Hybrid Transverse Magneto‐Thermoelectric Cooling in Artificially Tilted Multilayers

In artificially tilted multilayers comprising two different conductors that are alternately and obliquely stacked, transverse thermoelectric conversion occurs, in which charge and heat currents are interconverted in the orthogonal direction. Although transverse thermoelectric conversion also occurs in homogeneous materials as an intrinsic transport phenomenon owing to the effects of magnetic fields, magnetization, and spins on conduction carriers, such magneto‐thermoelectric effects are investigated independently of thermoelectrics for artificially tilted multilayers. Here, this study shows that the synergy of these different principles improves the performance of transverse thermoelectric conversion. Using lock‐in thermography techniques, transverse thermoelectric conversion processes are visualized in artificially tilted multilayers and the experiments clarify how nonuniform charge currents are converted into orthogonal heat currents. Through the measurements of temperature change under magnetic fields, the contributions of the magneto‐thermoelectric effects are quantified in the artificially tilted multilayers and magnetically enhanced hybrid transverse thermoelectric cooling is demonstrated. By replacing one of the conductors in the multilayer with permanent magnets, the same functionality is obtained even in the absence of magnetic fields, paving the way for the creation of “thermoelectric permanent magnets” that exhibit efficient transverse thermoelectric conversion together with spontaneous magnetization. This study provides a new material design guideline for transverse thermoelectrics.


Introduction
Thermoelectric cooling is a promising technology for the efficient thermal management of electronic devices. [1]Conventional thermoelectric cooling is driven by the Peltier effect, in which a charge current J c applied to a conductor is converted into a heat current J q .Because of the parallel relationship between J c and J q , DOI: 10.1002/aenm.202302375 the Peltier effect is classified as a longitudinal thermoelectric effect.Due to the longitudinal geometry, a thermoelectric module based on the Peltier effect usually consists of many pairs of p-and n-type conductors arranged alternately and connected in series.Such a complex 3D structure consisting of many junctions often has problems such as low mechanical durability, high manufacturing costs, and efficiency losses due to contact resistances. [2]These issues limit the applicability of thermoelectric cooling technologies.The same problems apply to thermoelectric power generation based on the Seebeck effect.
Research on transverse thermoelectric effects is gaining momentum with the aim of improving the versatility of thermoelectric conversion technologies and expanding their applications. [3]ransverse thermoelectric effects allow the interconversion between J c and J q in the orthogonal direction.Owing to this feature, simple and versatile thermoelectric cooling as well as power generation can be achieved.The output power of transverse thermoelectric conversion can be increased by increasing the size of materials without constructing complex 3D structures, and the energy losses due to intermediated electrodes and substrates can be reduced.Although transverse thermoelectric conversion has many advantages, it is still in the basic research phase owing to various issues; e.g., its thermopower has not reached a practical level.
Transverse thermoelectric conversion is driven by six principles that can be broadly classified into phenomena occurring in homogeneous materials and those occurring in hybrid/composite materials. [3][20][21][22][23][24][25][26][27] As typified by the Nernst/Ettingshausen effects, most transverse thermoelectric effects appear in conductors under external magnetic fields or in magnetic materials with spontaneous magnetization, and these effects have been actively investigated in Figure 1.LIT measurements of thermoelectric effects in an artificially tilted multilayer.a) Schematic of the measurement setup for LIT.J c denotes a charge current applied to a sample.By using an electromagnet, a magnetic field H with magnitude H was applied to a sample in the transverse direction, i.e., y direction.b) Schematic of the artificially tilted multilayer sample.The blue and orange parts of the sample correspond to Bi 88 Sb 12 and Bi 0.2 Sb 1.8 Te 3 , respectively, for the samples used for Figures 2-7.J q and  denote the net direction of a heat current generated by the transverse thermoelectric effects and tilt angle in the artificially tilted multilayer.c) Input charge current and output temperature changes induced by the thermoelectric effects and Joule heating during the LIT measurements.f and J c represent the frequency and amplitude of the square-wave-modulated alternating charge current applied to the sample, respectively.In all the LIT measurements, we fixed J c = 1 A. d) Example of the lock-in amplitude A and phase  images for the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayer.
the fields of spin caloritronics [28][29][30] and topological materials science. [9,12]In contrast, transverse thermoelectric conversion in goniopolar materials and artificially tilted multilayers does not require magnetic fields or magnetization and appear due to anisotropic carrier conduction originating from anisotropic crystalline and artificial structures, respectively, i.e., the offdiagonal Seebeck/Peltier effect.Despite having similar functionalities, these transverse thermoelectric conversion phenomena have been studied independently.Their interdisciplinary fusion will bring innovation to transverse thermoelectrics, potentially solving the technological problems associated with thermoelectric converters.
In this study, we demonstrate hybrid transverse thermoelectric cooling by superimposing magneto-thermoelectric effects on artificially tilted multilayers.Using thermoelectric imaging techniques based on lock-in thermography (LIT), [16,31,32] we experimentally visualize the transverse thermoelectric cooling processes due to the structure-induced off-diagonal Peltier effect (ODPE) in artificially tilted multilayers.When the multilayers exhibit the magneto-Peltier effect (MPE) [33] and ordinary Ettingshausen effect (OEE), [4][5][6][7] LIT-based thermoelectric imaging under magnetic fields allows us to separate the temperature change signals due to structure-induced ODPE from those due to MPE and OEE and to estimate each contribution quantitatively.An appropriate design of the multilayer structure and magnetic-field direction H considering the symmetry of the magneto-thermoelectric effects makes it possible to improve the performance of transverse thermoelectric cooling through the hybridization of multiple phenomena.This result provides a novel guideline for increasing the thermopower and figure of merit of transverse thermoelectric conversion, leading to the development of versatile and efficient thermal management technologies.

