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 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 in the direction parallel and perpendicular rT direction (Figs. 2(a) and 2(b)). Figures 2(c) and to the input current, respectively. The most well- 2(d) show the voltage difference "V in the Ni known longitudinal electric transport phenomenon is slab as a function of H for various values of the the anisotropic magnetoresistance (AMR) effect, temperature difference "T, where "V was obtained where the electrical resistivity changes with the by removing the offset due to the H-independent relative angle 3M between the M direction and the thermopower. The "V signals exhibit clear H-even input current.13) In isotropic magnetic materials, the dependence; when H ?rT (H krT ), the magni- AMR obeys the following equation: tude of "V increases (decreases) with increasing |H| 2 and the field-induced change of "V is proportional ðMÞ¼? þð ?Þ cos M; ½1 k to "T (Fig. 2(e)). Importantly, the "V signals in where ;k (;?) is the resistivity when M is parallel the H ?rT (H krT) configuration saturate at (perpendicular) to the input charge current. On the around 70H F 0.4 T (0.1 T), which corresponds to other hand, the most well-known transverse electric the saturation field of the Ni slab (note that the transport phenomenon is the anomalous Hall effect difference in the saturation field is due to the shape (AHE), where the charge current is bent in the magnetic anisotropy). This result indicates that the direction perpendicular to M.14) In a similar manner behavior of "V is determined by M,notH. The to these phenomena, the thermoelectric conversion H-even dependence of the thermopower is a feature properties also depend on the M direction in of the AMSE (see Eq. [2] and note that the magnetic materials (Fig. 1). asymmetric field dependence of the Seebeck coef- 2.1. Longitudinal magneto-thermoelectric ficient called the Umkehr effect30) is absent in effects. The longitudinal thermoelectric effects in isotropic polycrystalline materials). The anisotropy magnetic materials are called the anisotropic magne- of the Seebeck coefficient in the Ni slab was to-Seebeck effect (AMSE) and the anisotropic estimated to be 93% at room temperature. As magneto-Peltier effect (AMPE), where the Seebeck shown in the above example, the AMSE can be and Peltier coefficients depend on 3M, respec- investigated simply by measuring the magnetic field 15)–29) tively. The 3M dependence of the Seebeck dependence of the longitudinal thermopower. Since coefficient S is similar to that of the AMR; if the such measurements are well established, many magnetic material is isotropic, the symmetry of S is experiments on the AMSE have been reported so expressed as far. 72 K. UCHIDA [Vol. 97,

(a) (c) (e) 1.0 0.8 H ⊥ ∇T Ni slab 0.8 0.6 ΔT = 1.54 K 1.18 K V)

μ 0.75 K 0.6 ( 0.4

V 0.38 K Δ H ⊥ ∇T 0.2 0.4 z |μ0H| = 0.6 T ∇T H y 0 0.2 x V)

-0.6 -0.3 0 0.3 0.6 μ

( 0 μ0H (T) V

(b) (d) Δ 0 H || ∇T -0.2 ΔT = 0.38 K -0.2 -0.4 0.75 K ∇ V) H || T μ

( -0.4 |μ0H| = 0.1 T

H V 1.18 K -0.6 Δ -0.6 ∇T 1.54 K -0.8 -0.8 -1.0 -0.2 -0.1 0 0.1 0.2 0 12

μ0H (T) ΔT (K)

Fig. 2. (Color online) (a),(b) Schematic illustrations of the setups for measuring the AMSE. The electric voltage between the ends of the straight Ni slab along the temperature gradient rT was measured with applying a magnetic field H in the directions (a) perpendicular and (b) parallel to rT. (c),(d) The magnetic field 70H dependence of the voltage "V in the Ni slab for various values of the temperature difference "T, measured for the (c) H ?rT and (d) H krT configurations. The voltage offset due to the H- independent thermopower was subtracted. The magnitude of the AMSE signal in the H krT configuration is twice as large as that in the H ?rT configuration, in a similar manner to the AMR. (e) "T dependence of "V in the Ni slab at |70H| F 0.6 T (0.1 T) in the H ?rT (H krT) configuration. The details on these experiments are described in Ref. 25.

Meanwhile, the direct observation of the AMPE magnitude and sign of the current-induced temper- requires unconventional thermal measurement tech- ature modulation, respectively. The ? image also niques. In 2018, we realized the observation of the includes the information on the time delay of the temperature modulation induced by the AMPE by temperature modulation due to thermal diffusion. using the active infrared emission microscopy tech- The heat release and absorption induced by the nique called lock-in thermography (LIT).25),31),32) In AMPE appear on the boundaries between the areas the experiments of thermoelectric effects based on with different 3M values, even in the absence of the LIT, the spatial distribution of infrared radiation junction structures. One of the simple ways to create thermally emitted from the surface of a sample is such boundaries is to form a non-uniform magnet- measured using an infrared camera while applying a ization configuration, as illustrated in Fig. 3(a). square-wave-modulated AC charge current Jc with However, non-uniform magnetization configurations the amplitude Jc, frequency f, and zero DC offset to are not suitable for systematic measurements because the sample. The thermal images oscillating with the it is difficult to change the magnetization distribution same frequency as the input charge current are with high controllability. Therefore, the temperature extracted through Fourier analysis. The contribution modulation induced by the AMPE has been observed of the thermoelectric effects (/ Jc) can be separated mainly in uniformly magnetized U-shaped materials, 2 from the Joule-heating background (/ Jc )by where a charge current is applied along the U-shaped extracting the first harmonic response of the thermal structure (Fig. 3(b)). This configuration also leads to images, because the Joule heating generated in this the non-uniform 3M distribution; the AMPE-induced condition is constant with time. As a result of the temperature modulation appears around the corners Fourier analysis, the obtained thermal images are of the U-shaped structure, that is, the regions transformed into the lock-in amplitude A and phase between the area satisfying M ? Jc and the area ? images, which show the distributions of the satisfying M k Jc. Figure 3(d) shows an example of No. 2] Transport phenomena in spin caloritronics 73

(a) Anisotropic magneto-Peltier effect (d)7 (e) 8.0 Area 2 24 Heat absorption (output) Area 4 (mK) 4.0 Heat release H AMPE

A ○ θH = 0

0 (mK) 0 M 360 AMPE T Δ

(deg) -4.0

Jq cos2θH Magnetic conductor AMPE φ Jc (input) 0 -8.0 0306090

θH (deg)

(b) (f) Area 3 y H (M) θM

θH Magnetic conductor Jc x z Area 1 Area 5 y 2243 4 y

H (M) H (M) Jc θM θ θ 115Ni film 5 θ Jc M z H x z H x

H Jc

Jc 0.2 mm

(c) Anomalous Ettingshausen effect (g)1 (h) 1.0 Area 1 Area 5 (mK) 15H 0.5 AEE

A ○ 0 θH = 0 (mK) 0 M

360 AEE T Δ -0.5 J (output)

q (deg)

