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Iron-based binary ferromagnets for transverse thermoelectric conversion

An Author Correction to this article was published on 12 August 2020

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Thermoelectric generation using the anomalous Nernst effect (ANE) has great potential for application in energy harvesting technology because the transverse geometry of the Nernst effect should enable efficient, large-area and flexible coverage of a heat source. For such applications to be viable, substantial improvements will be necessary not only for their performance but also for the associated material costs, safety and stability. In terms of the electronic structure, the anomalous Nernst effect (ANE) originates from the Berry curvature of the conduction electrons near the Fermi energy1,2. To design a large Berry curvature, several approaches have been considered using nodal points and lines in momentum space3,4,5,6,7,8,9,10. Here we perform a high-throughput computational search and find that 25 percent doping of aluminium and gallium in alpha iron, a naturally abundant and low-cost element, dramatically enhances the ANE by a factor of more than ten, reaching about 4 and 6 microvolts per kelvin at room temperature, respectively, close to the highest value reported so far. The comparison between experiment and theory indicates that the Fermi energy tuning to the nodal web—a flat band structure made of interconnected nodal lines—is the key for the strong enhancement in the transverse thermoelectric coefficient, reaching a value of about 5 amperes per kelvin per metre with a logarithmic temperature dependence. We have also succeeded in fabricating thin films that exhibit a large ANE at zero field, which could be suitable for designing low-cost, flexible microelectronic thermoelectric generators11,12,13.

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Fig. 1: Transverse thermoelectric conversion, iron compounds and a nodal web.
Fig. 2: Large anomalous Nernst and Hall effects of Fe3X.
Fig. 3: Giant transverse thermoelectric conductivity for Fe3X.
Fig. 4: Evidence for the nodal web structure.

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Data availability

The data that support the plots within this paper and the other findings of this study are available from the corresponding author upon reasonable request.

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We thank T. Tsujikawa for assistance with thin-film fabrication. This work is partially supported by CREST (JPMJCR18T3), New Energy and Industrial Technology Development Organization (NEDO), PRESTO (JPMJPR15N5), Japan Science and Technology Agency, by Grants-in-Aids for Scientific Research on Innovative Areas (JP15H05882 and JP15H05883) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan, and by Grants-in-Aid for Scientific Research (JP16H02209, JP16H06345, JP19H00650) from the Japanese Society for the Promotion of Science (JSPS). The work at the Institute for Quantum Matter, an Energy Frontier Research Center, was funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under award DE-SC0019331. The work for first-principles calculations was supported in part by JSPS Grant-in-Aid for Scientific Research on Innovative Areas (JP18H04481 and JP19H05825) and by MEXT as a social and scientific priority issue (Creation of new functional devices and high-performance materials to support next-generation industries) to be tackled by using post-K computer (hp180206 and hp190169). The use of the facilities of the Materials Design and Characterization Laboratory at the Institute for Solid State Physics, The University of Tokyo, is acknowledged.

Author information

Authors and Affiliations



A.S., S. Minami, T.K., T.C. and T.H. contributed equally to this work. S.N. and R.A. conceived the project. S.N. planned the experiments. T.K. performed the high-throughput computational search. T.C. and Y.W. worked on the single-crystal growth and the preparation of samples. A.S., T.C. and Y.W. carried out the transport and magnetization measurements and analysed the data. T.H. and S. Miwa fabricated the thin film and performed its structural and chemical analyses and transport measurement. S. Minami, T.K., F.I., T.N., M.H. and R.A. performed the first-principles calculations. D.S.-H. performed chemical analyses and took the electron diffraction image. S.N., R.A., A.S., S. Minami, T.K., T.H. and F.I wrote the paper. All authors discussed the results and commented on the manuscript.

Corresponding author

Correspondence to Satoru Nakatsuji.

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Peer review information Nature thanks Ernst Bauer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Evidence for the D03 structure of Fe3X.

a, b, XRD pattern for Fe3Ga (a) and Fe3Al (b) obtained by Cu-Kα radiation (λ = 1.5401 Å) at room temperature. The solid circles and the solid line (red) represent the experimental results and the Rietveld refinement fit, respectively. The final weighted and expected R indicators and goodness-of-fit indicator S are RWP = 2.34%, Re = 1.49% and S = 1.55 for Fe3Ga and RWP = 1.91%, Re = 1.27% and S = 1.48 for Fe3Al, respectively. Vertical bars (green) below the curves indicate the major peak positions calculated for D03 Fe3Ga and Fe3Al, which are more than 1% of the main peak. The lower curve (orange) represents the difference between the experimental result and the Rietveld refinement. I, intensity. c, Selected area electron diffraction pattern for our single crystals of Fe3Ga (left) and Fe3Al (right) taken from the [110] plane.

Extended Data Fig. 2 Evidence for D03 structure of Fe3Ga and Fe3Al thin films.

a, Room temperature spectra obtained by XRD 2θ/ω-scans for the Fe3X thin films on an MgO substrate and the MgO substrate itself. The theoretical simulation patterns for the D03 Fe3Ga and Fe3Al structures are presented at the bottom. b, φ-scan patterns of the {202} planes of the Fe3Ga and Fe3Al layers, and the MgO substrate. c, 2θ/ω-scan patterns for the (111) plane of the Fe3Ga and Fe3Al thin-film layers.