Thermoelectric Conversion Mechanism and Sample System
The artificially tilted multilayer for transverse thermoelectric conversion consists of two different conductors that are stacked obliquely and alternately (Figure 1b).20][21][22][23][24][25][26][27] In other words, transverse thermoelectric conversion in the artificially tilted multilayer originates from the anisotropic structure itself, and is driven by the longitudinal Seebeck/Peltier effect.This process occurs to the maximum degree when one of the constituent materials is a p-type thermoelectric material and the other is an n-type material but occurs even with the same carrier type when the magnitude of the Seebeck/Peltier coefficient is different from each other.[20][21][22][23][24][25][26][27] Transverse thermoelectric conversion has been demonstrated in not only macroscale bulk materials but also nanoscale superlattices with tilted structures, which are often referred to as (p × n)-type multilayers, [34,35] although we focus only on bulk stacks in this study.However, the contributions of the magneto-thermoelectric effects in artificially tilted multilayers have not been investigated.
How do the magneto-thermoelectric effects contribute to transverse thermoelectric conversion in artificially tilted multilayers?In the following, we focus our discussion on chargecurrent-induced temperature modulation processes, with an emphasis on their deployment in thermoelectric cooling.First, recall that MPE refers to the magnetic-field dependence of the Peltier effect and that OEE refers to the generation of J q in the direction of the cross product of J c and H, both of which appear in conductors under magnetic fields.The transverse thermoelectric conversion performance due to structure-induced ODPE can increase directly when the Peltier coefficient increases owing to MPE, where it also depends on the electrical and thermal magnetoresistances.Furthermore, if the constituent materials of the multilayers exhibit OEE, the Ettingshausen heat current can be superimposed on structure-induced ODPE by properly selecting the direction of H to follow the symmetry of OEE.The combination of these processes is the simplest hybrid transverse magneto-thermoelectric conversion.Although this study focuses on the magnetic-field-induced effects, similar hybrid transverse thermoelectric conversion via anisotropic MPE [32] and the anomalous Ettingshausen effect [10,32] can be expected if H is replaced with magnetization using magnetic materials.
In this study, we demonstrate hybrid transverse magnetothermoelectric cooling based on a combination of structureinduced ODPE, MPE, and OEE.The main samples used are artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayers, where Bi 88 Sb 12 is an n-type thermoelectric material with large MPE and OEE and Bi 0.2 Sb 1.8 Te 3 is a p-type thermoelectric material with a large figure of merit for the Peltier effect.We confirmed that our Bi 88 Sb 12 slabs exhibit a large magnetoresistance, MPE, and OEE comparable to previous results [36,37] and our Bi 0.2 Sb 1.8 Te 3 slabs exhibit no magnetoresistance and MPE and small OEE (Figures S1, S2, Supporting Information).We prepared two artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayers with a tilt angle of  = 45°and a layer thickness of t = 1.0 mm (Sample A) and with  = 21°and t = 0.5 mm (Sample B) by a spark plasma sintering (SPS) method, as described in Section 4. Sample A was designed to optimize the magnetic-field-independent ODPE contribution (Figure S3, Supporting Information).To check the dependence of the magnetothermoelectric effects in the artificially tilted multilayers on , Sample B was also prepared, which has a smaller transverse thermopower, larger effective electrical conductivity along the charge current, and smaller effective thermal conductivity along the heat current.In Section 2.6, to demonstrate the zero-field operation of the hybrid transverse magneto-thermoelectric conversion, we also use an artificially tilted multilayer based on permanent magnets, in which the Bi 0.2 Sb 1.8 Te 3 layers are replaced with Nd 2 Fe 14 Btype magnets, with  = 26°and t = 0.5 mm (Sample C).The trans-port properties of our Bi 88 Sb 12 , Bi 0.2 Sb 1.8 Te 3 , and Nd 2 Fe 14 B-type magnet are presented in Table 1.

