall effect demonstrates an efficient electric spin-charge conversion with a notable spin Hall angle of over 6%. In addition, the anomalous Nernst effect produces a significant transverse voltage at room temperature without a magnetic field, displaying unique temperature dependence with a maximum transverse Seebeck coefficient of 440 nV K-1 and a Nernst angle of ≈62%. Such an innovative thermoelectric signal arises from the efficient thermo-spin conversion effect, where the up-spin and down-spin electrons move in opposite directions under a temperature gradient. The present study highlights the potential of FeGaTe to enhance thermoelectric devices through efficient thermo-spin conversion without the need for a magnetic field.

Abnormal thermally-stimulated dynamic organic phosphorescence

Dynamic luminescence behavior by external stimuli, such as light, thermal field, electricity, mechanical force, etc., endows the materials with great promise in optoelectronic applications. Upon thermal stimulus, the emission is inevitably quenched due to intensive non-radiative transition, especially for phosphorescence at high temperature. Herein, we report an abnormal thermally-stimulated phosphorescence behavior in a series of organic phosphors. As temperature changes from 198 to 343 K, the phosphorescence at around 479 nm gradually enhances for the model phosphor, of which the phosphorescent colors are tuned from yellow to cyan-blue. Furthermore, we demonstrate the potential applications of such dynamic emission for smart dyes and colorful afterglow displays. Our results would initiate the exploration of dynamic high-temperature phosphorescence for applications in smart optoelectronics. This finding not only contributes to an in-depth understanding of the thermally-stimulated phosphorescence, but also paves the way toward the development of smart materials for applications in optoelectronics.

Comparative Study of the Orientation and Order Effects on the Thermoelectric Performance of 2D and 3D Perovskites

Calcium titanium oxide has emerged as a highly promising material for optoelectronic devices, with recent studies suggesting its potential for favorable thermoelectric properties. However, current experimental observations indicate a low thermoelectric performance, with a significant gap between these observations and theoretical predictions. Therefore, this study employs a combined approach of experiments and simulations to thoroughly investigate the impact of structural and directional differences on the thermoelectric properties of two-dimensional (2D) and three-dimensional (3D) metal halide perovskites. Two-dimensional (2D) and three-dimensional (3D) metal halide perovskites constitute the focus of examination in this study, where an in-depth exploration of their thermoelectric properties is conducted via a comprehensive methodology incorporating simulations and experimental analyses. The non-equilibrium molecular dynamics simulation (NEMD) was utilized to calculate the thermal conductivity of the perovskite material. Thermal conductivities along both in-plane and out-plane directions of 2D perovskite were computed. The NEMD simulation results show that the thermal conductivity of the 3D perovskite is approximately 0.443 W/mK, while the thermal conductivities of the parallel and vertical oriented 2D perovskites increase with n and range from 0.158 W/mK to 0.215 W/mK and 0.289 W/mK to 0.309 W/mK, respectively. Hence, the thermal conductivity of the 2D perovskites is noticeably lower than the 3D ones. Furthermore, the parallel oriented 2D perovskites exhibit more effective blocking of heat transfer behavior than the perpendicular oriented ones. The experimental results reveal that the Seebeck coefficient of the 2D perovskites reaches 3.79 × 102 µV/K. However, the electrical conductivity of the 2D perovskites is only 4.55 × 10-5 S/cm, which is one order of magnitude lower than that of the 3D perovskites. Consequently, the calculated thermoelectric figure of merit for the 2D perovskites is approximately 1.41 × 10-7, slightly lower than that of the 3D perovskites.

Roll-to-Roll Printing of Anomalous Nernst Thermopile for Direct Sensing of Perpendicular Heat Flux

The anomalous Nernst effect (ANE) converts heat flux perpendicular to the plane into electricity, in sharp contrast with the Seebeck effect (SE), enabling mass production, large area, and flexibility of their devices through ordinary thin-film fabrication techniques. Heat flux sensors, one of the most promising applications of ANE, are powerful devices for evaluating heat flow and can lead to energy savings through efficient thermal management. In reality, however, SE caused by the in-plane heat flux is always superimposed on the measurement signal, making it difficult to evaluate the perpendicular heat flux. Here, ANE-type heat flux sensors that selectively detect a perpendicular heat flux are fabricated by adjusting the net Seebeck coefficient in their thermopile circuit with mass-producible roll-to-roll sputtering methods. The direct sensing of perpendicular heat flux using ANE-based flexible thermopiles, as well as their simple fabrication process, paves the way for the practical application of thin-film thermoelectric devices.