Magnetic conductor AEE cosθH φ -1.0 Jc (input) 0 0306090

θH (deg)

Fig. 3. (Color online) (a) A schematic illustration of the AMPE in a magnetic conductor with a non-uniform magnetization M configuration. (b) A schematic illustration of a U-shaped magnetic conductor typically used for measuring the AMPE and AEE. (c) A schematic illustration of the AEE in a uniformly magnetized magnetic conductor. Jc, Jq, and H denote the charge current applied to the magnetic conductor, heat current induced by the Peltier effect or the AEE, and magnetic field, respectively. (d) Lock-in amplitude AAMPE and phase ?AMPE images showing the AMPE-induced temperature modulation for the U-shaped 100-nm-thick Ni film on a glass substrate, measured at the field angle of 3H F 0°, charge current amplitude of 40 mA, and lock-in frequency of 25 Hz. (e) 3H dependence of "TAMPE (F AAMPE cos ?AMPE) on the areas 2 and 4 of the U-shaped Ni film. The solid curves show the cos 23H functions. (f ) Steady-state infrared image of the U-shaped Ni thin film with black-ink coating and the definitions of 3H and 3M. 3H (3M) represents the angle between H and the Dx direction (between M and Jc), where M is aligned along H. The areas 1, 3, and 5, surrounded by white dotted lines, and the areas 2 and 4, the corner of the U-shaped structure, represent different parts of the Ni film. (g) Lock-in amplitude AAEE and phase ?AEE images showing the AEE-induced temperature modulation for the U-shaped 100-nm- thick Ni film on a sapphire substrate, measured at 3H F 0°, charge current amplitude of 75 mA, and lock-in frequency of 25 Hz. (h) 3H dependence of "TAEE (F AAEE cos ?AEE) on the areas 1 and 5 of the U-shaped Ni film. The solid curves show the cos 3H function. The details on these experiments are described in Ref. 28. the experimental results of the AMPE in a poly- (Fig. 3(f )). The pure AMPE contribution was crystalline Ni film with a U-shaped structure, separated from other thermoelectric contributions measured by the LIT technique.28) The LIT images by measuring the dependence of the LIT images on were measured while applying H in the x-y plane at the sign and/or angle of the magnetic field.25),28) an azimuthal angle 3H from the Dx direction When 3H F 0°, we observed clear temperature-mod- 74 K. UCHIDA [Vol. 97, ulation signals appearing predominantly around the large anisotropy of the Seebeck/Peltier coefficient.27) corners (areas 2 and 4 in Fig. 3(f )) of the U-shaped The experimental demonstration of this prediction is structure. The sign of the temperature modulation on desired. the area 2 is opposite to that on the area 4 because 2.2. Transverse magneto-thermoelectric ef- of the lock-in phase difference of 9180°. We also fects. The transverse thermoelectric effects in confirmed that the sign of the AMPE signal is magnetic materials are called the anomalous Nernst 33)–44) reversed at 3H F 90° and the signal disappears at effect (ANE) and the anomalous Ettingshausen 45)–52) 3H F 45°; the 3H dependence of the AMPE signals effect (AEE), which are the thermoelectric follows the cos 23H symmetry (Fig. 3(e)). This behav- analogues of the AHE. In the ANE (AEE), an input ior is consistent with Eq. [2] based on the trigono- heat (charge) current induces a transverse charge metric relations between 3M and 3H. As demonstrated (heat) current in the direction perpendicular to the here, the AMPE enables thermoelectric cooling and M direction. The symmetries of the ANE and AEE heating in a single material without junction are respectively expressed as46) structures. Owing to the absence of junctions, the jc,ANE ¼ SANEðm rTÞ; ½3 thermoelectric output of the AMPE can be enhanced j ¼ ðm rV Þ: ½4 by constructing simple thermopile structures26) and q,AEE AEE reconfigured by changing the shape of the magnetic jc,ANE (jq,AEE) is the charge (heat) current density materials or the magnetization configuration. These driven by the ANE (AEE), m is the unit vector of characteristics provide new concepts in thermal M, SANE (&AEE) is the anomalous Nernst (Etting- management technologies for electronic and spin- shausen) coefficient, < is the electrical conductivity, tronic devices. and rT (rV) is the temperature gradient (electric Because the thermoelectric performance of the field) applied to the magnetic material. The anom- AMSE/AMPE is still very low compared with alous Nernst and Ettingshausen coefficients are conventional thermoelectric devices, it is necessary related by to find or develop magnetic materials with large AEE ¼ SANET; ½5 anisotropy of the Seebeck/Peltier coefficient. To improve the thermoelectric performance, the which is the Onsager reciprocal relation for the AMSE/AMPE was measured not only in Ni but transverse thermoelectric conversion in magnetic also in various ferromagnetic metals.25),29) Although materials. Based on this symmetry, the ANE/AEE Ni exhibits clear anisotropy of the Seebeck/Peltier exhibits a convenient scaling law that is entirely coefficient, the AMSE/AMPE in polycrystalline Fe different from that of the longitudinal thermoelectric was observed to be negligibly small. This behavior is effects. In the case of the ANE, the output voltage quantitatively reproduced by first-principles-based (power) can be increased simply by elongating the Boltzmann transport calculations, which clarified device length (enlarging the device area) perpendic- that spin-flip electron transitions due to the spin- ular to the temperature gradient without forming orbit interaction are the key mechanism in the a multitude of serial p-n junctions. Furthermore, AMSE/AMPE.27) The magnitude of the AMSE/ the thermoelectric output of the ANE/AEE can be AMPE signals in Ni95Pt5 and Ni95Pd5 was found to actively controlled through the manipulation of be larger than that in pure Ni; the anisotropy of the M.47),48),50) Thus, the ANE (AEE) has the potential Seebeck/Peltier coefficient of Ni95Pt5 reaches 912%. to realize simple and versatile thermal energy However, the experiments also show that excess Pt harvesting or heat-current sensing (thermal energy and Pd contents decrease the anisotropy of the management) applications. Although the primary coefficient. These results indicate that the doping of studies on the ANE/AEE were conducted a long time heavy elements with strong spin-orbit interaction to ago,53)–55) the number of studies was quite limited. ferromagnetic materials is useful for improving the However, the ANE has received renewed attention in thermoelectric conversion efficiency of the AMSE/ spin caloritronics since the discovery of the SSE, and AMPE, but the material dependence in such alloys experimental methods to separate the SSE from the is not simple and not fully understood. However, ANE have been investigated.56),57) These develop- materials science studies to find magnetic materials ments have significantly promoted research on the that show large AMSE/AMPE are already in ANE itself. In particular, since the observation of progress. In this vein, Masuda et al. predicted that the giant ANE in magnetic topological materials in several ferromagnetic ordered alloys exhibit very 2018,39) physics and materials science researches have No. 2] Transport phenomena in spin caloritronics 75 further accelerated and become a trending develop- ANE thermopower exhibits the odd dependence on ment in condensed matter physics. In contrast to the the magnetization direction, that is, the H-odd ANE, the AEE was investigated only in typical dependence. In contrast to isotropic bulk materials, ferromagnetic metal slabs since the 1920s.53)–55) This ANE measurements for thin films are performed in situation was changed by the LIT technique; in 2018, two different configurations due to the huge differ- Seki et al. reported the visualization of the AEE- ence between the in-plane and out-of-plane dimen- induced temperature modulation in ferromagnetic sions. One configuration is the in-plane magnetized FePt thin films.45) Subsequently, the AEE has been (IM) configuration, where H (rT) is applied along observed in various materials in both bulk and film the in-plane (out-of-plane) direction (Fig. 4(a)). The forms, where the U-shaped structure is often used to IM configuration is suitable for thermal energy demonstrate the symmetry of the AEE (Figs. 3(b) harvesting and heat sensing applications because and 3(c)). An example of the AEE measurements ANE-based thermoelectric generation can be realized using a Ni film is shown in Figs. 3(g) and 3(h).28) By simply by forming films onto heat sources. In using the LIT method, the AMPE and AEE can be contrast, it is difficult to estimate SANE quantitatively measured simultaneously but can be separated from in the IM configuration because of the difficulty in each other owing to the different symmetries.25),28),29) estimating the temperature difference between the 57) In 2019, it was demonstrated that SmCo5-type top and bottom of thin films. The other config- permanent magnets exhibit the large AEE.49) uration is the perpendicularly magnetized (PM) The ANE can be characterized by measuring the configuration, where H (rT ) is applied along the magnetic field dependence of the transverse thermo- out-of-plane (in-plane) direction (Fig. 4(b)). The PM power in magnetic materials. Following Eq. [3], the configuration is widely used for the quantitative