Visualization of Off-Diagonal Peltier Effect in Artificially Tilted Multilayers
Transverse thermoelectric conversion processes in artificially tilted multilayers have been investigated using finite-element calculations [22,25] but have not been directly observed experimentally.Here, we clarify how nonuniform charge currents in artificially tilted multilayers generate transverse heat currents using the LIT technique, which makes it possible to visualize the spatial distribution and temporal response of temperature modulation induced by thermoelectric effects with high temperature and spatial resolutions. [16,31,32]In the LIT measurements, when a periodic charge current is applied to a sample, thermal images oscillating at the same frequency as the current are extracted through Fourier analysis (Figure 1a).The thermal images obtained are transformed into lock-in amplitude A and phase  images (Figure 1d).The A image shows the distribution of the magnitude of the current-induced temperature modulation and the  image shows the distribution of the sign of the temperature modulation as well as the time delay due to thermal diffusion.To observe the thermoelectric effects using the LIT method, we measured the spatial distribution of infrared radiation thermally emitted from the surface of the sample using an infrared camera while applying a rectangularly-modulated alternating charge current with amplitude J c (= 1 A), frequency f, and zero offset to the sample along the x direction.By extracting the first-harmonic response of the detected thermal images, we can separate the contribution of the thermoelectric effects (∝ J c ) from that of Joule heating (∝ J c 2 ) because Joule heating generated by such an alternating current is constant over time (Figure 1c).By increasing f, we can identify heat-source positions owing to the reduction in the heat diffusion length, and clarify how the Peltier heat generated locally at the junction interfaces gives rise to transverse thermoelectric conversion.The detected infrared radiation is converted into temperature information through the calibration described in ref. [32].During the LIT measurements, an in-plane H (with magnitude H) was applied along the y direction (Figure 1a,b).All the LIT measurements were performed at room temperature and atmospheric pressure.Figure 2g,h (2o,p) shows the f dependence of the A and  values averaged over one Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 pair, which are denoted as A ave and  ave , respectively, in the cross-section (top-side) configuration, where the averaged area is marked with a white rectangle in Figure 2c (2k) (note that the rectangle in Figure 2c appears as a white line to extract the information near the sample edge).The magnitude of A ave increases monotonically with a reduction in f, approaching the steady-state temperature modulation magnitude.The signal magnitude at low f values in the top-side configuration exceeds that in the cross-section configuration, even though the results are for the same sample.This suggests that it is difficult to obtain the magnitude of the temperature modulation at the topmost surface in the cross-section configuration due to the limitation of the spatial resolution (≈20 μm) of the thermal images and slightly rounded sample corners, and that the top-side configuration is suitable for quantitative discussions about the transverse thermoelectric conversion performance.Therefore, in the following, only the results for the topside configuration are presented.