Polycrystalline bismuth nanowire networks for flexible longitudinal and transverse thermoelectrics

This paper reports on the preparation and the characterization of structural, electrical and thermoelectric properties of nanocomposite films formed from three-dimensional networks of polycrystalline bismuth (Bi) nanowires (NWs). The samples were fabricated by electrodeposition within polycarbonate (PC) templates with crossed cylindrical nanopores, yielding self-supported networks of Bi crossed nanowires (CNWs) with mean diameter values ranging from 23 nm to 230 nm. Temperature changes in electrical resistance and thermopower were studied by considering electric and thermal currents flowing in the plane of the films. While the values of the Seebeck coefficient are close to those of polycrystalline Bi for diameters greater than 100 nm, a progressive decrease in thermopower appears at smaller diameters, due to an increasing contribution of surface charge carriers as the diameter decreases. Transverse thermoelectricity based on the Nernst effect was also demonstrated on a network of Bi CNWs 230 nm in diameter. Such hierarchical architectures based on Bi CNWs are extremely robust, offering a reliable solution for the next generation of flexible thermoelectric devices.

Large Anomalous Nernst Effects at Room Temperature in Fe3 Pt Thin Films

Heat current in ferromagnets can generate a transverse electric voltage perpendicular to magnetization, known as anomalous Nernst effect (ANE). ANE originates intrinsically from the combination of large Berry curvature and density of states near the Fermi energy. It shows technical advantages over the conventional longitudinal Seebeck effect in converting waste heat to electricity due to its unique transverse geometry. However, materials showing giant ANE remain to be explored. Herein,  a large ANE thermopower of Syx ≈ 2 µV K-1 at room temperature in ferromagnetic Fe3 Pt epitaxial films is reported, which also show a giant transverse thermoelectric conductivity of αyx ≈ 4 A K-1  m-1 and a remarkable coercive field of 1300 Oe. The theoretical analysis reveals that the strong spin-orbit interaction in addition to the hybridization between Pt 5d and Fe 3d electrons leads to a series of distinct energy gaps and large Berry curvature in the Brillouin zone, which is the key for the large ANE. These results highlight the important roles of both Berry curvature and spin-orbit coupling in achieving large ANE at zero magnetic field, providing pathways to explore materials with giant transverse thermoelectric effect without an external magnetic field.

Berry curvature contributions of kagome-lattice fragments in amorphous Fe-Sn thin films

Amorphous semiconductors are widely applied to electronic and energy-conversion devices owing to their high performance and simple fabrication processes. The topological concept of the Berry curvature is generally ill-defined in amorphous solids, due to the absence of long-range crystalline order. Here, we demonstrate that the Berry curvature in the short-range crystalline order of kagome-lattice fragments effectively contributes to the anomalous electrical and magneto-thermoelectric properties in Fe-Sn amorphous films. The Fe-Sn films on glass substrates exhibit large anomalous Hall and Nernst effects comparable to those of the single crystals of topological semimetals Fe₃Sn₂ and Fe₃Sn. With modelling, we reveal that the Berry curvature contribution in the amorphous state likely originates from randomly distributed kagome-lattice fragments. This microscopic interpretation sheds light on the topology of amorphous materials, which may lead to the realization of functional topological amorphous electronic devices.

Anomalous Hall Conductivity and Nernst Effect of the Ideal Weyl Semimetallic Ferromagnet EuCd2 As2

Weyl semimetal is a unique topological phase with topologically protected band crossings in the bulk and robust surface states called Fermi arcs. Weyl nodes always appear in pairs with opposite chiralities, and they need to have either time-reversal or inversion symmetry broken. When the time-reversal symmetry is broken the minimum number of Weyl points (WPs) is two. If these WPs are located at the Fermi level, they form an ideal Weyl semimetal (WSM). In this study, intrinsic ferromagnetic (FM) EuCd₂ As₂ are grown, predicted to be an ideal WSM and studied its electronic structure by angle-resolved photoemission spectroscopy, and scanning tunneling microscopy which agrees closely with the first principles calculations. Moreover, anomalous Hall conductivity and Nernst effect are observed, resulting from the non-zero Berry curvature, and the topological Hall effect arising from changes in the band structure caused by spin canting produced by magnetic fields. These findings can help realize several exotic quantum phenomena in inorganic topological materials that are otherwise difficult to assess because of the presence of multiple pairs of Weyl nodes.

Visualization of Tunable Weyl Line in A-A Stacking Kagome Magnets

Kagome magnets provide a fascinating platform for a plethora of topological quantum phenomena, in which the delicate interplay between frustrated crystal structure, magnetization, and spin-orbit coupling (SOC) can engender highly tunable topological states. Here, utilizing angle-resolved photoemission spectroscopy, the Weyl lines are directly visualized with strong out-of-plane dispersion in the A-A stacked kagome magnet GdMn₆ Sn₆ . Remarkably, the Weyl lines exhibit a strong magnetization-direction-tunable SOC gap and binding energy tunability after substituting Gd with Tb and Li, respectively. These results not only illustrate the magnetization direction and valence counting as efficient tuning knobs for realizing and controlling distinct 3D topological phases, but also demonstrate AMn₆ Sn₆ (A = rare earth, or Li, Mg, or Ca) as a versatile material family for exploring diverse emergent topological quantum responses.

