Tomoya Higo (Project Associate Professor, Department of Physics / Project Assistant Professor, Institute for Solid State Physics)

Kota Kondo (Senior Researcher, RIKEN)

Muhammad Ikhlas (3rd Year Doctoral Student, Graduate School of Frontier Sciences)

Ryota Uesugi (Graduate School of Frontier Sciences, 2nd Year Master's Student)

Daisuke Hamane (Technical Specialist, Institute for Solid State Physics)

Yoshichika Otani (Professor, Institute for Solid State Physics / Professor, Trans-scale Quantum Science Collaborative Research Organizations / Team Leader, RIKEN)

Satoru NAKATSUJI (Professor, Department of Physics / Professor, Graduate School of Frontier Sciences / Project Professor, Institute for Solid State Physics / Director, Trans-scale Quantum Science Collaborative Research Organizations)

Key points of the presentation

• In antiferromagnetic materials, which are attracting worldwide attention as next-generation magnetic materials, we observed a giant magnetic response that can be directed in any direction regardless of the sample geometry.
• Demonstrated a new multi-level memory function that will lead to the development of non-volatile magnetic memory.
• Development of an anomalous Nernstian heat flow sensor with a high degree of freedom in device geometry and high resistance to magnetic field disturbance.

Summary of Presentations

A research group led by Project Associate Professor Tomoya Higo, Graduate School of Science, The University of Tokyo, and Professor Satoru Nakatsuji, Institute for Solid State Physics, Graduate School of Science and Graduate School of Frontier Sciences, The University of Tokyo, and Trans-scale Quantum Science Institutes, has developed an anomalous Nernstian heat flow sensor with a high degree of freedom in device shape and high resistance to magnetic field disturbances. Professor Yoshichika Ohtani (concurrently serving as Team Leader, RIKEN Center for Emergent Matter Science), Senior Researcher Kota Kondo, RIKEN Center for Emergent Matter Science, and Professor C. L. Chien, Johns Hopkins University, USA, and their research group have jointly developed a new magnetic material for the BEYOND 5G generation, which is required for power saving, ultra-high speed and ultra-high density. The research group, in collaboration with Prof. C. L. Chien and his colleagues at John Hopkins University, USA, has discovered that the manganese compound _Mn3Sn, an antiferromagnet ^{(Note 1)} that is attracting attention as a central material for magnetic devices for the Beyond 5G generation, can obtain a giant magnetic response that can be directed in all directions without being affected by shape (shape magnetic anisotropy: ^{(Note 2)} ), which has been a problem in device fabrication up to now. Using this property, we have successfully demonstrated a new multi-level memory function ^{(Note 3} ) useful for next-generation memory development and developed an anomalous Nernst ^{(Note 4)} heat flow sensor with a high degree of freedom in device geometry and high resistance to external magnetic field disturbances.

Antiferromagnetic materials have the following characteristics: (i) spin ^{(Note 1)} dynamics in the THz band is 2-3 orders of magnitude faster than that of ferromagnetic materials, (ii) they do not create leakage magnetic fields, and (iii) they offer a high degree of freedom in material selection. Therefore, by replacing the ferromagnetic material ^{(Note 1)} used in existing magnetic devices, devices with even higher speed and density can be expected. (iv) The properties of negligibly small shape magnetic anisotropy and high degree of freedom of device shape, demonstrated by this research group, together with the above properties (i)-(iii), are expected to bring a breakthrough in the development of next-generation magnetic devices using antiferromagnetic materials. This research result has been published in the German International Journal of Science, "Adaptive Magnetism".

The research results were published online in the German international scientific journal " Advanced Functional Materials " on February 25, 2021.

Publication details

Background of the research
Many magnetic materials are used in our daily life. Ferromagnetic and antiferromagnetic materials are known as representative examples. Ferromagnetic materials, which are widely used as materials for magnets, have the property that their spins are aligned in one direction and have large magnetization. Ferromagnetic materials show a response to electricity, heat, and light that is proportional to their magnetization. Therefore, the magnitude and direction of the response can be controlled by magnetization. For example, in nonvolatile magnetic memory (MRAM), which is expected as a technology to reduce power consumption in PCs and smartphones, the electrical response of a tunnel magnetoresistive element consisting of a ferromagnetic metal layer, a nonmagnetic insulating layer, and a ferromagnetic metal layer, which changes according to the magnetization direction of the ferromagnetic layer, is used as the information recording unit for "0" and "1. This magnetoresistive element uses the electrical response that changes with the direction of the magnetization of the ferromagnetic layer as the "0" and "1" information recording unit. In this magnetoresistive element, the magnetization is oriented perpendicular to the film, which allows for higher density and lower power consumption. These characteristics are similar for devices using magnets and other ferromagnetic materials, and their functionality can be greatly improved by optimizing the direction in which the magnetization easily turns (easy magnetization axis).