(a) In-plane magnetized (IM) (c) (e) configuration 1.0 1.0 Magnetic z conductor )

) Pt/Fe -1 y -1 S0 x V K V K 0 μ μ 0.5 ( ( ∇T 0 S

S Au/Fe

[Pt(1)/Fe(1)] Cu/Fe -1.0 5 Substrate -4-20 2 4 0 246810 H μ0H (T) N

(b) Perpendicularly magnetized (PM) (d) (f) configuration 1.0 1.0 Pt/Fe H z S0 ) ) -1

y -1 Au/Fe

x V K V K 0 μ μ 0.5 ( ( 0

∇ S

T S Cu/Fe [Pt(1)/Fe(1)] -1.0 5 -4-20 2 4 0 246810

μ0H (T) N

Fig. 4. (Color online) (a),(b) Schematic illustrations of the (a) IM and (b) PM configurations used for measuring the ANE in a magnetic conductor film on an insulating substrate. (c),(d) 70H dependence of the transverse thermopower S in the [Pt(1)/Fe(1)]5 multilayer film in the (c) IM and (d) PM configurations. The numbers in parentheses represent the layer thickness in nanometers and the subscript represents the number of the Pt/Fe bilayers, indicating that the total thickness of the [Pt(1)/Fe(1)]5 multilayer film is 10 nm. S0 is the ANE contribution in the thermopower. (e),(f ) N dependence of S0 in the Pt/Fe, Au/Fe, and Cu/Fe multilayer films in the (e) IM and (f ) PM configurations. N denotes the number of the nonmagnetic metal/Fe interfaces. The total thickness of the multilayers is fixed at 10 nm, indicating that the interface density increases with increasing N. The details on these experiments are described in Ref. 37. 76 K. UCHIDA [Vol. 97,

