Permanent-magnet-based transverse thermoelectric generator with high fill factor driven by anomalous Nernst effect

A transverse thermoelectric generator for magnetic-field-free and high-density power generation utilizing the anomalous Nernst effect is constructed and its performance is characterized. By alternately stacking two different permanent magnets with the large coercivity and anomalous Nernst coefficients of opposite sign, transverse thermoelectric voltage and power can be generated in the absence of external magnetic fields and enhanced owing to a thermopile structure without useless electrode layers. In the permanent-magnet-based stack, the magnetic attractive force enables easy construction of the thermopile structure with a high fill factor. In this study, we construct a bulk module consisting of twelve pairs of SmCo$_5$- and Nd$_2$Fe$_{14}$B-type permanent magnets with respectively having the positive and negative anomalous Nernst coefficients, whose fill factor reaches ~80%, whereas that of conventional thermoelectric modules based on the Seebeck effect is typically 30-60%. We demonstrate magnetic-field-free anomalous Nernst power generation up to 177 $\mu$W at a temperature difference of 75 K around room temperature, which corresponds to the largest anomalous Nernst power density of 65 $\mu$W/cm$^2$. The presented module structure concept will provide a design guideline for high-performance transverse thermoelectric power generation.


MANUSCRIPT
In the urgent issue of sustainable energy solutions, thermoelectric generation technology attracts much attention as a promising avenue for harvesting waste heat and converting it into electricity.The conventional thermoelectric generation is driven by the Seebeck effect, which induces an electric field E in the direction parallel to a temperature gradient T.Thus, the Seebeck effect is classified into a longitudinal thermoelectric effect.Due to the parallel relationship between E and T, a thermoelectric generator (TEG) based on the Seebeck effect needs to consist of many legs of p-and n-type semiconductors, which are arranged in isolation to prevent a short-circuit fault and connected with each other in series on the hot and cool sides by electrode materials to enhance the output power.Such a Π-shaped module configuration imposes two problems that reduce the output power.2][3] The second problem is caused by the low fill factor which is the area density of the active thermoelectric materials within the module.5][6] The fill factor of conventional bulk TEGs based on the Seebeck effect is typically in the range of 30~60% 5,7,8 and at most ~70%. 9These two problems prevent the efficient power generation, resulting in limited applications of the thermoelectric generation technology.

2
A key to overcome the first problem is a utilization of transverse thermoelectric effects, which generate an electric field E in the direction perpendicular to T.1][12][13][14][15] To utilize this geometrical advantage, many studies have recently focused on developing physics, materials science, and applications of transverse thermoelectric phenomena. 37][18][19][20][21][22] As shown in Fig. 1(a), the ANE-driven electric field EANE is in the cross-product direction (y-axis) of T (x-axis) and the spontaneous magnetization (z-axis) in a magnetic material as the following equation: where SANE is the anomalous Nernst coefficient and m is the unit vector of the magnetization.[12][13] However, conventional transverse TEGs have other problems.The aforementioned second problem regarding the fill factor still remains in conventional transverse TEGs.The scalable Nernst device with the coil geometry has been recently demonstrated with a relatively high fill factor (~70%) by thinning the insulator layers. 13Meanwhile, the fill factor of transverse TEG with the thermopile geometry was still 26% because it requires the adequate spaces to form a zigzag circuit by the single thermoelectric materials and electrodes. 14Therefore, the effective way to improve the fill factor in the thermopile geometry needs to be established.Furthermore, ANE and the ordinary Nernst effect in many materials work only under external magnetic fields. 10,11,22,23In the case of ANE, the elongation of the magnetic materials in y-axis increases the ANE-induced thermoelectric voltage, whereas m necessarily directs along the hard axis of shape magnetic anisotropy (z-axis) due to the orthogonal relationship between E ANE and m.4][25] However, the use of permanent magnets in the thermopile geometry has not been demonstrated so far.