Magneto-Thermoelectric Effects in Artificially Tilted Multilayers
Now we are in a position to discuss the contributions of the magneto-thermoelectric effects in the artificially tilted multilay-ers.The temperature change due to MPE (OEE) is known to exhibit an even (odd) dependence on H. Thus, to quantify the MPE and OEE contributions, we acquired LIT images under positive and negative magnetic fields and separated the H-evendependent component from the H-odd-dependent component using the following equations: Here, A even (A odd ) and  even ( odd ) respectively represent the lock-in amplitude and phase exhibiting the H-even (H-odd) dependence, which includes the MPE (OEE) contribution (note that the H-independent contribution is included in A even and  even ). [32,37]igure 3a,b shows the raw A and  images for Sample A in the top-side configuration at f = 1.0 Hz and  0 H = 0.8 T (a, H || +y direction) and −0.8 T (b, H || −y direction).By substituting the data in the raw images into Equations ( 1)-( 4), we obtained the A even (A odd ) and  even ( odd ) images at  0 |H| = 0.8 T, as shown in Figure 3c (3d).The H-even-and H-odd-dependent components exhibit different temperature distributions, suggesting that the temperature changes are caused by several different thermoelectric effects.
Figure 4c shows the |H| dependence of the A even signal for Sample A around the Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 interface position, marked with a white rectangle in Figure 4a, at f = 1.0 Hz.With an increase in |H|, the A even signal increases monotonically, while the  even values remain constant (Figure 4b,d).This nonsaturating magnetic-field dependence is consistent with the behavior of the magneto-Seebeck effect, i.e., the reciprocal of MPE, in Bi 88 Sb 12 (Figure S1a,b in the Supporting Information).Thus, we conclude that the field-induced enhancement of the A even signals in the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayer is due to MPE in Bi 88 Sb 12 .5b and the f dependence of  odd in Figure 5d).The |H| dependence of the A odd signal for Sample A in the Bi 88 Sb 12 region, marked with a white rectangle in Figure 5a, at f = 1.0 Hz is plotted as blue circles in Figure 5e.The A odd signal increases with increasing |H| and becomes saturated for  0 |H| >0.6 T, while the  odd values remain constant (Figure 5e,f).This behavior is consistent with the magnetic-field dependence of the transverse thermopower due to the ordinary Nernst effect, i.e., the reciprocal of OEE, in Bi 88 Sb 12 (see the black curve in Figure 5e; Figure S2, Supporting Information).This result confirms that OEE also gives rise to the transverse thermoelectric conversion in the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayer.
Because the total output is important for actual thermoelectric applications, we next estimated the H dependence on the temperature modulation signal averaged over one Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 pair, i.e., A ave , which includes structure-induced ODPE, MPE, and OEE. Figure 6a shows the A ave signal as a function of H for Sample A at f = 0.1 Hz.The magnitude of A ave exhibits a clear H dependence and is increased by applying a positive field owing to the superposition of MPE and OEE.As indicated by the closed circles in Figure 6b, the H-induced enhancement ratio for Sample A is estimated to be  ≡ [A ave (H) − A ave (0 T)]/A ave (0 T) ≈11% for  0 H >0.6 T. The  value can be further increased by optimizing  and t for the artificially tilted multilayers.To demonstrate this, we performed the same measurements on Sample

Steady-State Hybrid Transverse Magneto-Thermoelectric Cooling
The experiments presented in Section 2.3 revealed that both MPE and OEE enhance the transverse thermoelectric conversion in artificially tilted multilayers.Here, we demonstrate that the hybrid transverse magneto-thermoelectric conversion is useful for steady-state cooling.Although the contribution of Joule heating was excluded in the LIT measurements, the competition between the thermoelectric effects and Joule heating must be considered under steady-state conditions.We measured the current-induced temperature change ΔT ave from room temperature averaged over the Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 junction with a constant charge current I applied along the x direction.To obtain steady-state ΔT ave values, the temperature of the sample surface was recorded after waiting 30 s from the I application using standard thermography instead of LIT. Figure 7a shows the ΔT ave values as a function of ΔT ave value at a positive (negative) current.As expected, the ΔT TE signal is proportional to I, whereas the ΔT J signal is proportional to I 2 (Figure 7b,c).The magnitude of ΔT TE is enhanced by applying positive H owing to the contributions of the magnetothermoelectric effects, but ΔT J is independent of the sign of H because the magnetoresistance exhibits the H-even dependence (Figure S1c,d in the Supporting Information).As the relative contributions of the thermoelectric effects and Joule heating depend on the thermal boundary conditions, the steady-state cooling performance can be improved by optimizing the thermal design of the device.

