Roll‐to‐Roll Printing of Anomalous Nernst Thermopile for Direct Sensing of Perpendicular Heat Flux

The anomalous Nernst effect (ANE) converts heat flux perpendicular to the plane into electricity, in sharp contrast with the Seebeck effect (SE), enabling mass production, large area, and flexibility of their devices through ordinary thin‐film fabrication techniques. Heat flux sensors, one of the most promising applications of ANE, are powerful devices for evaluating heat flow and can lead to energy savings through efficient thermal management. In reality, however, SE caused by the in‐plane heat flux is always superimposed on the measurement signal, making it difficult to evaluate the perpendicular heat flux. Here, ANE‐type heat flux sensors that selectively detect a perpendicular heat flux are fabricated by adjusting the net Seebeck coefficient in their thermopile circuit with mass‐producible roll‐to‐roll sputtering methods. The direct sensing of perpendicular heat flux using ANE‐based flexible thermopiles, as well as their simple fabrication process, paves the way for the practical application of thin‐film thermoelectric devices.


Introduction
Heat is the final form of all kinds of energy; therefore, heat management is an important task for our society for sustainable development, especially with the recent rapid development of information technology.Monitoring heat flow can provide essential information for such management, and much attention has been paid to the research and development of sensors to detect heat flow.In addition, such heat flux sensors have been found useful for evaluating various thermal properties that have been difficult to observe directly with thermometers, such as heat absorption/dissipation and core temperatures inside the objects.3] To date, all thermoelectric technology has relied on the Seebeck effect (SE), which generates electromotive forces in parallel with the temperature difference. [4][7][8][9] However, the fabrication of mass-producible, flexible, and large-area thermoelectric devices has been difficult because the materials are often brittle and the geometry of the longitudinal thermoelectric conversion requires a complicated structure called a -shaped array composed of pand n-type semiconductors.
On the other hand, the anomalous Nernst effect (ANE) observed in magnetic metals is different.The electromotive force in ANE is generated in the direction perpendicular to magnetization and temperature gradient (∇T).[12][13][14][15][16][17][18][19] This transverse geometry is essential for mass production, flexibility, and wide coverage area of the devices.And it enables sample and device fabrication techniques commonly used for thin films, such as sputtering and the roll-to-roll (R2R) manufacturing process using flexible film substrates.However, applications using ANE have not been made until recently due to the low thermoelectric conversion efficiency.23][24][25][26][27][28][29] In addition, extensive work has been reported on the fabrication of thin films of these magnetic metals and on ANE-type thermopile devices fabricated on flexible substrates [13] as well as on rigid substrates [10,[14][15][16][17][18][19] for their applications.
Heat flux sensors based on ANE are mainly used to evaluate the heat flux flowing perpendicular to the surface of the measured object (perpendicular heat flux).The electromotive force generated by ANE and SE is perpendicular to each other in the ideal situation, where ∇T is applied (and the heat flux flows) only in the perpendicular direction (Figure 1a).Therefore, the sensor (Figure 1d) can directly measure the ANE signal and accurately evaluate the perpendicular heat flux.On the other hand, in a practical situation where ∇T is applied in an oblique direction with its in-plane component (Figure 1c), the SE signal generated by the in-plane heat flux (Figure 1b) is superimposed on the ANE signal generated by the perpendicular heat flux in the magnetic metals.Thus, one of the challenges in the application of the ANEtype sensors is to remove the undesirable offset signal resulting from the electromotive force proportional to the difference in the Seebeck coefficient (ΔS xx ) between the magnetic metal lines and the electrode lines.Except for common laboratory techniques using the magnetic field sweep, ΔS xx must be set to zero to eliminate the offset.6][17][18] However, to date, the validity of this concept has never been demonstrated nor even investigated for perpendicular heat flux sensing using ANE.