39)–41),44) estimation of SANE, although it often requires a large at room temperature. The large ANE/AEE magnetic field to align M of films along the out-of- in SmCo5-type permanent magnets has also been plane direction. discussed in terms of the intrinsic mechanism; the Figure 4 shows an example of the experimental experimental results are well reproduced by first- results of the ANE in multilayer films comprising principles calculations, in which the intrinsic band alternately stacked ferromagnetic and nonmagnetic structure and the chemical potential shift due to metals.37) Here, the multilayer film can be regarded carrier doping were taken into account.49),52) Another as a single effective magnetic material. Figures 4(c) strategy for enhancing the ANE/AEE is to optimize and 4(d) show the 70H dependence of the transverse the magnetic multilayer structures. As shown in thermopower S in a Pt/Fe multilayer film formed on Figs. 4(e) and 4(f ), the ANE in alternately stacked a single-crystalline Gd3Ga5O12 (111) substrate in the ferromagnetic metal/nonmagnetic metal multilayers IM and PM configurations, respectively. S is defined was found to be enhanced by increasing the number as (V/"T)(Lz/Ly) in the IM configuration and (V/ of interfaces while keeping the total thickness "T)(Lx/Ly) in the PM configuration, where V is constant. Although the enhancement of the ANE the voltage between the ends of the film, "T is the in multilayers seems to be a universal trend,37),58)–60) temperature difference between the ends of the the microscopic mechanism is not yet clarified. As sample including the substrate, and Lx,y,z is the discussed above, not only investigations of bulk length of the sample along the x, y,andz directions. transport properties but also multilayer design and The S values exhibit clear H-odd dependence and interface engineering are essential in the studies of saturate when M is aligned along H, indicating that the ANE/AEE. the ANE provides the dominant contribution to the transverse thermopower and that the field-induced 3. Conversion between spin and heat currents ordinary Nernst effect is negligibly small. The ANE- In the field of spin caloritronics, various con- driven transverse thermopower S0 can be extracted version phenomena between spin and heat currents by extrapolating the S data in the high field region to have been discovered and investigated. The princi- zero field. Note that S0 º SANE in the IM config- ples of such thermo-spin effects are conceptually uration because of the difference in the thermal different from the magneto-thermoelectric effects conductivities between the film and substrate, while summarized in Sec. 2. In this section, we first review S0 F SANE in the PM configuration because of the the definition of spin currents, followed by a same temperature difference in the film and sub- summary of the basic behaviors and symmetries of strate. typical thermo-spin effects. For practical applications of the ANE, it is 3.1. Definition of spin current. The charge important to find and develop magnetic materials current density jc is defined by the continuity with large SANE. In general, SANE can be divided into equation for the charge density ; as 42),49) two components as d ¼rjc; ½7 SANE ¼ xxxy þ xyxx; ½6 dt where ;xx (;xy) is the diagonal (off-diagonal) compo- where t is time. This equation expresses the nent of the electrical resistivity tensor and ,xx (,xy)is conservation of electron charge. In a similar manner, the diagonal (off-diagonal) component of the thermo- the spin current density js is defined by the continuity electric conductivity tensor. The second term on the equation for the magnetization M as right-hand side of Eq. [6] originates from the AHE of dM fl ¼rj þ T; ½8 the longitudinal carrier ow induced by the Seebeck dt s effect. The first term originates from the intrinsic ANE, as ,xy directly converts rT into a transverse which expresses the conservation of angular momen- 3) electric field. A recent trend in improving SANE is tum. Here, . is the gyromagnetic ratio and M to find materials with large ,xy, in which the Berry includes not only the macroscopic spontaneous mag- curvature of the electronic bands near the Fermi level netization but also nonequilibrium components. plays an essential role. Materials with topological Equations [7] and [8] indicate that a spin current band structure, e.g., Co-based Heusler alloys, show transports magnetic moments or angular momentum, large values of ,xy due to their large Berry curvature, whereas a charge current transports electron charge. !1 which in turn lead to large SANE values of 6–8µVK In contrast to the charge current, which is a No. 2] Transport phenomena in spin caloritronics 77 conserved flow, the spin angular momentum dissi- (a) Charge current pates into, for example, the lattice system, and the spin current is a non-conserved flow that disappears within a certain distance in a certain time. Thus, the −e right-hand side of Eq. [8] contains the spin relaxation term T.Onasufficiently short length scale for spin relaxation to be negligible, the spin current can be Spin Charge approximated as a conserved flow. Therefore, spin current physics has progressed rapidly with the (b) Conduction electron spin current development of nanotechnology that enables the Up-spin electron construction of devices smaller than the spin relax- ation length. The spin current is a second-order tensor quantity containing two degrees of freedom, namely, a spatial component (the direction in which the spin current flows) and a spin polarization Down-spin electron component. However, the spin current can be treated as a vector quantity when the quantization axis of (c) Magnon spin current the spin is fixed (note that the operator r on the right-hand side of Eq. [8] acts on the spatial component). The spin current can be carried by m conduction carriers with spin angular momenta, such as conduction electrons,61),62) magnons or spin waves,63),64) and spinons.65) Hereafter, we focus on Fig. 5. (Color online) Schematic illustrations of (a) the charge spin-current transport phenomena driven by con- current, (b) the conduction electron spin current, and (c) the ! duction electrons and magnons, because they are the magnon spin current. e and m denote the electron charge and the magnetic moment, respectively. central foci of spintronics and spin caloritronics. 3.1.1. Conduction electron spin current. When an external force, such as an electric field, is applied to metals or semiconductors, a nonequilibrium charge current, i.e., Jc º 0 means Js º 0. An important case current is driven by conduction electrons on the is that the up- and down-spin electron flows have the Fermi surface. In a similar way, spins can be carried same magnitude but opposite directions, as depicted by conduction electrons acted on by an external in Fig. 5(b). This situation leads to the generation force; the conduction electron spin current exists only of a pure spin current without any charge current, in electric conductors. Assuming that the spin i.e., Jc F 0andJs º 0. The concept of the pure spin quantization axis is fixed, the charge current Jc and current plays a key role in various spin-transport conduction electron spin current Js are respectively phenomena and spintronic applications. Importantly, expressed as the conduction electron spin current can be injected into a nonmagnetic material using various methods Jc ¼ eðJ" þ J#Þ; ½9 including nonlocal spin-injection techniques61),62) and ! ff 62),66) Js ¼ ðJ" J#Þ; ½10 the spin Hall e ect (SHE). The propagation 2 length of the conduction electron spin current is 67) where J" (J#) is the up-spin (down-spin) electron called the spin diffusion length, which is on the flow, !e (e > 0) is the electron charge, and !/2is order of several nanometers in metals with strong the electron spin angular momentum (Figs. 5(a) and spin relaxation or spin-orbit interaction, such as Pt. 5(b)). The conduction electron spin current is often In contrast, the spin diffusion length can reach expressed in the same unit as the charge current by several hundreds of nanometers or several micro- multiplying Eq. [10] by 2e/!. When the magnitude of meters in conductors with weak spin-orbit interac- the up-spin electron flow is different from that of the tion. With modern microfabrication technologies and down-spin electron flow, the conduction electron spin thin-film deposition methods, vertical as well as current becomes finite. In ferromagnetic metals, in lateral magnetic junction structures smaller than which conduction electrons are spin-polarized, the the spin diffusion length can be easily fabricated. charge current is always accompanied by a spin Thus, the physics and behavior of the conduction 78 K. UCHIDA [Vol. 97, electron spin current have already been investigated Interfacial exchange interaction Conduction in detail in spintronics. (Spin-mixing conductance) Magnon electron spin current 3.1.2. Magnon spin current. A magnon is a spin current quasiparticle of a spin wave, which is the collective dynamics of localized magnetic moments in magnetic materials. The magnon spin current is the flow of Spin-dependent Seebeck effect spin angular momentum carried by magnons Spin Nernst effect Spin-dependent Peltier effect (Fig. 5(c)). The magnon spin current can exist even Spin Ettingshausen effect in magnetic insulators with no conduction electrons, and is always a pure spin current because magnons have no charge. Magnons follow the Bose-Einstein

statistics, and are thermally excited in magnetic Spin Hall effect Spin Peltier effect

fi fl Spin Seebeck effect materials at nite temperatures. However, a net ow Inverse spin Hall effect of spin angular momentum, that is, the magnon spin current, is not generated under thermal equilibrium conditions because magnons with wavenumbers k and !k exist in equal numbers. The magnon spin Charge Heat current is generated when there is an imbalance in current Seebeck/Peltier effects current the numbers of k and !k magnons due to some Magneto-thermoelectric effects external forces. The magnon dynamics can be Fig. 6. (Color online) Conversion phenomena between spin, obtained by solving the Landau-Lifshitz-Gilbert charge, and heat currents. The magneto-thermoelectric effects equation, which is the equation of motion for summarized in Fig. 1 are included in the conversion between magnetic moments: charge and heat currents. Spin-current transport phenomena are conceptually different from the magneto-thermoelectric effects. dm dm ¼m Heff þ m : ½11 dt Ms dt