Large Magneto-Transverse and Longitudinal Thermoelectric Effects in the Magnetic Weyl Semimetal TbPtBi

Magnetic topological semimetals provide new opportunities for power generation and solid-state cooling based on thermoelectric (TE) effect. The interplay between magnetism and nontrivial band topology prompts the magnetic topological semimetals to yield strong transverse TE effect, while the longitudinal TE performance is usually poor. Herein, it is demonstrated that the magnetic Weyl semimetal TbPtBi has high value for both transverse and longitudinal thermopower with large power factor (PF). At 300 K and 13.5 Tesla, the transverse thermopower and PF reach up to 214 µV K^-1 and 35 µW cm^-1  K^-2 , respectively, which are comparable to those of state-of-the-art TE materials. Combining first-principles calculations, longitudinal magnetoresistance and planar Hall resistance measurements, and two-band model fitting, the large transverse thermopower and PF are attributed to both bipolar effect and large Hall angle. Moreover, the imperfectly compensated charge carriers and large transverse magnetoresistance induce the maximum magneto-longitudinal thermopower of 251 µV K^-1 with a PF of 24 µW cm^-1  K^-2 at 150 K and 13.5 Tesla, which is two times higher than that at zero magnetic field. This work demonstrates the great potential of topological semimetals for TEs and offers a new excellent candidate for magneto-TEs.

Tunable anomalous Hall and Nernst effects in MM'X compounds

Based on first-principles calculations, the anomalous Hall conductivity (AHC) and anomalous Nernst conductivities (ANCs) of the XMnP (X = Ti, Zr, Hf) compounds are evaluated, and the possibility to tailor such properties in compounds susceptible to changing the magnetization directions is also investigated. We observe large changes in the calculated AHC and ANC for different magnetization directions that are originating from changes in the band structure all over the whole Brillouin zone. Our study gives a promising clue on engineering magnetic intermetallic compounds for tunable transverse thermoelectric applications.

Sm-Co-based amorphous alloy films for zero-field operation of transverse thermoelectric generation

Transverse thermoelectric generation using magnetic materials is essential to develop active thermal engineering technologies, for which the improvements of not only the thermoelectric output but also applicability and versatility are required. In this study, using combinatorial material science and lock-in thermography technique, we have systematically investigated the transverse thermoelectric performance of Sm-Co-based alloy films. The high-throughput material investigation revealed the best Sm-Co-based alloys with the large anomalous Nernst effect (ANE) as well as the anomalous Ettingshausen effect (AEE). In addition to ANE/AEE, we discovered unique and superior material properties in these alloys: the amorphous structure, low thermal conductivity, and large in-plane coercivity and remanent magnetization. These properties make it advantageous over conventional materials to realize heat flux sensing applications based on ANE, as our Sm-Co-based films can generate thermoelectric output without an external magnetic field. Importantly, the amorphous nature enables the fabrication of these films on various substrates including flexible sheets, making the large-scale and low-cost manufacturing easier. Our demonstration will provide a pathway to develop flexible transverse thermoelectric devices for smart thermal management.

Machine Learning for Harnessing Thermal Energy: From Materials Discovery to System Optimization

Recent advances in machine learning (ML) have impacted research communities based on statistical perspectives and uncovered invisibles from conventional standpoints. Though the field is still in the early stage, this progress has driven the thermal science and engineering communities to apply such cutting-edge toolsets for analyzing complex data, unraveling abstruse patterns, and discovering non-intuitive principles. In this work, we present a holistic overview of the applications and future opportunities of ML methods on crucial topics in thermal energy research, from bottom-up materials discovery to top-down system design across atomistic levels to multi-scales. In particular, we focus on a spectrum of impressive ML endeavors investigating the state-of-the-art thermal transport modeling (density functional theory, molecular dynamics, and Boltzmann transport equation), different families of materials (semiconductors, polymers, alloys, and composites), assorted aspects of thermal properties (conductivity, emissivity, stability, and thermoelectricity), and engineering prediction and optimization (devices and systems). We discuss the promises and challenges of current ML approaches and provide perspectives for future directions and new algorithms that could make further impacts on thermal energy research.

High-Power-Density Energy-Harvesting Devices Based on the Anomalous Nernst Effect of Co/Pt Magnetic Multilayers

The anomalous Nernst effect (ANE) is a thermomagnetic phenomenon with potential applications in thermal energy harvesting. While many recent works studied the approaches to increase the ANE coefficient of materials, relatively little effort was devoted to increasing the power supplied by the effect. Here, we demonstrate a nanofabricated device with record power density generated by the ANE. To accomplish this, we fabricate micrometer-sized devices in which the thermal gradient is 3 orders of magnitude higher than conventional macroscopic devices. In addition, we use Co/Pt multilayers, a system characterized by a high ANE thermopower (∼1 μV/K), low electrical resistivity, and perpendicular magnetic anisotropy. These innovations allow us to obtain power densities of around 13 ± 2 W/cm³. We believe that this design may find uses in harvesting wasted energy, e.g., in electronic devices.