In this study, we demonstrate the first ANE-based heat flux sensor that directly and selectively detects the perpendicular heat flux, where the Seebeck coefficients of the magnetic metal (Fe-Ga alloy) and electrode material (Ni-Cu alloy) in the sensor patterns are adjusted to be nearly equal.The sensor, which is specifically designed to eliminate the contributions from SE (ΔS xx ≈ 0), allows direct sensing of the perpendicular heat flux even in a practical situation where ∇T is applied in an oblique direction (Figure 1f,h).This is in sharp contrast to the results obtained using the unoptimized sensor with ΔS xx ≈ 10 μV K −1 , which shows almost an order of magnitude larger ANE signal induced by the in-plane heat flux than that induced by the perpendicular heat flux (Figure 1e,g).In addition, the SE-free sensor can be made using the flexible film fabricated by a simplified process designed for R2R sputtering systems.Our demonstration of the direct sensing of the perpendicular heat flux fabricated by the R2R sputtering paves the way for real-life applications of ANEtype flexible thermoelectric devices, which have been limited to academic research to date.

Characterization of Fe-Ga and Ni-Cu Thin Films
Generally, the ANE signal takes the value of the order of 0.1 μV K −1 and grows linearly with the magnetization (S ji = Q ji  0 M: S ji is the ANE signal, Q ji is the anomalous Nernst coefficient, μ 0 is the permeability in a vacuum, M is the magnetization).In recent years, much larger ANE breaking the conventional scaling law with the magnetization has been found [20] in magnetic materials with topologically non-trivial band structures (topological magnets) such as Mn 3 Sn, [21] Co 2 MnGa, [22] Fe 3 Ga, [28] Fe 3 Al, [28] and Fe 3 Sn, [29] providing a new guideline based on the band topology to enhance ANE.Surprisingly, the iron-based Fe-Ga alloy has been reported to exhibit disorder-insensitive large ANE with the order of 1 μV K −1 [30] and even without annealing after film deposition. [31]Therefore, we chose the Fe-Ga alloy as the ANE material to fabricate a flexible heat flux sensor.
To characterize the Fe-Ga films fabricated on poly(ethylene terephthalate) (PET) substrates at room temperature by a sput-tering method (Experimental Section), we first performed X-ray fluorescence (XRF) spectrometry, X-ray diffraction (XRD), and magnetotransport measurements.The composition of the Fe-Ga films was confirmed by XRF to be Fe 79 Ga 21 .Figure 2a shows the XRD patterns of the Fe 79 Ga 21 and Fe films obtained by the 2- scan using Cu-K 1 radiation ( = 1.541Å).In both Fe 79 Ga 21 and Fe films, the (110) peak of the bcc-Fe structure was observed at 44.8 and 44.1 deg with the patterns of the PET substrates, respectively.These peaks indicate that the lattice constant of Fe 79 Ga 21 is slightly expanded by 0.04 Å from that of Fe due to the Ga substitution of Fe. [32] The results of the ANE measurements at room temperature under the in-plane heat flux and the perpendicular magnetic field are shown in Figure 2b.As previously reported, the Fe films show a small ANE of S yx ≈ 0.1 μV K −1 . [33,34]In contrast, in the Fe 79 Ga 21 films, the ANE is strongly enhanced and reaches S yx = −2.1 μV K −1 with a reversed sign.The longitudinal resistivity  xx , Seebeck coefficient S xx , and Hall resistivity  yx (Figure 2c) of the Fe 79 Ga 21 films are confirmed to be 157 μΩ cm, −17.9 μV K −1 , and 6.0 μΩ cm, respectively, at room temperature.
Since S yx depends on  xx of the material, it is important to further analyze S yx for the discussion of the intrinsic contributions to ANE. S yx can be described by two elements as the following equation, [31,35] Here the first term (S I =  xx  yx ) comes from the transverse electromotive force due to the intrinsic ANE generated by the transverse thermoelectric conductivity  yx , while the second term (SII =  yx / xx S xx ) corresponds to the anomalous Hall voltage induced by SE.Evaluating  yx , we find that S I and S II , It should be noted that S I is about twice as large as S II , indicating that the transverse thermoelectric conductivity  yx is the main origin of the observed ANE signal consistent with the previous report, [31] and suggesting that the Fermi level shift due to Ga doping should be the origin of the enhancement of  yx and S I .