Here, Heff is the effective magnetic field including (Fig. 6). The spin-mixing conductance enables the the contributions of the external magnetic field, generation of magnon spin currents by injecting exchange interaction, magnetic dipole interaction, conduction electron spin currents into magnetic and magnetic anisotropy; Ms is the saturation mag- materials. Furthermore, it enables the detection of netization; and , is the Gilbert damping constant. magnon spin currents by converting them into The first term in Eq. [11] describes the precession conduction electron spin currents. This interconver- motion of m around the Heff direction, which can be sion is essential in the SSE and its Onsager reciprocal derived from the Heisenberg equation of motion. The called the spin Peltier effect (SPE), discussed in second term is the relaxation term phenomenologi- Sec. 3.3. cally introduced to direct m in the Heff direction. Due 3.2. Spin-dependent Seebeck and Peltier to the Gilbert damping, the magnon spin current is effects: Thermo-spin conversion based on con- also a non-conserved quantity. However, the prop- duction electron transport. Let us recall the agation length of the magnon spin current can reach longitudinal electron transport in a conductor. The the order of micrometers or millimeters in materials charge current density jc and heat current density 63),64) with small , values, such as yttrium iron garnet jq are driven by the electrochemical potential Y3Fe5O12 (YIG), which is significantly longer than gradient r7 and temperature gradient rT. The the spin diffusion length of the conduction electron linear-response transport can be expressed as ! spin current. The magnon spin current is typically jc L11 L12 r=e generated by nonlocal spin injection,64) microwave- ¼ ; ½12 j L L rT driven spin pumping,63) and temperature-gradient- q 21 22 driven SSE.10),12) where the magneto-thermoelectric effects are not The magnon spin current in a magnetic material described explicitly. In general, the Onsager recip- and the conduction electron spin current in a metal rocal relation holds between the off-diagonal compo- can be interconverted via the interfacial exchange nents of the transport coefficient matrix L12 and L21, interaction at the magnetic material/metal junction, which correspond to the Seebeck and Peltier effects, which is known as the spin-mixing conductance68) respectively. No. 2] Transport phenomena in spin caloritronics 79

The conduction electron spin current (with the librium temperature difference between up- and density js) extends the electron transport phenom- down-spin electrons, called spin heat accumulation, ena. The transport phenomena in ferromagnetic in a similar nanopillar device.72) The spin-heat conductors are often represented by up- and down- current conversion phenomena described in Eq. [13] spin electron flows when the spin quantization axis is appear only in itinerant electron systems. Their fixed. Here, not only the electrical conductivity and mechanisms are completely different from those of (electronic) thermal conductivity but also the See- the SSE and SPE, as described in the next beck and Peltier coefficients exhibit spin dependence. subsection. For example, the electrical conductivity for up-spin 3.3. Spin Seebeck and Peltier effects: Ther- electrons <" is different from that for down-spin mo-spin conversion based on magnon transport. electrons <# in ferromagnetic conductors. The driving The rapid development of spin caloritronics was forces in the spin-dependent electron transport are triggered by the discovery of the SSE in which a spin the spin-dependent electrochemical potential gra- current is generated as a result of a temperature dient r7",# and rT, and the transport equation is gradient applied to a junction system comprising a expressed as magnetic material and a conductor. Because the 0 1 0 10 1 first experiment on the SSE reported in 2008 was jc M11 M12 M13 rð" þ #Þ=e B C B CB C performed using a junction of a ferromagnetic metal @ j A ¼ @ M M M A@ rð Þ=e A; 9) s 21 22 23 " # (Ni81Fe19) and a paramagnetic metal (Pt), the SSE jq M31 M32 M33 rT was initially discussed in terms of spin transport by conduction electrons, i.e., the aforementioned spin- ½13 dependent Seebeck effect, which occurs only in metals 73) where !r(7" D 7#)/e corresponds to !r7/e in and semiconductors. However, it was experimen- Eq. [12] and !r(7" ! 7#)/e is the driving force due tally demonstrated in 2010 that the SSE occurs in a to the spin accumulation gradient. The heat current magnetic insulator in which transport by conduction and conduction electron spin current are directly electrons is completely frozen.10),12) These experi- coupled if the off-diagonal components of Eq. [13] are ments upset the conventional interpretation and finite. For example, if the M23 component is finite, the revealed that the SSE originates from thermally conduction electron spin current is generated by a excited magnon transport, because magnons can temperature gradient. This phenomenon is known as carry spin currents even in insulators.74)–80) Since the spin-dependent Seebeck effect because it is driven the discovery of the SSE in magnetic insulators, the by the spin dependence of the Seebeck coefficient. experimental techniques and theoretical understand- Equation [13] also holds the Onsager reciprocal ing of this phenomenon have developed dramatically. relations, and various thermo-spin effects that Most of the recent SSE experiments were performed correspond to each off-diagonal component exist. using magnetic insulators because the insulator- Many of these phenomena have already been based systems allow us to obtain a relatively large observed experimentally. In 2010, Slachter et al. heat-spin current conversion capability and to used nonlocal spin-injection/detection methods in a separate the contribution of the conduction-elec- lateral spin-valve structure and successfully observed tron-driven magneto-thermoelectric effects from the the spin accumulation induced by the temperature magnon-spin-current contribution, enabling system- difference between ferromagnetic/paramagnetic atic and reliable investigation of the SSE.81) Consid- metal interfaces.69) This is the first direct detection ering the difference in the driving carriers between of the spin-dependent Seebeck effect. In 2011, Le the SSE and the spin-dependent Seebeck effect, it Breton et al. demonstrated temperature-gradient- may be expected that the former would be referred induced spin injection into Si via a tunnel junction, to as “magnon Seebeck effect” and the latter as “spin which is called the Seebeck spin tunneling, in a Seebeck effect”. However, as mentioned above, the ferromagnetic metal/oxide/Si junction system.70) SSE experiment was reported earlier than the In 2012, Flipse et al. observed the spin-dependent observation of the spin-dependent Seebeck effect by Peltier effect, the reciprocal of the spin-dependent Slachter et al. In addition, the term “spin Seebeck Seebeck effect, in a nanopillar spin-valve device effect” and the experimental method in Ref. 9 were consisting of two ferromagnetic metal layers sepa- already widely used in 2010 when the direct rated by a nonmagnetic metal.71) Subsequently, observation of the spin-dependent Seebeck effect Dejene et al. reported the observation of a nonequi- was reported. Thus, the spin-caloritronics commun- 80 K. UCHIDA [Vol. 97, ity has decided to continue to refer to the magnon- metal Pt. When rT is applied to YIG, a magnon spin driven thermo-spin conversion as the SSE, while the current is generated along the gradient due to the conduction-electron-driven thermo-spin conversion is thermally excited dynamics of localized magnetic distinguished from the SSE by calling it the spin- moments (Fig. 7(a)). The magnon spin current in dependent Seebeck effect.6) Although the terminolo- YIG is converted into a conduction electron spin gies of the thermo-spin effects may be confusing current with the spatial direction Js and the spin because of the historical reasons, the SSE and the polarization vector < in the Pt layer via the spin- spin-dependent Seebeck effect are completely differ- mixing conductance at the Pt/YIG interface, where ent phenomena. The same situation also applies to Js is normal to the Pt/YIG interface plane and < is the magnon-driven SPE and the conduction-electron- parallel to M of YIG. This conduction electron spin driven spin-dependent Peltier effect (Fig. 6). current in the Pt layer is then converted by the Here, the basic mechanism and behavior of the strong spin-orbit interaction into the charge current SSE are summarized. A typical system used for Jc satisfying the following symmetry: measuring the SSE is a junction structure consisting Jc / < Js: ½14 of a ferrimagnetic insulator YIG and a paramagnetic