In this study, we present a concept of bulk transverse TEGs based on ANE to realize the high fill factor and magneticfield-free operation simultaneously.Figures 1(a) and (b) show the schematics of the components and module structure for proposed transverse TEG, respectively.Transverse TEG consists of alternately stacked two different permanent magnets with positive and negative SANE intermediated by thin insulator layers.As the proof-of-concept demonstration, we fabricate permanent-magnet-based transverse TEG comprising many SmCo 5 -and Nd 2 Fe 14 B-type permanent magnet slabs respectively having positive and negative S ANE . 23The use of permanent magnets as the components in the thermopile structure allows us to easily construct TEG with a fill factor of ~80%, which is much higher than the fill factors in the literature. 13,14All the SmCo 5 4][25][26][27][28] An ANE-induced thermoelectric voltage is generated without an external magnetic field and its magnitude is ideally equal to the calculated one from SANE of SmCo5 and Nd2Fe14B.As a result of the structural design, the maximum ANE-induced output power reaches 177 µW at a temperature difference ΔT = 75 K, which corresponds to the ANEinduced power density of 65 µW/cm 2 .This power density is the largest value among transverse TEGs based on ANE. 29 The important point of transverse TEG structure in Fig. 1(b) is to utilize not only the positive and negative S ANE values but also the magnetic attractive force due to the remanent magnetization of the permanent magnets.The series circuit can be formed by inserting the thin insulator layers between the neighboring magnets and electrically connecting the ends of magnets to sum up the transverse thermoelectric voltage in a zigzag way.The circuit structure drastically increases the fill factor by the reduction of superfluous spaces for electrical wiring between the magnets.The magnetic attractive forces between the permanent magnets allow the construction of a dense stack of themselves and stabilization of the remanent magnetization along z-axis owing to the stray field of neighboring magnets.
First, we investigated the thermoelectric and magnetic properties of the SmCo5-and Nd2Fe14B-type permanent magnet slabs.We used SmCo 5 and Nd 2 Fe 14 B circular disks with a thickness of 0.5 mm and diameter of 20 mm having the easy axis of magnetic anisotropy along the thickness direction, which were commercially available from Magfine Corporation.The surface of the Nd 2 Fe 14 B disks was coated by a Ni-Cu-Ni plating layer with a thickness of ~15 μm to prevent oxidization. 30To quantitatively estimate S ANE of these magnets without applying an external magnetic field, we used the LIT method.The LIT method enables the measurements of the anomalous Ettingshausen effect (AEE), the reciprocal effect of ANE, and the estimation of S ANE through the Onsager reciprocal relation: Π AEE = S ANE T with Π AEE being the anomalous Ettingshausen coefficient.4][25][26][27][28]  To characterize the fill factor, we observed the infrared image of the top surface of SmCo 5 /Nd 2 Fe 14 B-based TEG [Fig.

2(f)
].The fill factor can be estimated from the contrast of thermally emitted infrared intensity due to the difference in infrared emissivity between the metallic surfaces with low emissivity and paper towels with high emissivity.Here, the line profiles are taken along z-axis as shown in Fig. 2(g), where the infrared intensity at each z-position is averaged along y-axis.The contrast of infrared intensity was clearly observed between the slabs and their spaces, and the relative area of the slabs was estimated to be 81%, when the threshold infrared intensity value is set to be 95 [Fig.2(g)].
The contribution of the transverse thermoelectric conversion in each slab and the absence of a short-circuit fault in SmCo5/Nd2Fe14B-based TEG is confirmed through the AEE measurements by the LIT technique.Figure 3(a) shows a schematic of the LIT measurement setup for TEG.To quantitatively estimate the surface temperature, we coated the top surface of TEG by an insulating black ink with high infrared emissivity (0.94).4][25][26][27][28] The application of Jc generates an AEEinduced heat flow JQ,AEE in the cross-product direction of Jc and m as 31 As a result of the J Q,AEE generation, the temperature on the surfaces of the magnetic materials is modulated.By extracting the transient first-harmonic temperature modulation signals of the thermal images and transforming them into lock-in phase φ and amplitude A by Fourier analysis, the pure contribution of thermoelectric effects, such as AEE and the Peltier effect, can be visualized without the contamination by Joule heating. 26,27In magnetized permanent magnets, the AEE-induced temperature modulation free from the Peltier effect can be measured in the absence of an external magnetic field in the areas far from the sample edges. 23The spatial distribution of the temperature modulation allows us to confirm that all the SmCo5 and Nd2Fe14B slabs correctly operates without a short-circuit fault.which can be explained by the fact that Nd2Fe14B has lower κ than SmCo5 [Fig.2(c)]. 27Thus, the LIT measurements reveal that all the SmCo5 and Nd2Fe14B slabs positively contribute to the transverse thermoelectric conversion without a short-circuit fault, while the superfluous space for electrical wiring between the neighboring slabs are significantly reduced.