To develop the ANE-type sensor for the perpendicular heat flux, SE must be eliminated, that is, ΔS xx between the magnetic metal lines and the electrode lines must be zero.Given that Fe 79 Ga 21 films have a large negative Seebeck coefficient of S xx ≈ −17.9 μV K −1 , we select Ni 100−x Cu x alloy as the electrode material that exhibits a large negative S xx with a low resistivity suitable for the electrodes. [36]Figure 2d

Fabrication of ANE-Based Heat Flux Sensors
Here we discuss the detailed fabrication process of the sensor free from the SE contribution from the in-plane temperature gradient.We used an R2R sputtering system to fabricate the ANE magnetic metal (Fe 79 Ga 21 ) and electrode material (Ni 10 Cu 90 ) films on the PET substrates (Figure 3a).Note that the roll of flexible thin films with a width of 0.34 m can be obtained in this system.First, a bilayer of Fe 79 Ga 21 (100 nm) and Ni 10 Cu 90 (100 nm) was sequentially deposited at 100 °C.Next, the bilayer films were patterned into a meander structure by photolithography.Finally, the photolithography was processed again to form a thermopile structure shown in Figure 3b, consisting of ANE lines of the Fe 79 Ga 21 monolayer and electrode lines of the Fe 79 Ga 21 and Ni 10 Cu 90 bilayers (Figure 3c,d).A capping layer (SU-8 3005, KAYAKU Advanced Materials) was additionally fabricated after the sensor fabrication.
We designed the electrode lines with both Fe 79 Ga 21 and Ni 10 Cu 90 layers because this device structure can simplify the device fabrication process, allowing the deposition process to be completed in one step (Figure 3a).In addition, because the continuous lines of Fe 79 Ga 21 can prevent contact issues such as contact resistance and thermomechanical stress, the bilayer design in the electrode lines can reduce the internal resistance and improve the mechanical properties of the devices. [37] concern with this configuration is that the magnetic metal layer of the ANE lines and the electrode lines will generate an electromotive force of the opposite sign.However, if the conductivity of the electrode material is sufficiently larger than that of the magnetic material, the voltage generated in the magnetic metal layer of the electrode wire can be ignored by the shunt in the bilayer structure as discussed below.Assuming that the bilayer film is a parallel circuit, the sensor signal complies with the following equation, ( V can be estimated from the difference between V mag.(voltage from magnet wires) and V bi-ele.(voltage from bilayer electrode lines).V bi-ele.can be described with V mag.(voltage from the ANE lines), sheet conductance of the magnetic metal layer (G m ), and sheet conductance of the electrode material layer (G e ).Note that sheet conductance is the value that is the product of  xx and thickness (t).In our experiment, the Ni 10 Cu 90 layer has ≈10 times larger conductance than that of the Fe 79 Ga 21 layer (Figure 2d), so the reverse voltage produced in the electrode lines (V bi-ele.) is less than 10% of the signal in the ANE line.
Another concern with the bilayer structure is the controllability of the S xx of the electrode lines.In this study, S xx of the magnetic metal (Fe-Ga) layer and the electrode material (Ni-Cu) layer are set to be the same, so the optimization of ΔS xx is not a problem at all, but even if S xx between the two layers are different, the combined S xx can be designed by the following method.The following equation can describe S xx of the bilayer film.
Here, S xx(bi-ele.) is the net Seebeck coefficient of the bilayer electrode, S xx(mag.) is the Seebeck coefficient of the ANE magnetic metal, and S xx(electrode) is the Seebeck coefficient of the electrode material.Figure 3e shows the temperature dependence of S xx of the Fe 79 Ga 21 film for the ANE lines and the Fe 79 Ga 21 /Ni 10 Cu film for the electrode lines on the PET substrate (50 μm) obtained by the R2R sputtering.As designed for this SE-free sensor, the difference ΔS xx between S xx of the Fe 79 Ga 21 monolayer and the Fe 79 Ga 21 /Ni 10 Cu 90 bilayer is confirmed to be less than 0.5 μV K −1 at room temperature, which is sufficiently small for the perpendicular heat flux sensing.