(a) (b) 0.2 (T) s

V M Metal film (Pt) 0 0.1 μ J (output) c 0 Conduction (c) 150 Inverse electron Pt-film/YIG-slab junction spin Hall effect spin current 10 Js )

Spin-mixing κ -1 conductance 100 (W m V K

Magnon μ ( -1

Spin Seebeck effect spin current 5 K SSE -1 S

50 ) m

Magnetic insulator ∇T (YIG) (input) 0 0 50 100 150 200 250 300 T (K) (d) (e) 2 Pt-film/YIG-slab junction

Metal film (Pt) 1 Jc (input) Conduction electron Spin Hall effect spin current J (mK) 0 1 mA Spin-mixing s SPE

conductance T 5 mA 2 Δ Magnon 0.1 T 10 mA Spin Peltier effect (mK) spin current -1 1 SPE

T 8.0 T

15 mA Δ m 0 0 5 10 15 ∇ Magnetic insulator T -2 Jc (mA) (YIG) (output) -10 -5 0 5 10

μ0H (T)

Fig. 7. (Color online) (a) A schematic illustration of the SSE in a junction system comprising a magnetic insulator (e.g., YIG) and a metal film (e.g., Pt). The SSE in this configuration is called the longitudinal SSE, because the input temperature gradient and output spin current are parallel to each other. Js denotes the spatial direction of the spin current. The spin polarization vector (black arrows) in the metal layer is aligned along the m direction in the insulator layer. (b) Temperature T dependence of the saturation magnetization Ms of the YIG slab. (c) T dependence of the transverse thermopower induced by the SSE SSSE in the Pt-film/YIG-slab junction system and the thermal conductivity 5 of the single-crystalline YIG slab. (d) A schematic illustration of the SPE in a junction system comprising a magnetic insulator and a metal film. (e) 70H dependence of the temperature modulation induced by the SPE "TSPE in the Pt/YIG system for various values of the input charge current Jc. The inset to (e) shows the Jc dependence of "TSPE at 70|H| F 0.1 and 8.0 T. The details on these experiments are described in Refs. 86 and 95. No. 2] Transport phenomena in spin caloritronics 81

This spin-to-charge current conversion is called the ductivity differ at temperatures higher than the peak inverse spin Hall effect (ISHE), while the conversion temperature. Although YIG is still most widely used of a charge current into a conduction electron spin in spin caloritronics, the SSE has been observed in current via the spin-orbit interaction is called the various materials including ferro(ferri)magnetic, par- spin Hall effect (SHE) (Fig. 6).66) Because the ISHE amagnetic,89) antiferromagnetic,90),91) multiferroic,92) enables spin currents to be detected as voltage and quantum spin materials,65) indicating that the signals, it is extensively used to measure spin current SSE is a universal transport phenomenon appearing phenomena. The symmetry of the ISHE causes the in a wide variety of materials. SSE thermopower to be generated in the direction The symmetry of the SSE thermopower is perpendicular to rT and M; the SSE can hence work similar to but different from that of the ANE as a transverse thermoelectric generator.81),82) In SSE thermopower. The SSE can be separated from the experiments, the metallic layer must be a thin film ANE by comparing the transverse thermopower in with a thickness comparable to the spin diffusion the IM configuration (Fig. 8(a)) and the PM config- length for efficient conversion from spin currents into urations (Fig. 8(b)).56),57) As shown above, in the IM voltage signals. In contrast, both bulk and thin film configuration, both the SSE and ANE exhibit the materials can be used as the magnetic insulator layer. transverse thermopower of which the sign is reversed Because the magnitude of the SSE-induced spin by reversing M. In contrast, in the PM configuration, current depends on the propagation length of sub- the SSE thermopower disappears due to the symme- thermal magnons, the ISHE voltage due to the SSE try of the ISHE (see Eq. [14] and note that Js k < in increases with increasing the thickness of the the PM configuration), while the ANE thermopower magnetic insulator layer and saturates at a thickness can appear because the rT, M, and inter-electrode of several micrometers in single-crystalline YIG.83)–85) directions are at right angles to one another. In fact, As discussed above, the combination of the SSE with an isotropic ferromagnetic metal film was shown to the ISHE enables transverse thermoelectric gener- exhibit isotropic ANE thermopower in the IM and ation using insulators, which cannot be realized with PM configurations (Figs. 8(c) and 8(d)), while the conventional thermoelectric effects. Pt/YIG system exhibits no thermopower in the PM A typical temperature-dependent behavior of configuration, except for the small contribution from the SSE-induced transverse thermopower, i.e., the the ordinary Nernst effect in the Pt layer (Figs. 8(e) ISHE voltage induced by the SSE, is shown in and 8(f )). This comparison confirms that the SSE Fig. 7(c).86) The sample system used in this experi- is irrelevant to the ANE induced by the magnetic ment is a junction comprising a single-crystalline proximity effect93) near the Pt/YIG interface. YIG slab and a Pt thin film. The SSE thermopower The Onsager reciprocal of the SSE is the SPE, in appears at temperatures lower than the Curie which a heat current is generated as a result of a temperature of YIG and disappears at absolute zero spin current (Fig. 6). It was first experimentally temperature. The temperature dependence of the observed in 2014 by Flipse et al., who also used Pt/ SSE thermopower is completely different from the YIG junction systems.94) As schematically illustrated magnetization curve of YIG (compare Fig. 7(b) and in Fig. 7(d), the SPE appears through the inverse 7(c)). When single-crystalline YIG is used, the SSE process of the SSE. When Jc is applied to the Pt film, thermopower increases with decreasing temperature a conduction electron spin current is generated in the and exhibits a peak at 930 K. The temperature at direction of the film thickness by the SHE, and the which the thermopower reaches its maximum is spin accumulation occurs near the Pt/YIG interface. comparable to that at which the thermal conductiv- The spin accumulation is polarized in the direction ity of the single-crystalline YIG becomes maximum, that satisfies the following relationship:66) where the thermal conductivity of YIG is determined J / < J : ½15 mainly by phonon transport. Therefore, the steep s c peak signal may be related to the phonon drag effect This spin accumulation is converted into a magnon on the SSE.87),88) There is also another argument that spin current in YIG via the spin-mixing conductance. the low-temperature enhancement of the SSE ther- The heat current generation due to the magnon spin mopower is determined not only by the phonon drag current is the SPE. When < in the Pt layer is parallel effect but also by the enhancement of the magnon or antiparallel to M of YIG, the amplitude of the propagation length because the temperature depend- magnetic moment precession in YIG changes owing ences of the SSE thermopower and thermal con- to the transfer of spin angular momentum, which 82 K. UCHIDA [Vol. 97,

