Masashi Miwa (Project Researcher, Department of Physics at the time of the research, Project Assistant Professor / Visiting Researcher, RIKEN)

Akito Sakai (Lecturer, Department of Physics)

Takuya Nomoto (Assistant Professor, Graduate School of Engineering / Visiting Researcher, RIKEN)

Motoaki Hirayama (Project Associate Professor, Graduate School of Engineering / Unit Leader, RIKEN)

Takashi Koretsune (Associate Professor, Graduate School of Science, Tohoku University / Visiting Professor, RIKEN)

Ryotaro Arita (Professor, Graduate School of Engineering / Team Leader, RIKEN)

Satoru Nakatsuji (Professor, Department of Physics / Project Professor, Institute for Solid State Physics, The University of Tokyo / Director, Trans-scale Quantum Science Collaborative Research Organizations)

Key points of the presentation

• Kagome lattice ^{(Note 1)} In polycrystalline ^{ferromagnetic}_Fe3Sn, we have discovered a giant magneto-thermoelectric effect about 10 times larger than that of iron alone.
• We have shown that a special electronic state called the nodal plane is the origin of the giant magnetothermoelectric effect ^{(Note 2)}.
• The discovery of the enhancement mechanism of the magnetothermoelectric effect originating from the Kagome lattice is expected to provide a new material design guideline for realizing high-performance magnetothermoelectric materials.

Announcement Summary

A research group led by Project Associate Professor Masashi Miwa, Associate Professor Akito Sakai, and Professor Satoru Nakatsuji at Graduate School of Science, The University of Tokyo, Associate Professor Takashi Koretsune at Graduate School of Science, Tohoku University, and Project Associate Professor Takuya Nomoto at RIKEN Center of Computational Materials Science, Graduate School of Engineering, The University of Tokyo, have announced that they have discovered an enhancement mechanism of magneto-thermoelectric effect originating from Kagome lattice. Visiting Professor, Center of Computational Materials Science, RIKEN), Associate Professor Motoaki Hirayama (Unit Leader, Topological Materials Design Unit, RIKEN Center for Emergent Matter Science), and Professor Ryotaro Arita (Team Leader, Computational Materials Science Team, RIKEN Center for Emergent Matter Science). (Team Leader, Computational Materials Science Team, Center for Emergent Matter Science, RIKEN) have discovered that a giant magneto-thermoelectric effect (=anomalous Nernst effect) occurs in the iron-dominated Kagome lattice ferromagnet Fe3Sn. In addition, computer simulations using first-principles calculations ^{(Note 3)} have revealed that a special electronic state called the nodal plane is the origin of the giant magnetothermoelectric effect in the Kagome-lattice ferromagnet _Fe3Sn.

The performance of the magnetothermoelectric effect is partly due to a physical quantity (= Berry curvature ^{(Note 4)} ) that originates from the topology of the electronic state and wavefunction intrinsic to the material. The mechanism of the enhancement of the magneto-thermoelectric effect has not yet been fully understood, but it has been clarified that the giant Berry curvature is induced by an electronic state called the nodal plane, which is derived from the Kagome lattice discovered in this study, and that the magneto-thermoelectric effect is enhanced. Such a peculiar electronic structure may also appear in magnetothermoelectric materials with Kagome lattice structure. The mechanism of enhanced magnetothermoelectric effect originating from the Kagome lattice discovered in this study is expected to provide a new material design guideline for future high-performance magnetothermoelectric materials.

The research results have been published in the American scientific journal Science Advances ( January 15, 2022).