Characterization of ANE-Based Heat Flux Sensors
To evaluate the sensitivity of the heat flux sensor, we employ the experimental setup shown in Figure 4a to apply uniform perpendicular heat flux q z and temperature gradient ∇T z similar to the previous reports (Experimental Section).Figure 4c shows the magnetic field dependence of the ANE signal V ANE of the SE-free ANE thermopile consisting of the Fe 79 Ga 21 and Fe 79 Ga 21 /Ni 10 Cu 90 wires at 300 K.As shown in Figure 3b and Figure 4b, the Fe 79 Ga 21 (Fe 79 Ga 21 /Ni 10 Cu 90 ) lines have a size of 15 mm-length × 100 μm-width (15 mm-length × 40 μm-width) with the separation by 10 μm.V ANE shows a clear hysteretic behavior as a function of the magnetic field for the in-plane (x) direction.Moreover, the zero field signals show a linear increase with the perpendicular heat flux q z = 0.56, 1.17, 1.78 kW m −2 (Figure 4d).This linear dependence provides the sensitivity of the heat flux of 0.23 μV W −1 m 2 (1.0 mV W −1 ).The observed sensitivity is about an order of magnitude larger than the previously reported sensitivity for a Fe-Al flexible sensor of 0.02 μV W −1 m 2 (0.2 mV W −1 ) [13] and even larger than the sensors on the rigid substrates. [10,14,15,19]Here, the difference comes mainly from the longer total length of the ANE lines since the sensor sensitivity can be written as −S yx × L∕, where L is the total length of the magnet wire, and  is the thermal conductivity (W K m −1 ) of the magnetic metal film.We estimate the sensitivity to be 0.16 μV W −1 m 2 using the bulk value of Fe 3 Ga for  = 19.0W m −1 K −1 . [28]o demonstrate the flexibility of the sensor, we also evaluated the sensor's sensitivity on the bending stage.The sensor was placed between a Cu heat sink with a curvature radius R stage = 10.5 mm and a bending heater via thermal interface silicone pads to apply the perpendicular heat flux q z = 1.78 kW m −2 (Figure 5a).Here the heat bath faces the sensor pattern surface, and the heater is attached to the PET substrate surface side, as shown in Figure 5b.The magnetic field dependence of the ANE signal (Figure 5c) showed that the same sensitivity as confirmed in the flat sensor is maintained even under the bending condition with R stage = 10.5 mm (the curvature radius of the sensor R sensor = 11 mm due to the 0.5 mmthick silicone pads).It was also observed that the switching magnetic field for the bent sensor was slightly larger than that for the flat one, that is, the sensor became more stable with respect to the magnetic field.This is because bending the PET substrate causes compressive strain in the Fe 79 Ga 21 lines for the longitudinal direction, resulting in the inverse magnetostriction effect.
In the present study, a compressive strain of ɛ = d/2R sensor and compressive stress of  = ɛE f are applied in the longitudinal direction of the Fe 79 Ga 21 lines when the film thickness (substrate thickness d) is sufficiently small compared to the substrate ones (R sensor ).Here E f is Young's modulus of Fe 79 Ga 21 .In the case of R sensor = 11 mm, the compressive stress of  ≈ 0.3 GPa is applied to the Fe 79 Ga 21 lines when E f is 130 GPa. [38]Therefore, the inverse magnetostriction effect induces uniaxial magnetic anisotropy along the transverse direction of the lines, [39][40][41][42][43][44] which aligns the magnetization to the direction suitable for the ANE signal.Although detailed dependences on the curvature radius and bending direction are left to future research, these results indicate that, in principle, heat flux sensing is possible even for objects with small radii up to the limit where the sensor pattern eventually breaks up since the smaller the curvature radius is, the larger the compressive strain and the more stable the direction of magnetization suitable for sensing becomes.