IM configuration PM configuration

(a) H (b) Metal film

Ly ∇T ∇T Lz Insulator

Lx slab H

1.0 (c) 1.0 (d) ) )

-1 Ni81Fe19-film/GGG-slab -1 Ni81Fe19-film/GGG-slab V K V K μ μ

) ( 0 ) ( 0 NiFe NiFe T T ∇ ∇ y y L L /( /( V V -1.0 -1.0 1.0 (e) 1.0 (f) ) )

-1 Pt-film/YIG-slab -1 Pt-film/YIG-slab V K V K μ μ

) ( 0 ) ( 0 YIG YIG T T ∇ ∇ y y L L /( /( V V -1.0 -1.0 -0.5 0 0.5 -5 0 5

μ0H (T) μ0H (T)

Fig. 8. (Color online) (a),(b) Schematic illustrations of the metal film/insulator slab junction system in the (a) IM and (b) PM configurations. Lx, Ly, and Lz denote the width, length, and thickness of the system, respectively. (c),(d) 70H dependence of the transverse thermopower in the Ni81Fe19-film/Gd3Ga5O12 (GGG)-slab junction system in the (c) IM and (d) PM configurations. The thermopower is defined as the thermoelectric voltage V normalized by the temperature gradient in the Ni81Fe19 film rTNiFe and Ly. (e),(f ) 70H dependence of the transverse thermopower in the Pt-film/YIG-slab junction system in the (e) IM and (f ) PM configurations. The thermopower is defined as V normalized by the temperature gradient in the YIG slab rTYIG and Ly. The details on these experiments are shown in Ref. 57. changes the number of magnons. An increase than the SSE experiments. In fact, few experimental (decrease) in the number of magnons corresponds studies on the SPE were reported for several years to the high (low) effective temperature of the magnon after its discovery until the establishment of versatile system. Therefore, the temperature near the Pt/YIG measurement methods for the spin-current-induced interface is changed by the nonequilibrium state temperature change. In 2016, we applied the LIT induced by the spin current injection. On the other technique to the measurement of the SPE, and hand, when < and M are orthogonal, no temperature successfully visualized the spin-current-induced tem- 32) change appears. The heat current Jq generated by perature change and its unique spatial distribution. the SPE thus obeys the symmetry The LIT method enables the measurement of the SPE with high temperature and spatial resolutions Jq /ð< MÞn; ½16 in a simple and versatile sample structure, which does where n is the normal vector of the magnetic not require micro/nanofabrication techniques. Based material/conductor junction interface.32) on the knowledge obtained from the LIT measure- Because the observation of the SPE requires ments, the SPE was subsequently observed by using highly sensitive and accurate temperature measure- a thermocouple sensor95) as well as a lock-in ments for thin-film devices, it is more challenging thermoreflectance method.96) Figure 7(e) displays No. 2] Transport phenomena in spin caloritronics 83 an example of the direct measurement of the by a magnetic field or spin injection. By utilizing this temperature change due to the SPE by attaching a property, high-performance magnetic sensors and thin thermocouple to the surface of a Pt-film/single- memories have been developed in spintronics, and crystalline YIG junction system.95) This result many researchers are conducting materials science indicates that the temperature change increases in and device engineering studies to further improve proportion to the charge current applied to the Pt the performance of the GMR and TMR devices.4),5) layer and that the sign of the temperature change is In such multilayer devices, not only the electrical reversed in response to the magnetization reversal of resistivity but also the thermal conductivity100) and YIG. It is also important to note that the temper- the Seebeck/Peltier coefficients101)–104) can change ature change signal is suppressed when a strong depending on whether the magnetization directions magnetic field is applied. This behavior results from of the ferromagnetic layers are parallel or antipar- the suppression of the thermal excitation of magnon allel. Improved thermoelectric conversion efficiency spin currents due to the Zeeman gap under a strong and thermal conductivity switching ratio may make magnetic field.83),95) Systematic studies on the SPE the principles and technologies of spin caloritronics performed using various measurement techniques useful for the thermal management of electronic and have led to the elucidation of its detailed behavior. spintronic devices. Theoretical studies on the SPE have also been All the thermo-spin effects introduced in Sec. 3 reported.97)–99) can be classified as the longitudinal effects because spin and heat currents flow parallel to each other. 4. Other spin-caloritronic phenomena Recently, basic studies on the transverse thermo-spin In Secs. 2 and 3, we discussed the magneto- effects have also been conducted. For example, in thermoelectric and thermo-spin effects in magnetic 2017, several groups reported the observation of the materials and their simple junction structures. In spin Nernst effect,105)–107) which is the thermal addition to such simple systems, spin-caloritronic analogue of the SHE. In the spin Nernst effect, a phenomena also appear in giant magnetoresistance conduction electron spin current is generated in (GMR) and tunneling magnetoresistance (TMR) nonmagnetic conductors via the spin-orbit interac- devices, which form the core of spintronic technolo- tion in the direction perpendicular to the applied heat gies. In the GMR (TMR) device in which a non- current (Fig. 6). These experiments suggest the magnetic metal (insulator) film is sandwiched be- existence of the spin Ettingshausen effect, the tween two ferromagnetic metal films, the electrical reciprocal of the spin Nernst effect, and its direct resistivity is larger when the magnetization directions observation is desired. As reviewed above, the of the adjacent ferromagnetic layers are antiparallel development of novel phenomena, principles, and than when they are parallel (Fig. 9). The switching functionalities based on the interplay between spin, of the magnetization configuration can be achieved charge, and heat currents is still ongoing in spin caloritronics. Parallel magnetization Antiparallel magnetization 5. Conclusions configuration configuration We have reviewed the thermoelectric effects J or J J or J c q c q unique to magnetic materials, i.e., the magneto- thermoelectric effects, and the conversion phenomena FM between spin and heat currents, i.e., the thermo-spin M NM effects. Although only several examples of such FM phenomena are introduced in this Review, new principles and phenomena are discovered in spin caloritronics every year. The background to this rapid development lies in the fact that the 2 # 2 Fig. 9. (Color online) A schematic illustration of the electric and transport coefficient matrix representing charge and thermal transport phenomena in a GMR or TMR device. In heat transport phenomena (Eq. [12]) is extended to fi GMR and TMR devices, two ferromagnetic (FM) metal lms are the 3 # 3 matrix by including a spin current separated by a nonmagnetic (NM) metal and insulator film, fi respectively. The transport coefficients in such structures are (Eq. [13]), which results in a signi cant increase in switched by changing the magnetization configuration of the the variety of transport phenomena. Moreover, the FM layers from parallel to antiparallel, and vice versa. introduction of other spin transport carriers, such as 84 K. UCHIDA [Vol. 97, magnons, has brought about a wider variety of supports and R. Iguchi, T. Hirai, and R. Modak for thermo-spin conversion phenomena. Research fields preliminary reviews of the manuscript. This work was in which novel phenomena are discovered frequently partially supported by CREST “Creation of Innova- are extremely rare and there is a significant amount tive Core Technologies for Nano-enabled Thermal of physics that remains unclear in spin caloritronics. Management” (JPMJCR17I1) and PRESTO “Phase The exploration of new principles has motivated Interfaces for Highly Efficient Energy Utilization” numerous experimental and theoretical researchers to (JPMJPR12C1) from JST, Japan; Grant-in-Aid for study spin-caloritronic phenomena. Challenging Exploratory Research (26600067) and What is the significance of spin caloritronics Grant-in-Aid for Scientific Research (A) (15H02012) from the viewpoint of applications? One of the from JSPS KAKENHI, Japan; and the NEC answers to this question is the utilization of novel Corporation. functionalities provided by the spin degree of free- dom, which cannot be realized with conventional References thermal energy engineering and thermoelectric tech- 1) Ashcroft, N.W. and Mermin, N.D. (1976) Solid nologies. Employing the transport phenomena intro- State Physics. Saunders College, Philadelphia. duced in this Review, various thermoelectric gener- 2) Boona, S.R., Myers, R.C. and Heremans, J.P. (2014) ation and thermal management functionalities can Spin caloritronics. Energy Environ. Sci. 7, 885– be realized, including the following: 910. • Magnetic-field-induced control of the sign and 3) Maekawa, S., Saitoh, E., Valenzuela, S.O. and Kimura, T. (eds.) (2017) Spin Current (2nd magnitude of thermopower, edition). Oxford University Press, Oxford. • Thermoelectric power generation and cooling 4) Bhatti, S., Sbiaa, R., Hirohata, A., Ohno, H., using insulators, Fukami, S. and Piramanayagam, S.N. (2017) • Construction of simple thermoelectric conver- Spintronics based random access memory: A – sion modules without using &-shaped thermo- review. Mater. Today 20, 530 548. 5) Hirohata, A., Yamada, K., Nakatani, Y., Prejbeanu, pile structures, I.L., Diény, B., Pirro, P. et al. (2020) Review on • Enhancement of thermoelectric output by spintronics: Principles and device applications. enlarging a lateral device area, J. Magn. Magn. Mater. 509, 166711. • Electronic cooling by a single magnetic material 6) Bauer, G.E.W., Saitoh, E. and van Wees, B.J. – without junction structures, (2012) Spin caloritronics. Nat. Mater. 11, 391 • fi 399. Recon guration of thermoelectric conversion 7) Johnson, M. and Silsbee, R.H. (1987) Thermody- characteristics by changing the shape of mag- namic analysis of interfacial transport and of the netic materials and their magnetization distri- thermomagnetoelectric system. Phys. Rev. B 35, bution, 4959–4972. • Active control of heat current directions and 8) Hatami, M., Bauer, G.E.W., Zhang, Q. and Kelly, P.J. (2007) Thermal spin-transfer torque in distributions. magnetoelectronic devices. Phys. Rev. Lett. 99, Currently, the thermoelectric conversion efficiency 066603. of the spin-caloritronic phenomena is much smaller 9) Uchida, K., Takahashi, S., Harii, K., Ieda, J., than that of the conventional Seebeck and Peltier Koshibae, W., Ando, K. et al. (2008) Observation ff – effects. However, both physics and materials science of the spin Seebeck e ect. Nature 455, 778 781. 10) Uchida, K., Xiao, J., Adachi, H., Ohe, J., studies are still in the early stages of development, Takahashi, S., Ieda, J. et al. (2010) Spin Seebeck and further discovery of new principles and improve- insulator. Nat. Mater. 9, 894–897. ment of the thermoelectric/thermo-spin conversion 11) Jaworski, C.M., Yang, J., Mack, S., Awschalom, efficiencies are expected in the future. D.D., Heremans, J.P. and Myers, R.C. (2010) Observation of the spin-Seebeck effect in a Acknowledgements ferromagnetic semiconductor. Nat. Mater. 9, 898–903. The experimental results shown in this Review 12) Uchida, K., Adachi, H., Ota, T., Nakayama, H., were obtained from the collaboration with S. Maekawa, S. and Saitoh, E. (2010) Observation Daimon, R. Das, D. Hou, R. Iguchi, R. Itoh, X.-F. of longitudinal spin-Seebeck effect in magnetic Jin, T. Kikkawa, T. Oyake, K. Oyanagi, Z. Qiu, E. insulators. Appl. Phys. Lett. 97, 172505. 13) McGuire, T. and Potter, R. (1975) Anisotropic Saitoh, T. Seki, J. Shiomi, Y. Shiomi, and K. magnetoresistance in ferromagnetic 3d alloys. Takanashi. The author thanks many collaborators IEEE Trans. Magn. 11, 1018–1038. and group members for valuable discussions and 14) Nagaosa, N., Sinova, J., Onoda, S., MacDonald, No. 2] Transport phenomena in spin caloritronics 85