Disorder- and Topology-Enhanced Fully Spin-Polarized Currents in Nodal Chain Spin-Gapless Semimetals

Recently discovered high-quality nodal chain spin-gapless semimetals MF_{3} (M=Pd, Mn) feature an ultraclean nodal chain in the spin up channel residing right at the Fermi level and displaying a large spin gap leading to a 100% spin polarization of transport properties. Here, we investigate both intrinsic and extrinsic contributions to anomalous and spin transport in this class of materials. The dominant intrinsic origin is found to originate entirely from the gapped nodal chains without the entanglement of any other trivial bands. The side-jump mechanism is predicted to be negligibly small, but intrinsic skew scattering enhances the intrinsic Hall and Nernst signals significantly, leading to large values of respective conductivities. Our findings open a new material platform for exploring strong anomalous and spin transport properties in magnetic topological semimetals.

Observation of a linked-loop quantum state in a topological magnet

Quantum phases can be classified by topological invariants, which take on discrete values capturing global information about the quantum state^1-13. Over the past decades, these invariants have come to play a central role in describing matter, providing the foundation for understanding superfluids⁵, magnets^6,7, the quantum Hall effect^3,8, topological insulators^9,10, Weyl semimetals^11-13 and other phenomena. Here we report an unusual linking-number (knot theory) invariant associated with loops of electronic band crossings in a mirror-symmetric ferromagnet^14-20. Using state-of-the-art spectroscopic methods, we directly observe three intertwined degeneracy loops in the material's three-torus, T³, bulk Brillouin zone. We find that each loop links each other loop twice. Through systematic spectroscopic investigation of this linked-loop quantum state, we explicitly draw its link diagram and conclude, in analogy with knot theory, that it exhibits the linking number (2, 2, 2), providing a direct determination of the invariant structure from the experimental data. We further predict and observe, on the surface of our samples, Seifert boundary states protected by the bulk linked loops, suggestive of a remarkable Seifert bulk-boundary correspondence. Our observation of a quantum loop link motivates the application of knot theory to the exploration of magnetic and superconducting quantum matter.

Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn6Sn6, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

Progress and prospects in magnetic topological materials

Magnetic topological materials represent a class of compounds with properties that are strongly influenced by the topology of their electronic wavefunctions coupled with the magnetic spin configuration. Such materials can support chiral electronic channels of perfect conduction, and can be used for an array of applications, from information storage and control to dissipationless spin and charge transport. Here we review the theoretical and experimental progress achieved in the field of magnetic topological materials, beginning with the theoretical prediction of the quantum anomalous Hall effect without Landau levels, and leading to the recent discoveries of magnetic Weyl semimetals and antiferromagnetic topological insulators. We outline recent theoretical progress that has resulted in the tabulation of, for the first time, all magnetic symmetry group representations and topology. We describe several experiments realizing Chern insulators, Weyl and Dirac magnetic semimetals, and an array of axionic and higher-order topological phases of matter, and we survey future perspectives.

Exchange-biased topological transverse thermoelectric effects in a Kagome ferrimagnet

Kagome metal TbMn₆Sn₆ was recently discovered to be a ferrimagnetic topological Dirac material by scanning tunneling microscopy/spectroscopy measurements. Here, we report the observation of large anomalous Nernst effect and anomalous thermal Hall effect in this compound. The anomalous transverse transport is consistent with the Berry curvature contribution from the massive Dirac gaps in the 3D momentum space as demonstrated by our first-principles calculations. Furthermore, the transverse thermoelectric transport exhibits asymmetry with respect to the applied magnetic field, i.e., an exchange-bias behavior. Together, these features place TbMn₆Sn₆ as a promising system for the outstanding thermoelectric performance based on anomalous Nernst effect.

Kagome metal TbMn₆Sn₆ was recently discovered to be a ferrimagnetic topological Dirac material. Here, the authors observe anomalous Nernst effect and anomalous thermal Hall effect which exhibit asymmetry with respect to the magnetic field.

Giant anomalous Nernst signal in the antiferromagnet YbMnBi2

A large anomalous Nernst effect (ANE) is crucial for thermoelectric energy conversion applications because the associated unique transverse geometry facilitates module fabrication. Topological ferromagnets with large Berry curvatures show large ANEs; however, they face drawbacks such as strong magnetic disturbances and low mobility due to high magnetization. Herein, we demonstrate that YbMnBi₂, a canted antiferromagnet, has a large ANE conductivity of ~10 A m^-1 K^-1 that surpasses large values observed in other ferromagnets (3-5 A m^-1 K^-1). The canted spin structure of Mn guarantees a non-zero Berry curvature, but generates only a weak magnetization three orders of magnitude lower than that of general ferromagnets. The heavy Bi with a large spin-orbit coupling enables a large ANE and low thermal conductivity, whereas its highly dispersive p_x/y orbitals ensure low resistivity. The high anomalous transverse thermoelectric performance and extremely small magnetization make YbMnBi₂ an excellent candidate for transverse thermoelectrics.