Publication details

Research Background
Recently, magneto-thermoelectric effect, which is a thermoelectric effect that occurs in magnetic materials, has attracted much attention as an innovative technology that can replace the existing thermoelectric technology. Thermoelectric conversion, which has been the subject of much research and development, is based on the Seebeck effect ^{(Note 2)}, a physical phenomenon in which an electromotive force is generated in the same direction as the temperature difference. This requires a modular structure in which a large number of columnar elements are arranged three-dimensionally, which makes it difficult to make thin-filmed, flexible, and large-area devices, and there is an inevitable significant performance degradation caused by multiple junctions. On the other hand, in power generation using the magneto-thermoelectric effect, electromotive force is generated in the direction perpendicular to the temperature difference and magnetization. Since the direction of power generation can be controlled by the direction of magnetization, a large-area, junctionless module structure like that shown in Figure 1a can be realized. With these features, the magneto-thermoelectric effect is expected to be an innovative thermoelectric conversion technology that will contribute to the realization of stand-alone power sources for IoT devices and an energy-saving society. In fact, a heat flow sensor based on thin-film magneto-thermoelectric effect has recently been developed and is attracting much attention.

The origin of the magneto-thermoelectric effect, which generates an electromotive force perpendicular to a temperature gradient, comes from the topological nature of the wave function ^{(Note 4)} that governs the motion of electrons in a magnetic material. The performance of the magneto-thermoelectric effect can be predicted by computer simulations using first-principles calculations and other methods. However, it is not obvious which electronic state is responsible for the origin of the magnetothermoelectric effect, since the nature of the electronic state and wavefunction differs from material to material. In order to search for materials with higher magneto-thermoelectric performance and to design materials, it is an important issue to elucidate the mechanism of enhancement of the universal magneto-thermoelectric effect.

Research Contents and Results
This research group focused on iron-based magnetic materials, which have a large Clark number ^{(Note 5} ) from the viewpoint of application, and are inexpensive and suitable for applications, to search for materials with a high-performance magnetothermoelectric effect. In the course of our search, we found that a polycrystalline Kagome-lattice ferromagnet _Fe3Sn (Figure 1b), which is composed of iron (Fe) and tin (Sn), exhibits a magneto-thermoelectric effect about 10 times larger than that of iron alone.

Figure 1: Thermoelectric conversion module utilizing magneto-thermoelectric effect and conceptual diagram of crystal structure of _Fe3Sn.
(a) Thermoelectric conversion module using the magneto-thermoelectric effect. Since the electromotive force generated by the magneto-thermoelectric effect is perpendicular to the temperature gradient and magnetization, a simple module structure with fewer junctions can be realized compared to conventional thermoelectric conversion modules using the thermoelectric effect. (b) Crystal structure of the Kagome lattice ferromagnet _Fe3Sn. _Fe3Sn has a stacked structure of Kagome lattice consisting of magnetic atoms of iron (Fe, red sphere) in the c-axis direction. It is expected to operate in various environments due to its high magnetic transition temperature of 490°C.

The magneto-thermoelectric effect is maintained near room temperature, making it suitable for waste heat recovery and thermoelectric applications near room temperature (Fig. 2a, b). Compared to the previously discovered materials _Co2MnGa ( Tc = 420°C) and Fe3Ga (Tc = 450°C), which exhibit a giant magneto-thermoelectric effect, the polycrystal has a higher Curie temperature ^{(Note 6)}Tc = 490°C, so it is expected that performance is not lost even at high temperatures. Polycrystals are also easier to fabricate than single crystals and are suitable for thermoelectric application research.

Figure 2: Magneto-thermoelectric effect in the Kagome lattice ferromagnet _Fe3Sn
Magnetic field dependence of (a) anomalous Nernst coefficient in _Fe3Sn. Purple and red values are at 200 K and 300 K, respectively. (b) Temperature dependence of the anomalous Nernst effect, showing a value of 3 μV/K near 400 K, which is comparable to a value about 10 times higher than that of iron alone. The temperature region in yellow in (b) is the temperature region used in waste heat recovery and thermoelectric applications near room temperature; the magneto-thermoelectric effect of _Fe3Sn can provide a large electromotive force in these temperature regions and is expected to be applied in a variety of environments.