Estimation of Figure of Merit
In this section, we estimate the magnetic-field dependence of the figure of merit for the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayer.The figure of merit Z T T for transverse thermoelectric conversion is defined as: where S T ,  xx , and  zz represent the total transverse thermopower, effective electrical conductivity along the charge current (x-direction), and effective thermal conductivity along the heat current (z-direction), respectively.[20][21][22][23][24][25][26][27] The contributions of MPE and the electrical and thermal magnetoresistances can be introduced as the field dependence of the transport coefficients in the equations for determining the ODPEdriven transverse thermopower,  xx , and  zz .However, in our artificially tilted multilayers, S T includes not only the structureinduced ODPE and MPE contributions but also the OEE contribution.Analytical calculation of the OEE contribution is difficult because of the nonuniform flows of charge and heat currents.Therefore, we measured the transverse thermoelectric voltage in Samples A and B by applying a temperature gradient and magnetic field and experimentally estimated the S T values (Figure S5, Supporting Information).By combining the measured S T values with the calculated  xx and  zz values, we determined the figures of merit for Sample A (Sample B) at 300 K to be Z T T = 0.20, 0.17, and 0.14 (0.15, 0.13, and 0.10) at  0 H = 0.8, 0, and −0.8 T, respectively.These results confirm that Z T T in the artificially tilted multilayers can be enhanced by the magneto-thermoelectric effects.

Hybrid Transverse Magneto-Thermoelectric Conversion in Artificially Tilted Multilayer Based on Permanent Magnets
Despite the usefulness of the magneto-thermoelectric effects, the application of an external magnetic field often hinders thermoelectric applications.To overcome this problem, we demonstrate hybrid transverse magneto-thermoelectric conversion in the absence of an external magnetic field by incorporating permanent magnets into an artificially tilted multilayer.Figure 8a shows a schematic of the artificially tilted Bi 88 Sb 12 /Nd 2 Fe 14 B multilayer with anisotropic Nd 2 Fe 14 B-type magnets that can be magnetized only in the direction perpendicular to the stacking plane.When the Nd 2 Fe 14 B layers are magnetized, stray fields due to the remanent magnetization of the Nd 2 Fe 14 B layers are applied to the Bi 88 Sb 12 layers, which drive the magneto-thermoelectric effects in Bi 88 Sb 12 .The photograph in Figure 8b shows that the block of the artificially tilted Bi 88 Sb 12 /Nd 2 Fe 14 B multilayer functions as a permanent magnet; the Nd 2 Fe 14 B layers exhibit a strong coercive force and remanent magnetization even after bonding them with the Bi 88 Sb 12 layers (Figure 8e).Sample C was cut from this large block.Figure 8c (8d) shows the A and  images for Sample C at f = 10.0 and 0.5 Hz in the cross-section (top-side) configuration.Although the temperature distributions for Sample C are qualitatively similar to those for Samples A and B, the sign of the transverse thermoelectric conversion for Sample C is opposite to that for Samples A and B because the Seebeck/Peltier coefficient of the Nd 2 Fe 14 B-type magnet is opposite in sign to that of Bi 0.2 Sb 1.8 Te 3 (Table 1).Figure 8f presents a comparison of the f dependence of the A ave signals at  0 H = 0 T for Sample C measured before and after magnetizing the Nd 2 Fe 14 B layers.The magnitude of the temperature change is significantly increased by magnetizing the Nd 2 Fe 14 B layers over the entire f range, confirming the contribution of the magneto-thermoelectric effects.As shown in the inset of Figure 8f, the magnetization-dependent enhancement ratio for Sample C is estimated to be  M = (A ave,mag − A ave,demag )/A ave,demag ≈ 8% in the absence of an external field, where A ave,mag (A ave,demag ) denotes the A ave value in the magnetized (demagnetized) state.Because of the small Seebeck/Peltier coefficient of the Nd 2 Fe 14 B-type magnet, the magnitude of the A ave signals for Sample C is one order of magnitude smaller than that for Samples A and B. Nevertheless, this experiment clearly indicates that the hybrid transverse magneto-thermoelectric conversion can be achieved without an external magnetic field, suggesting the importance of developing permanent magnets with large Seebeck/Peltier coefficients to realize efficient transverse thermoelectric conversion.The transverse thermoelectric conversion performance in the artificially tilted multilayers based on permanent magnets may also be improved by stacking three different materials, i.e., a permanent magnet and p-and n-type conductors showing large Seebeck/Peltier coefficients as well as large magneto-thermoelectric effects.
Finally, we discuss the origin of the magnetization-dependent enhancement of the transverse thermoelectric conversion in the artificially tilted multilayer based on permanent magnets.Although the remanent magnetization of the Nd 2 Fe 14 B layers generates a magnetic field in the Bi 88 Sb 12 layers, the configuration in Figure 8a does not satisfy the symmetry of OEE because of the absence of the magnetization component in the direction of the cross product of J c and J q .Thus, in Sample C, MPE is expected to manifest directly.However, because the stray field is non-uniform near the surfaces of the sample, a finite OEE contribution may also appear.To optimize artificially tilted multilayers based on permanent magnets, the design of not only transverse thermoelectric properties but also stray-field distributions is required.The use of isotropic magnets facilitates the control of the stray-field distributions.