In order to orient the easy axis of magnetization in a specific direction, materials and multilayer (interface) structures are designed using crystal magnetic anisotropy ^{(Note 2} ) derived from the crystal structure and interface magnetic anisotropy ^{(Note 2)} derived from the effect of heterogeneous material interfaces. On the other hand, ferromagnetic materials have the property that the energy is lowered when the magnetization is aligned in the longitudinal direction for rod-shaped materials and in the parallel direction for thin films. The effect of shape on the easy axis of magnetization is called "shape magnetic anisotropy," and its contribution increases in proportion to the size of the magnetization of the ferromagnetic material. Therefore, devices using ferromagnetic materials with large magnetization, which are expected to have a huge response, have less freedom in shape selection, and it is necessary to carefully consider the balance of shape, crystal, and interface magnetic anisotropy to obtain sufficient characteristics. One way to suppress the effects of shape magnetic anisotropy is to use antiferromagnets, which have zero net magnetization because neighboring spins cancel each other out. However, the antiferromagnetic property of having no magnetization is both an advantage and a disadvantage in device applications, as it is difficult to obtain the enormous response to electricity, heat, and light that ferromagnetic materials exhibit. Therefore, the above idea has not been experimentally verified.

Research Activities and Results
The research group has focused on the antiferromagnet _Mn3Sn (Figures 1a and 1b), which is composed of manganese (Mn) and tin (Sn). At room temperature, _Mn3Sn exhibits an anomalous Hall effect ^{(Note 5)} large enough to rival ferromagnetic materials (Nature, 527, 212 (2015)) and anomalous Nernst effect (Nature Phys. journal 13, 1085 (2017).) and magneto-optical Kerr effect ^{(Note 6} ) (Nature Photon. journal 12, 73 (2018). We have found that Mn3Sn exhibits a Furthermore, we were the first to find that _Mn3Sn is a topological magnetic material that exhibits a Weil magnetic state with Weil particles ^{(Note 7} ) (Nature Mater. journal 16, 1090 (2017). In other words, although _Mn3Sn is an antiferromagnet, it has a huge virtual magnetic field (equivalent to 100-1000 tesla (T) in real space) created by Weil particles in momentum space, which causes the above huge magneto-electric and thermo-electric responses, etc. to appear (Figure 1c).

Figure 1: Crystal and magnetic structures of the topological antiferromagnet _Mn3Sn, and virtual magnetic field in momentum space
(a) _Mn3Sn has a stacked Kagome lattice structure consisting of magnetic manganese atoms (Mn, red and yellow spheres) in the c-axis direction, and below 420 K (about 150 °C), Mn spins exhibit an inverse 120 degree structure called the It exhibits antiferromagnetic ordering. (b) Spins on the two-layer Kagome lattice show that units consisting of six spins, called clustered magnetic octupoles, shown as hexagons, are aligned in the same direction. (c) In _Mn3Sn, the orientation of the antiferromagnetic spin structure (clustered magnetic octupoles) in real space corresponds to the pair of Weil points (red (+) and blue (-) spheres) in momentum space and its virtual magnetic field. By changing the orientation of the magnetic octupole, the virtual magnetic field can be controlled.

Interestingly, the orientation of this virtual magnetic field corresponds to the clustered magnetic octupole ^{(Note 8} ) of the characteristic non-collinear antiferromagnetic spin structure of _Mn3Sn. By controlling the orientation of the clustered magnetic octupole in the Kagome lattice plane, the virtual magnetic field and its derived giant response can be controlled. More recently, we have developed a method to control the orientation of the clustered magnetic octupoles electrically as well as magnetically (Nature,580, 608 (2020). .