In order to clarify the origin of the magnetothermoelectric effect in the Kagome lattice ferromagnet _Fe3Sn, we predicted the performance of the magnetothermoelectric effect by computer simulation using first-principles calculations and analyzed the nature of electronic states and wave functions. As a result, we found that a peculiar electronic state called the nodal plane enhances a physical quantity called the Berry curvature, which is the origin of the magnetothermoelectric effect, and is the origin of the giant magnetothermoelectric effect observed in the Kagome lattice ferromagnet _Fe3Sn (Figure 3a, b ^{(Note 4)} ). The Berry curvature enhanced by the nodal plane exists as a connection between high symmetry points in the momentum space of the Kagome lattice ferromagnet _Fe3Sn, and can be attributed to the symmetry of the Kagome lattice. Such an electronic state called the nodal plane is not unique to _Fe3Sn, but may occur in any material that has a Kagome lattice. The mechanism of magneto-thermoelectric effect enhancement discovered in this study is expected to be applied to future material exploration.

Figure 3: Nodal plane in momentum space and the giant Berry curvature induced by it.
(a) Nodal plane in momentum space. The energy difference from the Fermi energy is denoted as E (meV). The nodal plane is defined by the band structure created by the different up and down spins, and thus appears as a three-dimensional two-dimensional structure in momentum space. (b) Berry curvature (Ωx) at E=50 meV. A large Berry curvature appears connecting the points with high symmetry derived from the Kagome lattice symmetry. This structure is consistent with the electronic state in momentum space created by the nodal plane shown in (a), indicating that this giant Berry curvature is derived from the nodal plane. Although it has been discussed by this research group that nodal lines defined between the same spins play an important role in the enhancement of the magneto-thermoelectric effect, this is the first confirmation that electronic states such as nodal planes are the origin of the giant magneto-thermoelectric effect.

Social Significance and Future Prospects
The Kagome lattice ferromagnet Fe3Sn discovered in this study is composed of iron and tin, which are inexpensive and non-toxic elements with high Clark number , and can be operated in any environment due to its high magnetic transition temperature of 490°C. Therefore, a great leap toward the practical application of thermoelectric modules and heat flow sensors using magnetothermoelectric effect Therefore, it is expected to make a great leap toward the practical application of thermoelectric modules and heat flow sensors using the magneto-thermoelectric effect. When it is put to practical use, it is expected to be used in IoT sensors and heat flow sensors as a power source that utilizes trace amounts of heat in the environment by recovering waste heat in various locations through its flexibility, thinness, and large area. We also plan to explore magneto-thermoelectric materials with high performance by utilizing a new magneto-thermoelectric effect enhancement mechanism called nodal planes. Computer simulations based on first-principles calculations will be used to efficiently predict the performance of materials that have nodal planes and can be used in a wide range of applications, and to elucidate a new mechanism for increasing magnetothermoelectric performance beyond the nodal plane.

This research is being conducted as part of the "Development of Functional Magnetic Materials and Devices Based on Topological Materials Science" research project (research supervisor: Masahito Ueda) under the "Creation of Materials and Devices with Innovative Functions Based on Topological Materials Science" research area of the Japan Science and Technology Agency (JST) Core Research for Evolutional Science and Technology (CREST) team research project (research supervisor: Masahito Ueda). The research project "Exploration of topological magnetic materials based on first-principles calculations" in the PRESTO "Topological Materials Science and Creation of Innovative Functions" research area (Research Director: Shuichi Murakami), the research project "Exploration of topological magnetic materials based on first-principles calculations" in JPMJPR20L7 (Research Director: Takuya Nomoto), the research project "Development of functional magnetic materials and creation of devices based on topology of electronic structures" in the "Materials and Devices with Innovative Functions" research area (Research Director: Masahito Ueda) The research project "A01: Correlation Effects between Localized Multipoles and Conduction Electrons," Grant-in-Aid for Scientific Research in the New Academic Area "J-Physics: Physics of Multipole Conduction Systems" (PI: Hisatomo Harima), MEXT, Japan, and the JSPS Grants-in-Aid for Scientific Research (JP 19H00650, JP 20H00650), and the JSPS Grant-in-Aid for Scientific Research (JP 19H00650, JP 20H00650). 19H00650, JP 20K22479, JP21H04437).