Conclusion
We demonstrated the hybrid transverse thermoelectric cooling by multiple phenomena including the magneto-thermoelectric effects in artificially tilted multilayers.Using the thermoelectric imaging technique based on LIT, the transverse thermoelectric cooling processes in the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayers were clarified.The LIT measurements under magnetic fields allowed us to separate the contributions of the magneto-thermoelectric effects exhibiting the even dependence on the magnetic field, i.e., MPE, and odd dependence, i.e., OEE, from the field-independent ODPE contribution.Through the systematic measurements and analyses, we quantified the contributions of each magneto-thermoelectric effect, and found that both MPE and OEE can improve the steady-state cooling capability and figure of merit of the artificially tilted multilayers.Furthermore, by replacing one of the constituent materials in the multilayer with permanent magnets, we demonstrated that hybrid transverse magneto-thermoelectric conversion can operate even in the absence of a magnetic field.The artificially tilted multilayers based on permanent magnets function as "thermoelectric permanent magnets" that have high transverse thermoelectric conversion performance together with spontaneous magnetization.This concept provides an unconventional strategy for increasing the transverse magnetothermoelectric conversion efficiency and suggests the possibility of transforming omnipresent permanent magnets into functional materials that enable electronic cooling and thermopower generation.Practical applications of the hybrid transverse magneto-thermoelectric conversion require the development of stable n-and p-type materials that exhibit large magnetothermoelectric effects, simultaneous achievement of the large magneto-thermoelectric conversion and its zero-field operation, reduction of the thermal conductivity by nanostructuring or phonon engineering, [38,39] and development of module structures suitable for this operation principle.

Experimental Section
Sample Preparation and Characterization: Samples A and B, i.e., the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayers, were prepared as follows.First, homogenous Bi 88 Sb 12 and Bi 0.2 Sb 1.8 Te 3 alloy slabs were synthesized.BiSb alloy powder (99.99% purity), obtained from Kojundo Chemical Laboratory Co., Ltd., was crushed using a planetary ball mill (PL-7, Fritsch Japan Co., Ltd.) at 350 rpm for 30 min.The crushed powder was then sieved through a 63-μm mesh.Next, a cylindrical Bi 88 Sb 12 ingot with a diameter of 10 mm was prepared via the SPS method under a pressure of 50 MPa at 245 °C for 5 min in vacuum conditions.A cylindrical Bi 0.2 Sb 1.8 Te 3 ingot with a diameter of 10 mm was also prepared via the SPS method under a pressure of 30 MPa at 445 °C for 4 min in vacuum conditions by using BiSbTe alloy powder (99.9% purity) with a particle size of <74 μm, which was obtained from Toshima Manufacturing Co., Ltd.The Bi 88 Sb 12 and Bi 0.2 Sb 1.8 Te 3 alloys are polycrystalline and their grain crystal orientations are random, indicating isotropic transport properties.Using a diamond wire saw, the ingots were sliced into many disks with a thickness of 1 mm (0.5 mm) for Sample A (Sample B).The Bi 88 Sb 12 and Bi 0.2 Sb 1.8 Te 3 discs were alternately stacked and bonded via the SPS method under a pressure of 30 MPa at 230 °C for 5 h.Finally, the bonded stack was cut into a rectangular shape with a size of ≈10 × 2 × 2 mm 3 and  = 45°( = 21°) for Sample A (Sample B) using the diamond wire saw.The elemental distributions and compositions of Samples A and B were characterized by scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) using Cross-Beam 1540ESB (Carl Zeiss AG).The samples for the SEM observations were prepared via mechanical polishing.As shown in Figure S6 (Supporting Information), the compositions of the bulk regions of Bi 88 Sb 12 and Bi 0.2 Sb 1.8 Te 3