We are in a position to demonstrate magnetic-field-free transverse thermoelectric power generation in SmCo 5 /Nd 2 Fe 14 Bbased TEG. Figure 4(a) shows the schematic and photograph of the setup for four-terminal measurements of thermoelectric power, where TEG was sandwiched by a heater and heat sink.When TEG is practically used, the current source will be replaced to a load resistor so that one can obtain the output power without an external power supply.The temperature of the heat sink was controlled by flowing coolant at 273 K.The actual ΔT inside TEG was estimated by measuring the thermal image of its side surface coated by the black ink.The hot and cool side temperatures (T h and T c ) are defined as the highest and lowest temperatures of the thermal image in TEG along the heat flow direction.
To investigate the pure contribution of the ANE-induced thermopower independent of the parasitic Seebeck-effect-induced thermopower, we measured the dependence of the open circuit voltage Voc on the remanent magnetization direction.We repetitively reversed the remanent magnetization between the +z and -z directions, represented by +M and -M states, by applying a pulse magnetic field of 8 T and measured Voc as a function of ΔT in the absence of an external magnetic field for two cycles [Fig.4(b)].We found that the sign of Voc/ΔT was reversed by reversing the magnetization direction as shown in the inset of Fig. 4(b), indicating that the Voc signal originates from pure ANE free from the offset due to the Seebeck effect.We confirmed that the V oc value is quantitatively consistent with the calculated value from S ANE of SmCo 5 and Nd 2 Fe 14 B [Fig. 2(a)] as the following equation: where n is the number of the SmCo 5 /Nd 2 Fe 14 B pairs, l the length of each slab along the E ANE direction, and h the height of each slab along the T direction, and  the averaged SANE value at temperatures ranging from Tc to Th.Here, we approximated  for SmCo5 and Nd2Fe14B by the SANE values at room temperature.Figure 4(b) shows the good matching between the measured and calculated Voc values, which confirms the fact that the thermoelectric voltage in our TEG is due purely to ANE.
The magnetic-field-free operation of the ANE-induced power generation was demonstrated by measuring the thermoelectric voltage V with applying a load current I load to TEG. Figure 4(c) shows the I load dependence of the output power P at various values of ΔT, where P is the product of V and I load .The high P, 177 μW at maximum when ΔT = 75 K and I load = 41 mA, was obtained owing to both the large V oc and small internal resistance of module R module , which is the slope of the I load -V curve.The R module of TEG was estimated to be 9.9 mΩ at ΔT = 21 K, whereas the value calculated from the σ values and dimensions of SmCo 5 and Nd 2 Fe 14 B is 9.1 mΩ; the deviation of R module from the calculated value due to the electrodes and junctions is only +8%.The inset of Fig. 4(c) shows the ΔT dependences of the maximum output power P max and power density per unit area ωmax, which is proportional to the fill factor.Owing to the high Pmax of 177 µW and high fill factor of ~80%, the resultant ωmax reaches 65 µW/cm 2 at ΔT = 75 K, which is the highest value among transverse TEGs based on ANE. 29 Finally, we discuss future developments and applications of permanent-magnet-based transverse TEG.Since the fill factor of TEG is determined by the thickness ratio between the magnetic materials and insulator layers, we can further increase the fill factor and ω max by using thinner insulator layers.Although the demonstrated P max of 177 µW can be used, for example, as stand-alone power supply for wireless sensor network systems, the further improvement of z ANE T in permanent magnets is required for widespread thermoelectric applications.This is because the commercial TEGs based on the Seebeck effect exhibit 70~80 mW/cm 2 at temperature differences of 60~70 K around room temperature 32,33 , which are still three orders of magnitude larger than that of the presented transverse TEG based on ANE.Decreasing κ and increasing SANE are the significant tasks, especially for permanent magnets with negative SANE, since small negative SANE of Nd2Fe14B is a bottleneck in the output of our TEG.Additionally, the thermal durability of TEG is limited by that of the remanent magnetization in Nd2Fe14B-type permanent magnets, which gradually decreases beyond ~400 K. 34 Meanwhile, since the magnetic force of SmCo5-and Nd2Fe14B-type permanent magnets is at the highest level, our TEG enables energy harvesting from everywhere permanent magnets are used.