In this study, polycrystalline thin films of the antiferromagnet _Mn3Sn were fabricated on silicon substrates using the sputtering method and the change in the anomalous Hall effect with respect to the magnetic field was measured. In the experiments in which the magnetic field was swept while changing the direction of the applied magnetic field from perpendicular to the plane of the film to in-plane directions ( θ andφ directions ), it was confirmed that multi-level memory was possible (Figures 2a and 2b). The anomalous Hall effect is proportional to the perpendicular component of the virtual magnetic field. Therefore, the change in the readout signal with magnetic field direction corresponds to the alignment of the magnetic octupole and virtual magnetic field in the magnetic field direction and the change in the projection component in the perpendicular direction. In other words, this result shows that the virtual magnetic field (parallel to the magnetic octupole) can be freely directed in all directions in three-dimensional space (Fig. 2c). This property is due to the fact that the magnetization of _Mn3Sn is so small that it is not affected by shape magnetic anisotropy and that it has magnetic easy planes in the Kagome lattice plane. We have also demonstrated that similar multi-level storage is possible in single-crystal (single grain) samples, albeit only in the two-dimensional plane parallel to the Kagome lattice (Figure 2d).

Figure 2: Measurement of the magnetic field dependence of the anomalous Hall effect in _Mn3Sn and demonstration of multi-level memory capability.
(a) Schematic diagram of the anomalous Hall effect measurement. The Hall voltage (resistivity) generated in the y-direction was measured by sweeping the magnetic field while changing the angle of the magnetic field from perpendicular to the film surface to the θ andφ directions. (b) Magnetic field dependence of Hall resistivity in _Mn3Sn polycrystalline thin film sample. The magnetic field was varied in the θ direction, and the same multi-level memory function was confirmed in the φ direction. (c) Schematic diagram showing the direction of stabilization of magnetic octupoles (red arrows) in poly- and single-crystalline samples. in the case of in-plane crystalline magnetic anisotropy like _Mn3Sn, the directionality appears in all directions after polycrystallization. (d) Magnetic field dependence of Hall resistivity in _Mn3Sn single crystal thin film sample. The magnetic field is varied in the θ direction. No multi-level memory function was observed in the φ direction. This indicates that the magnetic octupole and virtual magnetic field can be oriented in 3-D space/2-D plane in the poly/single crystal sample as shown in Figure 2c.

On the other hand, even in ferromagnets with sufficiently large crystalline magnetic anisotropy compared to shape magnetic anisotropy, multivalued memory is possible by a similar mechanism in the polycrystalline sample. However, in single-crystal samples, the direction of magnetization is restricted to one direction due to the large shape magnetic anisotropy, and only a binary signal can be obtained (Fig. 3a). The new information storage method discovered in the antiferromagnet _Mn3Sn shows the possibility of writing and reading not only "0" and "1" but also three or more information units in a single device consisting of a single grain of several to several 10 nm in size (Fig. 3b). Figure 3b). In the future, it is desirable to demonstrate the principle using a sample that has been miniaturized to the device size required for actual memory.

Figure 3: Magnetic anisotropy of ferromagnetic and antiferromagnetic materials consisting of a single grain
(a) Expected magnetization direction and readout signal in a single crystal/single grain sample of a ferromagnetic material with large crystal magnetic anisotropy. (b) Expected magnetization direction and readout signal in a single crystal/single grain sample of an antiferromagnet _Mn3Sn. Ferromagnets with large magnetization require large crystalline magnetic anisotropy to overcome the shape magnetic anisotropy that tries to make the magnetization lie within the film plane. In this case, strong uniaxial magnetic anisotropy is required and the readout signal becomes binary. In antiferromagnets with very small magnetization, the effect of shape magnetic anisotropy is almost negligible, and the orientation of magnetization (more precisely, magnetic octupoles or virtual magnetic field) can be aligned even with relatively weak crystal magnetic anisotropy of about planar magnetic anisotropy. In such cases, multi-level storage is possible.

The property of small influence of shape magnetic anisotropy also works in magnetic devices based on the anomalous Nernst effect. The anomalous Nernst effect is a thermoelectric effect that uses magnetic properties to convert heat into electricity, but unlike the Seebeck effect, it can generate electricity perpendicular to the heat flow (Figures 4a and 4b). The advantage of this technology is that conventional thin-film related technologies can be applied to fabricate large-area and flexible thermoelectric devices at low cost, and it is expected to be applied to heat flow sensors that visualize heat flow. Since the heat flow sensitivity of the sensor is proportional to the length of the element, a fine wire structure is required. When measuring the heat flow in the transverse direction, the magnetization (magnetic octupoles in the case of _Mn3Sn ) must be aligned toward the short side as shown in Fig. 4b. Since this magnetization direction is contrary to shape magnetic anisotropy, heat flow sensors using ferromagnetic materials obtain sufficient functionality for practical use by optimizing the crystal magnetic anisotropy and the film stacking structure.