Figure 2 .
Figure 2. Transverse thermoelectric conversion at zero magnetic field.a) Schematic of Sample A, i.e., the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayer with  = 45°and 1.0-mm-thick layers, in the cross-section configuration.b) Steady-state temperature T image for Sample A during the LIT measurement in the cross-section configuration.c,d) A (c) and  (d) images for Sample A for different values of f in the cross-section configuration.e,f) x-directional A and  profiles along the white dotted lines in the images in (c,d), respectively.g,h) f dependence of the amplitude A ave and phase  ave averaged over one Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 pair.i-p) Results for the top-side configuration.The data points in (g,h) [(o,p)] were obtained by averaging the temperature modulation signals in the areas defined by the white rectangles with a size of 183 × 4 (183 × 101) pixels in (c,d) [(k,l)], respectively.

Figure 2
Figure2shows the results of the LIT measurements for Sample A in the absence of a magnetic field.First, we measured the current-induced temperature modulation in a crosssectional configuration (Figure2a,b).The LIT images at high lock-in frequencies, for example, f = 10.0 Hz, indicate that the heating/cooling signals are localized near the junction interfaces between Bi 88 Sb 12 and Bi 0.2 Sb 1.8 Te 3 .Here, the A signals exhibit maxima along the oblique interfaces (Figure2c), whereas the  values at the positions of the A peaks vary by 180°for the neighboring interfaces (Figure2d).This is indeed the behavior exhibited by temperature modulation due to the Peltier effect.Importantly, as shown in the top image in Figure2c, the magnitude of the A signals is nonuniform along the oblique junction interfaces, indicating that the charge current flows nonuniformly in the artificially tilted multilayers: this is the origin of the transverse thermoelectric conversion.These local heat release/absorption

Figure 3 .
Figure 3. Separation of magneto-thermoelectric effects showing even and odd dependences on magnetic fields.a,b) A and  images for Sample A at f = 1.0 Hz in the top-side configuration, measured when the magnetic field with  0 H = 0.8 T (a) and −0.8 T (b) was applied along the y direction. 0 denotes the vacuum permeability.c) A even and  even images calculated from the raw images in (a,b).d) A odd and  odd images calculated from the raw images in (a,b).A even (A odd ) and  even ( odd ) denote the lock-in amplitude and phase showing the H-even (H-odd) dependence, respectively.

Figure 4 .
Figure 4. Contribution of MPE.a,b) A even (a) and  even (b) images for Sample A at f = 1.0 Hz and  0 |H| = 0.8 T in the top-side configuration.c,d) |H| dependence of the A even (c) and  even (d) signals at f = 1.0 Hz.The data points in (c) and (d) were obtained by averaging the temperature modulation signals in the area defined by the white rectangles with a size of 6 × 101 pixels in (a,b), respectively.

Figure
Figure 5a,b shows the A odd and  odd images for Sample A at  0 |H| = 0.8 T for different values of f.Clear A odd signals appear only in the Bi 88 Sb 12 regions and their magnitudes increase with a reduction in f (Figure 5c).As shown in Figure 3c,d, the positions of the A odd signals deviated from those of the A even signals.The almost uniform  odd values of ≈180°at low f indicate that the transverse thermoelectric cooling also occurs in the H-odddependent component (see the bottom image in Figure 5b and B with different  and t values.The open-circle data points in Figure 6b indicate that  reaches ≈15% for Sample B at  0 H = 1.0 T (see also the raw LIT data for Sample B in Figure S4, Supporting Information).