Geometrical Optimization and Transverse Thermoelectric Performances of Fe/Bi2Te2.7Se0.3 Artificially Tilted Multilayer Thermoelectric Devices

Transverse thermoelectric performance of the artificially tilted multilayer thermoelectric device (ATMTD) is very difficult to be optimized, due to the large degree freedom in device design. Herein, an ATMTD with Fe and Bi₂Te_2.7Se_0.3 (BTS) materials was proposed and fabricated. Through high-throughput calculation of Fe/BTS ATMTD, a maximum of calculated transverse thermoelectric figure of merit of 0.15 was obtained at a thickness ratio of 0.49 and a tilted angle of 14°. For fabricated ATMTD, the whole Fe/BTS interface is closely connected with a slight interfacial reaction. The optimizing Fe/BTS ATMTD with 12 mm in length, 6 mm in width and 4 mm in height has a maximum output power of 3.87 mW under a temperature difference of 39.6 K. Moreover the related power density per heat-transfer area reaches 53.75 W·m⁻². This work demonstrates the performance of Fe/BTS ATMTD, allowing a better understanding of the potential in micro-scaled devices.

Large anomalous Nernst effect and nodal plane in an iron-based kagome ferromagnet

Anomalous Nernst effect (ANE), converting a heat flow to transverse electric voltage, originates from the Berry phase of electronic wave function near the Fermi energy E_F. Thus, the ANE provides a sensitive probe to detect a topological state that produces large Berry curvature. In addition, a magnet that exhibits a large ANE using low-cost and safe elements will be useful to develop a novel energy harvesting technology. Here, we report our observation of a high ANE exceeding 3 microvolts per kelvin above room temperature in the kagome ferromagnet Fe₃Sn with the Curie temperature of 760 kelvin. Our theoretical analysis clarifies that a “nodal plane” produces a flat hexagonal frame with strongly enhanced Berry curvature, resulting in the large ANE. Our discovery of the large ANE in Fe₃Sn opens the path for the previously unexplored functionality of flat degenerate electronic states and for developing flexible film thermopile and heat current sensors.

An [FeIII30] molecular metal oxide

Dissolution of FeBr₃ in a mixture of acetonitrile and 3,4-lutidine in the presence of an amine results in the formation of an [Fe₃₀] molecular metal oxide containing alternating layers of tetrahedral and octahedral Fe^III ions. Mass spectrometry suggests the cluster is formed quickly and remains stable in solution, while magnetic measurements and DFT calculations reveal competing antiferromagnetic exchange interactions.

Signatures of Weyl Fermion Annihilation in a Correlated Kagome Magnet

The manipulation of topological states in quantum matter is an essential pursuit of fundamental physics and next-generation quantum technology. Here we report the magnetic manipulation of Weyl fermions in the kagome spin-orbit semimetal Co_{3}Sn_{2}S_{2}, observed by high-resolution photoemission spectroscopy. We demonstrate the exchange collapse of spin-orbit-gapped ferromagnetic Weyl loops into paramagnetic Dirac loops under suppression of the magnetic order. We further observe that topological Fermi arcs disappear in the paramagnetic phase, suggesting the annihilation of exchange-split Weyl points. Our findings indicate that magnetic exchange collapse naturally drives Weyl fermion annihilation, opening new opportunities for engineering topology under correlated order parameters.

Colossal angular magnetoresistance in ferrimagnetic nodal-line semiconductors

Efficient magnetic control of electronic conduction is at the heart of spintronic functionality for memory and logic applications^1,2. Magnets with topological band crossings serve as a good material platform for such control, because their topological band degeneracy can be readily tuned by spin configurations, dramatically modulating electronic conduction^3-10. Here we propose that the topological nodal-line degeneracy of spin-polarized bands in magnetic semiconductors induces an extremely large angular response of magnetotransport. Taking a layered ferrimagnet, Mn₃Si₂Te₆, and its derived compounds as a model system, we show that the topological band degeneracy, driven by chiral molecular orbital states, is lifted depending on spin orientation, which leads to a metal-insulator transition in the same ferrimagnetic phase. The resulting variation of angular magnetoresistance with rotating magnetization exceeds a trillion per cent per radian, which we call colossal angular magnetoresistance. Our findings demonstrate that magnetic nodal-line semiconductors are a promising platform for realizing extremely sensitive spin- and orbital-dependent functionalities.