Figure 4: Thermoelectric devices using the Seebeck effect and the anomalous Nernst effect.
(a) Schematic of a thermoelectric device with a three-dimensional pillar structure using the Seebeck effect. (b) Schematic of a thermoelectric device with a two-dimensional thermopile structure using the anomalous Nernst effect. The Seebeck effect/Nernst effect generates an electromotive force (voltage) in the parallel/perpendicular direction to the heat flow, respectively. Therefore, conventional thin-film fabrication and processing technologies can be applied to devices using the anomalous Nernst effect, and it is easy to make them large-area or flexible.

On the other hand, _{Mn3Sn, which} exhibits a huge anomalous Nernst effect originating from the virtual magnetic field, can align its magnetic octupoles and the direction of the virtual magnetic field without being affected by shape magnetic anisotropy, making it very easy to maintain its thermoelectric properties even in thin-wire samples. We fabricated a sensor consisting of Mn3Sn polycrystals and thin wires of electrodes (Fig. 5a) and measured the magnetic field dependence of the voltage generated by the anomalous Nernst effect, and confirmed that a large signal of about sub-mV appeared without inversion up to a large magnetic field of ±0.9 T (Fig. 5b). We also confirmed that the Nernst voltage at zero magnetic field is linearly proportional to the heat flow and functions as a heat flow sensor (Figure 5c). The heat flow sensitivity per unit area is 1.3 mV/W, which is comparable to previously reported anomalous Nernstian heat flow sensors using ferromagnetic materials and commercially available low-cost Seebeck heat flow sensors, while the stability against external magnetic field is 10-100 times higher (the sensor using ferromagnetic materials described above has a stability 10-100 times higher than that of the The heat flow sensor has been successfully developed by taking advantage of the new functionality of antiferromagnetic materials, which is that the reversed magnetic field is about 0.01-0.1 T for sensors using the ferromagnetic materials described above).

Figure 5: Heat flow sensing in an anomalous Nernstian thermoelectric device using antiferromagnet _Mn3Sn
(a) Schematic of an anomalous Nernstian heat flow sensor consisting of _{Mn3Sn and} electrodes, and image observed with an optical microscope. In the measurement, heat flow is applied to the sensor in the in-plane ( -z) direction and a magnetic field is applied in the in-plane ( y) direction, and the voltage generated by the anomalous Nernst effect is measured. (b) Dependence of the voltage generated in the _Mn3Sn anomalous Nernstian heat flow sensor on the magnetic field when the applied heat flow is changed. (c) Heat flow dependence of the voltage produced by the _Mn3Sn anomalous Nernstian heat flow sensor at zero magnetic field. The Nernst voltage is proportional to the heat flow, indicating that it functions as a sensor.

Future Prospects
Antiferromagnetic materials have the following advantages: (i) spin dynamics in the THz band is two to three orders of magnitude faster than that of ferromagnetic materials, and ultrafast devices can be expected, (ii) they do not create leakage magnetic fields and are suitable for high-density devices, and (iii) materials with a transition temperature above room temperature can be obtained from any metal, insulator, or semiconductor. Therefore, it has been attracting attention in recent years as a central material for magnetic devices of the Beyond 5G generation, which requires power saving, ultra-high speed drive, and ultra-high density. In this study, this research group has demonstrated a new antiferromagnetic functionality, (iv) negligibly small shape magnetic anisotropy and high flexibility of device shape, _{using the} antiferromagnetic material _Mn3Sn, which can read out information (huge electrical signals), which has been an issue in the application of antiferromagnetic materials.

The multi-level memory function in a single-grain memory device is a technology that will lead to the realization of a brain-like computer that simulates cranial nerves and a quantum computer, and together with the already known advantages (i)-(iii) of antiferromagnets, such as high density and ultrahigh speed, it is expected to be used in the next generation of spintronics devices. (i)-(iii), which are already known advantages of antiferromagnets such as high density and ultrahigh speed, will lead to a breakthrough in the development of next-generation spintronics devices. In addition, in anomalous Nernstian heat flow sensors, where the fine wire structure of magnetic materials is important, it will be possible to fabricate sensors with a high degree of freedom in device geometry and high resistance to external magnetic field disturbances, and it is expected that anomalous Nernstian heat flow sensors that greatly surpass existing Seebeck heat flow sensors in terms of performance and cost will be developed.