Figure 5 .
Figure 5. Contribution of OEE.a,b) A odd (a) and  odd (b) images for Sample A at  0 |H| = 0.8 T for different values of f in the top-side configuration.c,d) f dependence of the A odd (c) and  odd (d) signals at  0 |H| = 0.8 T. e,f) |H| dependence of the A odd (e) and  odd (f) signals at f = 1.0 Hz (blue circles).The black curve in (e) shows the |H| dependence of the magnitude of the transverse thermoelectric voltage |V| for a Bi 88 Sb 12 slab at a temperature difference of ΔT = 4.2 K (see also Figure S2, Supporting Information).The data points in (c-f) were obtained by averaging the temperature modulation signals in the areas defined by the white rectangles with a size of 69 × 101 pixels in (a,b).

Figure 6 .
Figure 6.Magnetic-field dependence of averaged temperature modulation.a) H dependence of the A ave signal for Sample A at f = 0.1 Hz. b) H dependence of  ≡ [A ave (H) − A ave (0 T)]/A ave (0 T) for Sample A (closed circles) and Sample B (open circles), i.e., the artificially tilted Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 multilayer with  = 21°and 0.5-mm-thick layers, at f = 0.1 Hz.The data points in this figure were obtained by averaging the temperature modulation signals in the area defined by the white rectangle in Figure 2k.

Figure 7 .
Figure 7. Steady-state hybrid transverse magneto-thermoelectric cooling.a) Charge-current I dependence of ΔT ave , i.e., the steady-state temperature change from room temperature averaged over one Bi 88 Sb 12 /Bi 0.2 Sb 1.8 Te 3 pair, at  0 H = 0.8 T (diamonds) and −0.8 T (triangles).b) |I| dependence of ΔT TE , i.e., the steady-state temperature change from room temperature induced by the thermoelectric effects.c) |I| dependence of ΔT J , i.e., the steady-state temperature change from room temperature induced by Joule heating.

Figure 8 .
Figure 8. Transverse thermoelectric conversion in an artificially tilted multilayer based on permanent magnets.a) Schematic of Sample C, i.e., the artificially tilted Bi 88 Sb 12 /Nd 2 Fe 14 B multilayer with  = 26°and 0.5-mm-thick layers, in the top-side configuration.M denotes the spontaneous magnetization of the Nd 2 Fe 14 B-type magnets.b) Photograph of the artificially tilted Bi 88 Sb 12 /Nd 2 Fe 14 B multilayer block with magnetic metal spheres attached by attraction due to the remanent magnetization of the Nd 2 Fe 14 B-type magnets.c,d) A and  images for Sample C with the magnetized Nd 2 Fe 14 B-type magnet layers at f = 10.0 and 0.5 Hz in the cross-section (c) and top-side (d) configurations.e) H dependence of the magnetization M of the Nd 2 Fe 14 Btype magnet at room temperature.f) f dependence of the A ave signal for Sample C with the magnetized (red circles) and demagnetized (black circles) Nd 2 Fe 14 B-type magnet layers in the top-side configuration.The inset of (f) shows the f dependence of  M = (A ave,mag − A ave,demag )/A ave,demag , where A ave,mag (A ave,demag ) denotes A ave in the magnetized (demagnetized) state.The data points in (f) were obtained by averaging the temperature modulation signals in the area defined by the white rectangle with a size of 150 × 101 pixels in (d).All the LIT data in this figure were measured in the absence of an external magnetic field.

Table 1 .
Transport coefficients of Bi 88 Sb 12 , Bi 0.2 Sb 1.8 Te 3 , and Nd 2 Fe 14 B-type magnet used in this study., , S S(N) , and Z S(N) T represent the electrical conductivity, thermal conductivity, Seebeck (Nernst) coefficient, and dimensionless figure of merit for the Seebeck (Nernst) effect with T being the absolute temperature, respectively.