Extended Data Fig. 3 ANE of Fe3X and experimental setup for both bulk and thin films.

a, Magnetic field dependence of the ANE obtained for the Fe3X thin films (50 nm) and the α-Fe thin film (50 nm) using the in-plane temperature gradient. b, Schematic of the experimental setup for the ANE measurement using the in-plane temperature gradient. c, Schematic of the experimental setup for the ANE measurement using the out-of-plane temperature gradient.

Extended Data Fig. 4 Schematic of the μ-TEG based on the ANE.

The thermopile consists of a square-shaped substrate (black frame) and an alternating array of Fe3X (yellow) and gold wires (brown) placed on the substrate and these two wires are connected in a zigzag configuration. A temperature gradient is applied perpendicular to the plane. The thickness of the wire is designed to be 1 μm.

Extended Data Fig. 5 Energy dependence of the Hall conductivity and transverse thermoelectric conductivity, and the effect of the SOC on the nodal web structure.

a, Energy dependence of −σyx obtained from the first-principles calculations at T = 0. b, Energy dependence of −αyx/T calculated based on the Mott relation (Methods). c, Temperature dependence of −αyx/T at various energies. df, Band structure of the nodal web around the L point for different strengths of the SOC: 0% (d), 20% (e) and 100% (f). We also show the contour plot of the bandgap in the kKUkWW′ plane.

Extended Data Fig. 6 Longitudinal electric and thermal transport properties and magnetization for Fe3X.

a, b, Temperature dependence of the longitudinal resistivity ρxx for Fe3Ga (a) and Fe3Al (b). c, d, Temperature dependence of the Seebeck coefficient Sxx for Fe3Ga (c) and Fe3Al (d). e, f, Temperature dependence of the thermal conductivity κxx for Fe3Ga (e) and Fe3Al (f). #100, #110 and #111 represent the samples used for the transport measurements in B || [100], [110] and [111], respectively. The inset in b shows the T2 dependence of ρxx for Fe3Ga #100 (red) and Fe3Al #100 (blue). The inset in c shows the log–log plot of −Sxx versus T for Fe3Ga #100 (red) and Fe3Al #100 (blue). The solid and broken lines represent the T and T1.5 dependence, respectively. The solid and broken lines in e and f show the estimated electric and lattice contributions to the thermal conductivity (Supplementary Information). g, h, Magnetization curve for Fe3Ga (g) and Fe3Al (h) at T = 5 K under B || [100], [110] and [111]. The insets in g and h are the T3/2 dependence of M(T).

Extended Data Fig. 7 Specific heat and two contributions to the anomalous Nernst effect.

a, Temperature dependence of the specific heat divided by temperature C/T for Fe3X. The solid lines represent the fit by the combination of the electronic and Debye-type phonon specific heat and ferromagnetic magnon contribution (Supplementary Information). The inset shows the T1/2 dependence of C/T at low temperatures. b, c, αyxρ (b) and −σyxρSxx (c). The ANE is the sum of the two terms, that is, Syx = αyxρ − σyxρSxx (Supplementary Information).

Extended Data Fig. 8 Anisotropy in the Nernst coefficient and Hall resistivity.

ad, Magnetic field dependence of the Nernst coefficient −Syx for Fe3Ga (a) and Fe3Al (b), and the Hall resistivity ρyx for Fe3Ga (c) and Fe3Al (d) in B || [100], [110] and [111]. eh Temperature dependence of −Syx for Fe3Ga (e) and Fe3Al (f), and ρyx for Fe3Ga (g) and Fe3Al (h) in B || [100], [110] and [111].

Extended Data Fig. 9 Anisotropy in the transverse thermoelectric conductivity −αyx, Hall conductivity −σyx and Berry curvature.

a, b, Scaling relation of −αyx for M || [110] (a) and M || [111] (b) versus T/Tm. c, d, Scaling relation of −σyx for M || [110] (c) and M || [111] (d) versus T/Tm. The solid lines in ad are obtained by the first-principles calculations. The scaling parameters used here are summarized in Extended Data Table 1. Details are the same as Fig. 3c, d for M || [100] in the main text. e, f, Contour plot of the Berry curvature Ωn,z of the lower-energy band n in the vicinity of the nodal web structure around the L point for M || [110] (e) and M || [111] (f). Details are the same as Fig. 4e for M || [100] in the main text.

Extended Data Table 1 List of the scaling parameters and magnitude of σyx and σxx at T ≈ 0

Supplementary information

Supplementary Information

This file contains Supplementary Sections 1–6.

Supplementary Table 1

Materials list based on the high-throughput computation.

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Sakai, A., Minami, S., Koretsune, T. et al. Iron-based binary ferromagnets for transverse thermoelectric conversion. Nature 581, 53–57 (2020).

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