In conclusion, we constructed ANE-based transverse TEG with the high fill factor and demonstrated its magnetic-fieldfree operation.As the proof-of-concept demonstration, we used the SmCo 5 -and Nd 2 Fe 14 B-type permanent magnets with the large coercivities, large remanent magnetization, and S ANE of the opposite sign.The pairs of the SmCo 5 and Nd 2 Fe 14 B slabs were integrated into high-density TEG, whose fill factor surprisingly reaches ~80%.Using the LIT method, all the SmCo 5 and Nd 2 Fe 14 B slabs were confirmed to positively contribute to the transverse thermoelectric conversion without a short-circuit fault.
An ANE-induced output power of 177 µW was generated at a temperature difference of 75 K without an external magnetic field, which corresponds to the largest power density of 65 μW/cm 2 among TEGs based on ANE.This study manifests the importance to develop permanent magnet materials with large positive and negative SANE values together with large remanent magnetization.The device architecture proposed here will be a design guideline for high-performance transverse thermoelectric power generation.
photograph of our transverse TEG consisting of alternately stacked twelve SmCo5/Nd2Fe14B pairs.We inserted ~0.05-mmthick paper towel layers soaked with heat-resistant glue (Aron Alpha Tough-power) between the slabs to avoid the reduction of the ANE voltage due to shunting effects.After the glue cured, we cut the stacked discs into a rectangular shape with a size of 8.2 mm (|| T) × 16.5 mm (|| E) × 16.5 mm (|| the stacking direction) so that the Nd2Fe14B surfaces were exposed on the planes attaching to electrodes and heat source/sink by the removal of the Ni-Cu-Ni plating layers.The ends of the neighboring SmCo5 and Nd2Fe14B slabs were manually and carefully connected by attaching indium to form a zigzag series circuit without a short-circuit fault.Then, the stacked SmCo5 and Nd2Fe14B slabs were magnetized by applying a pulse magnetic field of +8 T in the stacking direction.The adhesion of the slabs is reinforced by their magnetic attractive force.In this structure, the ANE voltage in all the slabs positively contributes to the total voltage owing to the positive (negative) SANE of SmCo5 (Nd2Fe14B) when the T and m directions in all the slabs are the same.The inset of Fig.2(e) shows a top view of TEG, which confirms that the slabs are stacked with high density and separated by the thin insulator layers.
Figures 3(b) and (c) show the examples of the φ and A images at f = 1.0 Hz and Jc = 1 A, respectively.The thermoelectric signals on the top surface of SmCo5/Nd2Fe14B-based TEG were clearly observed with high area density.Importantly, the SmCo 5 and Nd 2 Fe 14 B respectively show the spatially homogeneous A signals, which is consistent with the feature of AEE with m along z-axis [Fig.3(c)].This uniformity confirms that Jc flows in a zigzag way [indicated by black arrows in Fig. 3(b)] without a short-circuit fault.Because of the opposite direction of Jc and opposite sign of Π AEE between SmCo 5 and Nd 2 Fe 14 B, the resultant temperature modulation due to AEE shows the same sign in all the slabs, which was confirmed by the almost same φ values on the whole area of the top surface [Fig.3(b)].As shown in Fig. 3(c), the SmCo5 slabs show the larger A signals than the Nd2Fe14B slabs due to larger ΠAEE [Fig.2(a)].Figures 3(d) and (e) show the line profiles of φ and A taken along z-axis, where the signals are averaged along y-axis, within the area indicated by a 4.5 mm square in Figs.3(b) and (c), respectively.The Nd2Fe14B slabs show the large φ delay and the rapid drop in A as f increases,

8 FIG. 1 . 9 FIG. 2 . 10 FIG. 3 . 11 FIG. 4 .
FIG. 1. Schematics of permanent magnets showing ANE and insulator layers (a) and integrated transverse TEG (b).The electric field induced by ANE EANE is generated in the cross-product direction (y-axis) of a temperature gradient T (x-axis) and the spontaneous magnetization (z-axis) in a magnetic material.By alternately stacking two different permanent magnets with positive and negative anomalous Nernst coefficients SANE intermediated by insulator layers, a high-density module is obtained.n is the number of the pairs of the permanent magnets.Electrodes are attached at the ends of the permanent magnets.