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Profile

Ken-ichi Uchida was born in Kanagawa Prefecture, Japan in 1986. He obtained his B. Eng. (2008) and M. Sc. Eng. (2009) degrees from Keio University, Yokohama, Japan, and his Ph. D. (2012) degree from Tohoku University, Sendai, Japan. He was an assistant professor (2012–2014) and an associate professor (2014–2016) at Institute for Materials Research, Tohoku University. He has been a group leader of Spin Caloritronics Group, Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science in Japan (since 2016) and a cross-appointment professor at Institute for Materials Research, Tohoku University (since 2019). He has worked mainly on spintronics, spin caloritronics, and thermoelectrics. His important achievements include the discovery of the spin Seebeck effect in metals (2008) and insulators (2010), discovery of spin current generation from sound waves (2011) and surface plasmons (2015), thermal imaging of the spin Peltier effect (2016), and first direct observation of the anisotropic magneto-Peltier effect (2018) and magneto- Thomson effect (2020). He received many awards including JSPS Ikushi Prize from Japan Society for the Promotion of Science (2011), Young Scientists’ Prize, Commendation for Science and Technology from Ministry of Education, Culture, Sports, Science and Technology (2013), Gottfried Wagener Prize from German Innovation Award (2014), Nagase Prize from Frontier Salon Foundation (2014), Yamato Scientific Award from Yamato Scientific Co., Ltd. (2014), NISTEP Award from National Institute of Science and Technology Policy (2015), Funai Research Award from The Funai Foundation for Information Technology (2019), Marubun Research Encourage- ment Award from Marubun Research Promotion Foundation (2019), and JSPS Prize from Japan Society for the Promotion of Science (2020).