Large magnon-induced anomalous Nernst conductivity in single-crystal MnBi

Thermoelectric modules are a promising approach to energy harvesting and efficient cooling. In addition to the longitudinal Seebeck effect, transverse devices utilizing the anomalous Nernst effect (ANE) have recently attracted interest. For high conversion efficiency, it is required that the material have a large ANE thermoelectric power and low electrical resistance, which lead to the conductivity of the ANE. ANE is usually explained in terms of intrinsic contributions from Berry curvature. Our observations suggest that extrinsic contributions also matter. Studying single-crystal manganese-bismuth (MnBi), we find a high ANE thermopower (∼10 μV/K) under 0.6 T at 80 K, and a transverse thermoelectric conductivity of over 40 A/Km. With insight from theoretical calculations, we attribute this large ANE predominantly to a new advective magnon contribution arising from magnon-electron spin-angular momentum transfer. We propose that introducing a large spin-orbit coupling into ferromagnetic materials may enhance the ANE through the extrinsic contribution of magnons.

Transition metal nitrides and their mixed crystals for spintronics

Anti-perovskite transition metal nitrides exhibit a variety of magnetic properties-such as ferromagnetic, ferrimagnetic, and paramagnetic-depending on the 3dtransition metal. Fe₄N and Co₄N are ferromagnetic at room temperature (RT), and the minority spins play a dominant role in the electrical transport properties. However, Mn₄N is ferrimagnetic at RT and exhibits a perpendicular magnetic anisotropy caused by tensile strain. Around the magnetic compensation in Mn₄N induced by impurity doping, researchers have demonstrated ultrafast current-induced domain wall motion reaching 3000 m s^-1at RT, making switching energies lower and switching speed higher compared with Mn₄N. In this review article, we start with individual magnetic nitrides-such as Fe₄N, Co₄N, Ni₄N, and Mn₄N; describe the nitrides' features; and then discuss compounds such as Fe_4-xA_xN (A = Co, Ni, and Mn) and Mn_4-xB_xN (B = Ni, Co, and Fe) to evaluate nitride properties from the standpoint of spintronics applications. We pay particular attention to preferential sites of A and B atoms in these compounds, based on x-ray absorption spectroscopy and x-ray magnetic circular dichroism.

Large Anomalous Hall and Nernst Effects in High Curie-Temperature Iron-Based Heusler Compounds

The interplay between topology and magnetism has recently sparked the frontier studies of magnetic topological materials that exhibit intriguing anomalous Hall and Nernst effects owning to the large intrinsic Berry curvature (BC). To better understand the anomalous quantum transport properties of these materials and their implications for future applications such as electronic and thermoelectric devices, it is crucial to discover more novel material platforms for performing anomalous transverse transport studies. Here, it is experimentally demonstrated that low-cost Fe-based Heusler compounds exhibit large anomalous Hall and Nernst effects. An anomalous Hall conductivity of 250-750 S cm-1 and Nernst thermopower of above 2 µV K-1 are observed near room temperature. The positive effect of anti-site disorder on the anomalous Hall transport is revealed. Considering the very high Curie temperature (nearly 1000 K), larger Nernst thermopowers at high temperatures are expected owing to the existing magnetic order and the intrinsic BC. This work provides a background for developing low-cost Fe-based Heusler compounds as a new material platform for anomalous transport studies and applications, in particular, near and above room temperature.

Leveraging bipolar effect to enhance transverse thermoelectricity in semimetal Mg2Pb for cryogenic heat pumping

Toward high-performance thermoelectric energy conversion, the electrons and holes must work jointly like two wheels of a cart: if not longitudinally, then transversely. The bipolar effect — the main performance restriction in the traditional longitudinal thermoelectricity, can be manipulated to be a performance enhancer in the transverse thermoelectricity. Here, we demonstrate this idea in semimetal Mg₂Pb. At 30 K, a giant transverse thermoelectric power factor as high as 400 μWcm⁻¹K⁻² is achieved, a 3 orders-of-magnitude enhancement than the longitudinal configuration. The resultant specific heat pumping power is ~ 1 Wg⁻¹, higher than those of existing techniques at 10~100 K. A large number of semimetals and narrow-gap semiconductors making poor longitudinal thermoelectrics due to severe bipolar effect are thus revived to fill the conspicuous gap of thermoelectric materials for solid-state applications.

Heat pumping is in high demand at cryogenic temperature, but whether thermoelectricity can take on cryogenic heat pumping is an open question. Here, the authors answer this question by leveraging bipolar effect to enhance transverse thermoelectricity in semimetal Mg₂Pb for cryogenic heat pumping.

