No. 2] Proc. Jpn. Acad., Ser. B 97 (2021) 69 Review Transport phenomena in spin caloritronics † By Ken-ichi UCHIDA*1,*2,*3, (Edited by Hiroyuki SAKAKI, M.J.A.) Abstract: 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. Keywords: spin caloritronics, spin current, spin Seebeck effect, spin Peltier effect, magneto- thermoelectric effect, magnetic material mainly focused on thermoelectric power generation 1. Introduction based on the Seebeck effect and electronic cooling Thermoelectric effects enable direct interconver- based on the Peltier effect. sion between heat and electricity.1) One of the In addition to the Seebeck and Peltier effects, representative thermoelectric effects is the Seebeck various thermoelectric transport phenomena appear effect, discovered by T. J. Seebeck in 1821. This effect in a conductor in the presence of a magnetic field H converts a heat current into a charge current in metals or in a magnetic material with spontaneous magnet- and semiconductors. Its performance is described by ization M.2) Such phenomena include the magneto- the Seebeck coefficient, which is defined as the ratio of Seebeck/Peltier effect, in which the Seebeck/Peltier the generated electric field to the applied temperature coefficient depends on the magnitude and direction of gradient. The Onsager reciprocal of the Seebeck effect H or M, and the Nernst (Ettingshausen) effect, in is called the Peltier effect, discovered by J. C. A. which a heat (charge) current induces a transverse Peltier in 1834. Since the discovery of these funda- charge (heat) current perpendicular to H or M mental effects, physics, materials science, and appli- (Fig. 1). In magnetic conductors, the magneto- cation-oriented studies on thermoelectric effects have thermoelectric effects appear even in the absence of an external magnetic field owing to the action of the *1 Research Center for Magnetic and Spintronic Materials spin-orbit interaction on spin-polarized conduction (CMSM), National Institute for Materials Science (NIMS), electrons. Although these magneto-thermoelectric Tsukuba, Ibaraki, Japan. effects have been known for a long time, some of *2 Institute for Materials Research, Tohoku University, Sendai, Miyagi, Japan. these phenomena have not been investigated in *3 Center for Spintronics Research Network, Tohoku detail. The magneto-thermoelectric effects are fasci- University, Sendai, Miyagi, Japan. † nating research subjects that remain to be studied Correspondence should be addressed: K. Uchida, Research from fundamental and applied points of view. Center for Magnetic and Spintronic Materials (CMSM), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, In the past few decades, extensive research on Ibaraki 305-0047, Japan (e-mail: [email protected]). spintronics, in which electron spins are actively doi: 10.2183/pjab.97.004 ©2021 The Japan Academy 70 K. UCHIDA [Vol. 97, Output Longitudinal effect Charge current Heat current Input Output Output M Anisotropic Anisotropic magnetoresistance effect magneto-Peltier effect current Charge M Anisotropic Anisotropic magneto-thermal Input Input magneto-Seebeck effect resistance effect Heat current (Maggi-Righi-Leduc effect) Output Transverse effect Charge current Heat current Input M Anomalous Hall effect Anomalous Ettingshausen effect current Charge Anomalous Output Anomalous thermal Hall effect Input Nernst effect Heat current (Righi-Leduc effect) Fig. 1. (Color online) Electric, thermal, and thermoelectric transport phenomena in magnetic materials. exploited as new information and energy carriers in spin-polarized heat current and introduced the term addition to electron charge, has been carried out all “spin caloritronics”.8) One of the triggers for the rapid over the world.3) The field of spintronics has seen development of spin caloritronics is the discovery of both important scientific discoveries and industrial the spin Seebeck effect (SSE), which refers to the applications, such as hard disk drive read heads, generation of a spin current as a result of a heat magnetoresistive sensors, and magnetic random current in magnetic materials.9)–12) To clarify the access memories.4),5) A key concept in spintronics is mechanism of the SSE, many condensed matter the spin current, which is a pure flow of spin angular physicists began research on spin caloritronics. momentum without an accompanying charge cur- Today, spin caloritronics has grown into an inter- rent. The spin current is used for information writing disciplinary field which is studied worldwide. Since and reading in spintronic devices. The concept of the discovery of the SSE, novel thermo-spin con- the spin current has also triggered the discovery of version principles have been discovered one after various spin-dependent and spin-driven transport another, and unconventional thermoelectric func- phenomena; principles and techniques for generat- tionalities based on spin caloritronics have been ing, detecting, and controlling spin currents have demonstrated. developed rapidly since the beginning of the 21st The aim of this Review is to summarize the basic century. behaviors, spin-charge-heat current conversion sym- In this stream, the interplay between spin, metries, and functionalities of various spin-calori- charge, and heat currents has been extensively tronic phenomena. This Review is organized as investigated. The research field based on the combi- follows. In Sec. 2, we focus on the conversion between nation of thermoelectrics and spintronics is called charge and heat currents in magnetic materials, that spin caloritronics.2),6) This field originated from the is, the magneto-thermoelectric effects that depend on theoretical study by Johnson and Silsbee in 1987, the M direction (Fig. 1). Although detailed explan- which established the nonequilibrium thermodynam- ations of magnetic-field-dependent magneto-thermo- ics of the spin-charge-heat interaction in metal-based electric effects which appear even in nonmagnetic magnetic heterostructures.7) Several decades later, materials are omitted, the symmetries of these effects Hatami et al. theoretically predicted that the M are the same as those of the magnetization-dependent direction of a ferromagnet can be reversed by a effects if the magnetization is replaced by an external No. 2] Transport phenomena in spin caloritronics 71 magnetic field. In Sec. 3, after introducing the 2 SðMÞ¼S? þðS À S?Þ cos M; ½2 concept of spin currents, we review basic properties k of the conversion between spin and heat currents, where Sk (S?) is the Seebeck coefficient when M is that is, the thermo-spin effects. Because spin currents parallel (perpendicular) to the input heat current. are carried not only by conduction electrons but also The AMSE has been observed in various magnetic by the collective dynamics of local magnetic mo- materials and nanostructures. Such observations and ments, i.e., magnons, a wide variety of thermo-spin the Onsager reciprocal relation (& F ST with & being effects appear in magnetic materials and their the Peltier coefficient) indicate the existence of the junction structures. Section 4 is a supplementary AMPE.23) The direct observation of the temperature section that summarizes spin-caloritronic phenomena modulation induced by the AMPE, reported in other than the effects described in the previous 2018,25) revealed the unconventional thermoelectric sections. Section 5 is devoted to the conclusions and conversion functionalities of this phenomenon. For prospects. The author anticipates that this Review example, the AMPE enables reconfigurable electronic will further invigorate basic science and application cooling/heating in a single material without junction studies on spin caloritronics, and accelerate new structures, which cannot be realized if only the entry into this field from various research areas. conventional Peltier effect is used. Figure 2 shows an example of the experimental 2. Conversion between charge and heat results of the AMSE in a polycrystalline Ni slab with currents in magnetic materials a rectangular shape.25) The electric voltage between As summarized in Fig. 1, the conversion be- the ends of the Ni slab was measured at room tween charge and heat currents in magnetic materials temperature with applying a temperature gradient is classified into two categories: “longitudinal effect” rT along the y direction and H (with the magnitude and “transverse effect”, in which the output current is H) in the direction perpendicular or parallel to the generated