Journal

Journal name	Science Advances
Title of paper	Large anomalous Nernst effect and nodal plane in an iron-based kagome ferromagnet
Author(s)	Taishi Chen*, Susumu Minami*, Akito Sakai*, Yangming Wang, Zili Feng, Takuya Nomoto, Motoaki Hirayama, Rieko Ishii, Takashi Koretsune, Ryotaro Arita, Satoru Nakatsuji† (* : equal contribution, †: corresponding author) Satoru Nakatsuji† (* : equal contribution, †: corresponding author)
DOI number	10.1126/sciadv.abk1480
Abstract URL	http://www.science.org/doi/10.1126/sciadv.abk1480

Terminology

Note 1 Kagome lattice

Refers to a crystal structure in which atoms are arranged in a cage-like arrangement. In _Fe3Sn discovered in this study, iron (Fe) atoms form a Kagome lattice, as shown in Figure 1b. ↑up

Note 2 Conventional thermoelectric technology (Seebeck effect) and magneto-thermoelectric effect (anomalous Nernst effect )

When a temperature difference is applied to a material, an electromotive force is generated in the same direction as the temperature difference (Seebeck effect) because electrons (carriers) that serve as current carriers move along the temperature difference. On the other hand, in magnetic materials, the movement of carriers is bent due to the presence of magnetization, and electromotive force is also generated in the direction perpendicular to the magnetization and heat flow (anomalous Nernst effect). In the case of the Seebeck effect, since the electromotive force occurs in parallel with the temperature gradient, many junctions are required to create a thermoelectric conversion module, and such a module is called a Π-type device. On the other hand, in the case of the anomalous Nernst effect, the electromotive force is generated perpendicular to the temperature gradient (Figure 1a), making it possible to create a very simple thermoelectric conversion module, which is expected to have various advantages in applications. ↑up

Note 3 First-principles calculations

First-principles calculation is a method of using a computer to calculate the motion of electrons in matter according to the Schrodinger equation of quantum mechanics. In this research, first-principles calculations based on density functional theory are used. Density functional theory is a method of calculating properties of matter based on electron density among first-principles calculations, and is frequently used in the fields of solid state physics and quantum chemistry, and calculations are performed using large-scale computers such as supercomputers. ↑up

Note 4: Berry curvature, topological properties of wavefunctions

The Berry curvature is defined by the wave function on momentum space. The Berry curvature makes the electrons behave as if they were in a magnetic field (virtual magnetic field) in momentum space, giving them motion perpendicular to the temperature gradient. This effect is one of the origins of the magneto-thermoelectric effect's unique electromotive force perpendicular to the temperature gradient. The Berry curvature is due to the topological nature of the wavefunction; in _Fe3Sn, the nodal plane produces a huge Berry curvature (Fig. 3ab). It can be interpreted that the giant virtual magnetic field imparts a larger lateral motion to the electrons, and the nodal plane is the origin of the giant magneto-thermoelectric effect. ↑up

Note 5 Clark number

The Clark number represents the percentage of elements that exist near the earth's surface. A material with a higher Clark number means that it is more abundant in our surroundings, which is one indicator of inexpensive and easy-to-apply materials. Iron is the metal with the second highest Clark number after aluminum, making it a very suitable material for application. ↑up

Note 6 Curie temperature

Curie temperature refers to the temperature above which a material loses its properties as a ferromagnetic material (magnet). The Curie temperature varies depending on the material, and is approximately 490°C for _the Kagome lattice ferromagnet _{Fe3Sn, which} we discovered this time. Since the magneto-thermoelectric effect is caused by the magnetic properties of the material (magnet), the magneto-thermoelectric effect is lost above the Curie temperature. Therefore, it is important to search for materials with high Curie temperature and high magneto-thermoelectric performance. ↑up