Phase equilibria among η-Fe2Al5 and its higher-ordered phases

Phase equilibria among the η-Fe₂Al₅ phase and its higher-ordered phases with the η framework structure were determined experimentally. The solubility range of the η phase at elevated temperature does not differ remarkably from that in previous studies, but this phase is found to undergo complicated phase transformations upon cooling. Four phases are present, namely η', η", η"' and η ^m, with higher-order atomic orderings in the c-axis chain sites of the orthorhombic crystal structure of the parent η phase. The η" and η"' phases form on the Al-poor and Al-rich sides, respectively, in equilibrium with the ζ-FeAl₂ phase below ~415°C and θ-Fe₄Al₁₃ phase below ~405°C. The η' and η ^m phases become stable below 312°C and 343°C with the peritectoid reactions η' → η ^m + η"' and η ^m → η + η", respectively. The η phase is not stable below 331°C with the eutectoid reaction of η ^m + η"' → η. On the basis of these findings, we unraveled the phase equilibria among the η-Fe₂Al₅ phase and its higher-ordered phases with the η framework structure.

Magneto-optical design of anomalous Nernst thermopile

The introduction of spin caloritronics into thermoelectric conversion has paved a new path for versatile energy harvesting and heat sensing technologies. In particular, thermoelectric generation based on the anomalous Nernst effect (ANE) is an appealing approach as it shows considerable potential to realize efficient, large-area, and flexible use of heat energy. To make ANE applications viable, not only the improvement of thermoelectric performance but also the simplification of device structures is essential. Here, we demonstrate the construction of an anomalous Nernst thermopile with a substantially enhanced thermoelectric output and simple structure comprising a single ferromagnetic material. These improvements are achieved by combining the ANE with the magneto-optical recording technique called all-optical helicity-dependent switching of magnetization. Our thermopile consists only of Co/Pt multilayer wires arranged in a zigzag configuration, which simplifies microfabrication processes. When the out-of-plane magnetization of the neighboring wires is reversed alternately by local illumination with circularly polarized light, the ANE-induced voltage in the thermopile shows an order of magnitude enhancement, confirming the concept of a magneto-optically designed anomalous Nernst thermopile. The sign of the enhanced ANE-induced voltage can be controlled reversibly by changing the light polarization. The engineering concept demonstrated here promotes effective utilization of the characteristics of the ANE and will contribute to realizing its thermoelectric applications.

Engineering new limits to magnetostriction through metastability in iron-gallium alloys

Magnetostrictive materials transduce magnetic and mechanical energies and when combined with piezoelectric elements, evoke magnetoelectric transduction for high-sensitivity magnetic field sensors and energy-efficient beyond-CMOS technologies. The dearth of ductile, rare-earth-free materials with high magnetostrictive coefficients motivates the discovery of superior materials. Fe_1-xGa_x alloys are amongst the highest performing rare-earth-free magnetostrictive materials; however, magnetostriction becomes sharply suppressed beyond x = 19% due to the formation of a parasitic ordered intermetallic phase. Here, we harness epitaxy to extend the stability of the BCC Fe_1-xGa_x alloy to gallium compositions as high as x = 30% and in so doing dramatically boost the magnetostriction by as much as 10x relative to the bulk and 2x larger than canonical rare-earth based magnetostrictors. A Fe_1-xGa_x - [Pb(Mg_1/3Nb_2/3)O₃]_0.7-[PbTiO₃]_0.3 (PMN-PT) composite magnetoelectric shows robust 90° electrical switching of magnetic anisotropy and a converse magnetoelectric coefficient of 2.0 × 10^-5 s m^-1. When optimally scaled, this high coefficient implies stable switching at ~80 aJ per bit.

A Monomaterial Nernst Thermopile with Hermaphroditic Legs

A large transverse thermoelectric response, known as the anomalous Nernst effect (ANE) has been recently observed in several topological magnets. Building a thermopile employing this effect has been the subject of several recent propositions. Here, a thermopile is designed and built with an array of tilted adjacent crystals of Mn₃ Sn. The design employs a single material and replaces pairs of P and N thermocouples of the traditional design with hermaphroditic legs. The design exploits the large lag angle between the applied field and the magnetization, which is attributed to the interruption of magnetic octupoles at the edge of the xy-plane. Eliminating extrinsic contact between the legs will boost the efficiency, simplify the process, and pave the way for a new generation of thermopiles.