This research was conducted in the research area of "Creation of Materials and Devices with Innovative Functions Based on Topological Materials Science" (Research Director: Masahito Ueda) of the Japan Science and Technology Agency (JST) Core Research for Evolutional Science and Technology (CREST) project, entitled "Development of Functional Magnetic Materials Using Topology of Electronic Structures and Creation of Devices" (Research Director: Masahito Ueda). (Research Director: Masahito Ueda), and the "Creation of Innovative Environmental Power Generation Technologies Using Micro Energy" research project (Research Director: Kenji Taniguchi, Deputy Research Director: Hiroyuki Akinaga) in the CREST "Creation of Innovative Basic Technologies for Energy Harvesting Using Topological Electronic Structures" research area (Research Director: Kenji Taniguchi, Deputy Research Director: Hiroyuki Akinaga). Research Project "A01: Correlation Effect between Localized Multipoles and Conduction Electrons" in the project "J-Physics: Physics of Multipole Conduction Systems" (Research Director: Hisatomo Harima), Grant-in-Aid for Scientific Research, Ministry of Education, Culture, Sports, Science and Technology, Japan, Project 15H05882 (Research Director: Kenji Taniguchi, Deputy Director General: Hiroyuki Akinaga). Grant-in-Aid for Scientific Research (No.16H06345, Design and Functional Exploration of Strongly Correlated Materials - Challenge to Nonequilibrium and Aperiodic Systems-), New Energy and Industrial Technology Development Organization (NEDO), "NEDO This project was conducted as a part of "NEDO Leading Research Program / New Energy and Environment Technology Leading Research Program / Research and Development of Thermal Power Generation Devices Using Weil Magnetic Materials" by NEDO (National Energy and Industrial Technology Development Organization).

Journal

Journal name	Advanced Functional Materials
Title of paper	Omnidirectional Control of Large Electrical Output in a Topological Antiferromagnet
Author(s)	Tomoya Higo, Yufan Li, Kouta Kondou, Danru Qu, Muhammad Ikhlas, Ryota Uesugi, Daisuke Nishio-Hamane, C. L. Chien, YoshiChika Otani, and Satoru Nakatsuji* (*: Responsible author)
DOI Number	10.1002/adfm.202008971
Abstract URL	https://doi.org/10.1002/adfm.202008971

Terminology

Note 1: Antiferromagnet, spin, and ferromagnet

A magnetic body is a material that possesses a microscopic magnet due to the spinning motion of electrons, called "spin". These magnetic bodies exhibit magnetic ordering in which macroscopic numbers of spins are aligned in some pattern, and are classified into (1) ferromagnetic bodies in which the spins are aligned in a uniform direction and exhibit large magnetization like a magnet and (2) antiferromagnetic bodies in which neighboring spins are aligned in an antiparallel or mutually canceling manner and the net magnetization is zero or very small. (2) antiferromagnets, in which the net magnetization is zero or very small due to the arrangement of neighboring spins in an antiparallel or canceling manner. ↑up

Note 2 Shape magnetic anisotropy, crystal magnetic anisotropy, and interface magnetic anisotropy

Magnetic materials have magnetic anisotropy, in which magnetization (N and S poles of a magnet) has a direction that is easy to orient (easy axis of magnetization) and a direction that is difficult to orient (difficult axis of magnetization). The origin of magnetic anisotropy is known, for example, as (1) crystal magnetic anisotropy, which originates from the crystal structure and atomic arrangement of magnetic materials, (2) interface magnetic anisotropy, which originates from an interface consisting of different materials and attempts to stabilize magnetization perpendicular to the interface, and (3) shape magnetic anisotropy, which is caused by an antimagnetic field dependent on the shape of the specimen. The antimagnetic field is a magnetic field that is generated by the magnitude of the magnetization. Since the antimagnetic field is proportional to the magnitude of magnetization, shape magnetic anisotropy is always present in any magnetic material with magnetization. The longitudinal direction for rod-shaped samples and the in-plane direction for thin-film samples are the easy axes (planes) for shape magnetic anisotropy. On the other hand, the hard axis for shape magnetic anisotropy is the shortitudinal direction for rod-shaped samples and the perpendicular direction for thin-film samples. ↑up