Seebeck-driven transverse thermoelectric generation

When a temperature gradient is applied to a closed circuit comprising two different conductors, a charge current is generated via the Seebeck effect¹. Here, we utilize the Seebeck-effect-induced charge current to drive 'transverse' thermoelectric generation, which has great potential for energy harvesting and heat sensing applications owing to the orthogonal geometry of the heat-to-charge-current conversion^2-9. We found that, in a closed circuit comprising thermoelectric and magnetic materials, artificial hybridization of the Seebeck effect into the anomalous Hall effect¹⁰ enables transverse thermoelectric generation with a similar symmetry to the anomalous Nernst effect^11-27. Surprisingly, the Seebeck-effect-driven transverse thermopower can be several orders of magnitude larger than the anomalous-Nernst-effect-driven thermopower, which is clearly demonstrated by our experiments using Co₂MnGa/Si hybrid materials. The unconventional approach could be a breakthrough in developing applications of transverse thermoelectric generation.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Anomalous transport due to Weyl fermions in the chiral antiferromagnets Mn3X, X = Sn, Ge

The recent discoveries of strikingly large zero-field Hall and Nernst effects in antiferromagnets Mn₃X (X = Sn, Ge) have brought the study of magnetic topological states to the forefront of condensed matter research and technological innovation. These effects are considered fingerprints of Weyl nodes residing near the Fermi energy, promoting Mn₃X (X = Sn, Ge) as a fascinating platform to explore the elusive magnetic Weyl fermions. In this review, we provide recent updates on the insights drawn from experimental and theoretical studies of Mn₃X (X = Sn, Ge) by combining previous reports with our new, comprehensive set of transport measurements of high-quality Mn₃Sn and Mn₃Ge single crystals. In particular, we report magnetotransport signatures specific to chiral anomalies in Mn₃Ge and planar Hall effect in Mn₃Sn, which have not yet been found in earlier studies. The results summarized here indicate the essential role of magnetic Weyl fermions in producing the large transverse responses in the absence of magnetization.

The large anomalous Hall (AHE) and anomalous Nernst effects (ANE) in antiferromagnets Mn₃Sn/Mn₃Ge are considered fingerprints of Weyl nodes residing near the Fermi energy. Here, the authors review the results from previous studies combining with new transport measurements on Mn₃Sn/Mn₃Ge single crystals, suggesting the essential role of magnetic Weyl fermions in explaining the AHE and ANE.

Prototype fabrication and performance evaluation of a thermoelectric module operating with the Nernst effect

The Nernst effect generates a voltage transverse to the temperature gradient in the magnetic field. Although the Nernst effect has the potential to realize novel devices in the field of thermoelectric generators and sensors, thermoelectric modules that operate with the Nernst effect have not yet been implemented. Therefore, in this study, a thermoelectric module utilizing the Nernst effect was developed as a prototype, and its performance was evaluated to identify technical issues. The proposed module is fabricated by arranging four rectangular bars of a BiSb-based sintered alloy on an AlN substrate and connecting all the bars in series with Cu plates. As a result of the measurement, when the magnetic field was 5 T, an output power of 0.48 mW was obtained with a temperature difference of 149 K, and a temperature difference of 82 mK occurred as a cooling operation with an applied electrical current of 100 mA.

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Thermoelectric module operating with the Nernst effect is developed as a prototype

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Power density of 86.7 μW/cm² is obtained with a temperature difference of 149 K

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Temperature difference of 82 mK occurs as a cooling operation

Transport phenomena in spin caloritronics

The interconversion between spin, charge, and heat currents is being actively studied from the viewpoints of both fundamental physics and thermoelectric applications in the field of spin caloritronics. This field is a branch of spintronics, which has developed rapidly since the discovery of the thermo-spin conversion phenomenon called the spin Seebeck effect. In spin caloritronics, various thermo-spin conversion phenomena and principles have subsequently been discovered and magneto-thermoelectric effects, thermoelectric effects unique to magnetic materials, have received renewed attention with the advances in physical understanding and thermal/thermoelectric measurement techniques. However, the existence of various thermo-spin and magneto-thermoelectric conversion phenomena with similar names may confuse non-specialists. Thus, in this Review, the basic behaviors, spin-charge-heat current conversion symmetries, and functionalities of spin-caloritronic phenomena are summarized, which will help new entrants to learn fundamental physics, materials science, and application studies in spin caloritronics.

Advanced Thermoelectric Design: From Materials and Structures to Devices

The long-standing popularity of thermoelectric materials has contributed to the creation of various thermoelectric devices and stimulated the development of strategies to improve their thermoelectric performance. In this review, we aim to comprehensively summarize the state-of-the-art strategies for the realization of high-performance thermoelectric materials and devices by establishing the links between synthesis, structural characteristics, properties, underlying chemistry and physics, including structural design (point defects, dislocations, interfaces, inclusions, and pores), multidimensional design (quantum dots/wires, nanoparticles, nanowires, nano- or microbelts, few-layered nanosheets, nano- or microplates, thin films, single crystals, and polycrystalline bulks), and advanced device design (thermoelectric modules, miniature generators and coolers, and flexible thermoelectric generators). The outline of each strategy starts with a concise presentation of their fundamentals and carefully selected examples. In the end, we point out the controversies, challenges, and outlooks toward the future development of thermoelectric materials and devices. Overall, this review will serve to help materials scientists, chemists, and physicists, particularly students and young researchers, in selecting suitable strategies for the improvement of thermoelectrics and potentially other relevant energy conversion technologies.