Note 3: Multi-level memory function

General memory devices store binary signals corresponding to "0" and "1" using high and low readout signals. A multi-level memory function is a function that allows a single element to store not only two values of "0" and "1" but also three or more values of information by setting multiple signal thresholds. For example, a 4-valued device can store 2 bits of information, and an 8-valued device can store 3 bits of information, and this function is expected to enable larger memory capacity. ↑up

Note 4: Anomalous Nernst effect

The Nernst effect is a phenomenon in which an electromotive force is generated in the direction perpendicular to the magnetic field and temperature gradient in a material capable of conducting electricity. This is caused by the bending of the electron flow from the high-temperature side to the low-temperature side due to the magnetic field when the magnetic field and temperature gradient are applied perpendicular to each other. In ferromagnetic materials with spontaneous magnetization or special antiferromagnetic materials with a virtual magnetic field, the Nernst effect appears even in a zero magnetic field, and this is called the anomalous Nernst effect. In this case, an electromotive force can be obtained by directing the magnetization or virtual magnetic field perpendicular to the temperature gradient instead of the magnetic field. Using the anomalous Nernst effect, there is no need to apply an external magnetic field, so power generation and heat flow sensing are possible using only temperature differences, and it is attracting attention from the perspective of energy harvesting. ↑up

Note 5 Anomalous Hall effect

The phenomenon in which an electromotive force is generated in a material capable of conducting electricity in a direction perpendicular to the magnetic field and electric current is called the Hall effect. This is caused by the direction of motion of electrons flowing as an electric current being bent by the magnetic field when a magnetic field and electric current are applied perpendicular to each other. In ferromagnetic materials with spontaneous magnetization, special antiferromagnetic materials with virtual magnetic fields (an effective magnetic field that exists in wavenumber space, a new physical concept that stems from the topology of the electronic structure), and spin liquids, the Hall effect occurs even when no external magnetic field is applied. This effect is called the anomalous Hall effect. ↑up

Note 6 Magneto-optical Kerr effect

When linearly polarized light is incident on a magnetic material, the polarization plane of the reflected light rotates according to the direction of magnetization, a phenomenon called the magnetooptic Kerr effect. The phenomenon in which the polarization plane of transmitted light rotates is called the magnetooptic Faraday effect. In general, the Carr effect, which uses reflected light, has been widely studied in magnetic metals that reflect light like a mirror, while the Faraday effect, which uses transmitted light, has been studied in magnetic insulators that transmit light like glass. These linear magneto-optic effects are used as the principle for magneto-optic elements in familiar applications such as magneto-optical disks and optical isolators. ↑up

Note 7 Weil Particle

Matter with a massless particle (Weil particle) described according to the Weil equation proposed by Hermann Weil in 1921 is called a Weil semi-metal. The Weil particle has been studied worldwide as a particle that describes neutrinos, and experiments at Super-Kamiokande revealed that neutrinos have minute masses, and the Weil particle was thought to be an illusory particle that does not exist in nature. In Weil semimetals, Weil points occur in pairs with different chirality (right-handed and left-handed degrees of freedom), and these pairs of Weil points correspond to the N and S poles of a magnet in momentum space. In ordinary Weil semimetals, the Weil points are created due to the crystal structure of the material. On the other hand, magnetic materials with Weil points created by magnetism are called Weil magnets (more broadly, topological magnets). In Weil magnets, it is possible to control the Weil points and the associated virtual magnetic field by controlling the magnetic order in an external field such as a magnetic field, which is an attractive property from the viewpoint of application. The virtual magnetic field generated between Weil points is large enough to correspond to an external magnetic field of 100-1000 tesla (T), and is the origin of the giant anomalous Hall effect and other phenomena. ↑up

Note 8 Cluster magnetic octupole

A magnet has two poles, N and S, but the spins arranged at each lattice point of a magnetic material also have two poles, which are also called magnetic dipoles. The characteristic combination of spins created when considering a unit with spins located at multiple lattice points is called a clustered magnetic multipole, and as the number of spins constituting the unit increases to one, two, or three, the name of the combination changes to magnetic dipole, quadrupole, octupole, and so on. In the spin structure of the antiferromagnet _Mn3Sn, the unit can be thought of as six spins arranged on two Kagome lattices and having a clustered magnetic octupole as shown in Figure 1b. This clustered multipole acts as a parameter that controls the Weil point and the direction of the virtual magnetic field in _Mn3Sn, for example, and even in combinations where the sum of the magnetizations is zero, it shows a giant response, as seen in ferromagnets. ↑up