Perpendicular Heat Flux Sensing using ANE-Based Heat Flux Sensors
Now we discuss the main topic of this study, namely, a perpendicular heat flux sensing by using the heat flux sensor with the compensated net Seebeck coefficient (ΔS xx ≈ 0) in a practical situation where ∇T is applied in an oblique direction with its in-plane component (Figure 1c).The temperature gradients in both in-plane and perpendicular directions (the yz-plane) are applied simultaneously to evaluate the sensing properties.In addition to the SE-free thermopile with the Fe 79 Ga 21 (100 nm) and Fe 79 Ga 21 (100 nm)/Ni 10 Cu 90 (100 nm) lines, a thermopile with the Fe 79 Ga 21 (100 nm) and Fe 79 Ga 21 (100 nm)/Cu (100 nm) lines was used as a reference sample for ΔS xx = 19.6 μV K −1 (Figure 3e). Figure 6a shows the experimental setup, which is the same as that for applying ∇T z , except that the heater is modified to generate the temperature gradient along an oblique direction in the yz-plane (Experimental Section, Figure S2, Supporting Information).Specifically, by placing a heating element (resistance heater) on only one side of the heater layer to cover the sample along an in-plane direction, that is, the x-axis, a uniform temperature gradient can be applied along the other in-plane direction, the y-direction.This heater is referred to here as the yz-plane heater.
Before evaluating the thermopiles, we measured the distribution of ∇T y in the x-direction using an in-plane temperature gradient sensor consisting of the Ni 10 Cu 90 (100 nm) lines on the PET substrate (Figure 5b).This sensor is fabricated by the same R2R methods as the other heat flux sensors, where the 10 lines with the 15 mm-length and 100 μm-width are placed parallel to the y-axis on a 20 mm × 20 mm PET substrate.∇T y of each line is obtained as ∇T y = −V SE ∕(S xx × l) from the output voltage generated by SE (V SE ), the Seebeck coefficient, given copper lines of S xx = −20.1 μV K −1 (Note S1, Figure S3, Supporting Information) and the length of the lines l = 15 mm. Figure 5c shows the averaged voltage of 10 wires for Q heater = 0.04, 0.16, 0.64, 1.44 W, and the 3 error bars, which shows a linear relation between ∇T y and Q heater with the slope of 1.15 K m −1 W −1 .We used this yz-plane heater to measure the properties of the sensors with and without the SE contributions at 300 K (Figure 1e-h).In the magnetic field sweep measurements, the signals originating from ∇T z due to ANE and ∇T y due to SE are expected to appear as a hysteresis loop and its offset, respectively.As shown in Figure 1e,f, the presence and absence of the offset voltage, respectively, indicate the thermopiles with and without the SE contributions, respectively.The absence of the offset in Figure 1f demonstrates that our SE-free ANE sensor can selectively detect the perpendicular heat flux.
In the following, we investigate more quantitatively the differences in sensor characteristics between the two sensors with and without SE contributions.First, we clarify the in-plane temperature gradient ∇T y as a function of the heater power by performing the experiments described in Figure 6a-c.On the other hand, the out-of-plane temperature gradient ∇T z can be obtained as a function of the input power using V ANE and several parameters of the magnetic metal wires (wire length L = 1.425 m and S yx = −2.1 μV K −1 ), as described by ∇T z = V ANE ∕(S yx × L). Figure 1g shows V SE and V ANE , respectively, which increase linearly with ∇T y and ∇T z for the thermopile with the SE contributions.The slope of the signals provides the thermoelectric conversion efficiency per length (V K −1 m), which can be converted to the thermoelectric conversion efficiency (V K −1 ) by adapting the total length of the sensor L = 15 mm × 95 = 1.425 m in the y-direction.The conversion efficiency per magnet/electrode pair is calculated to be 19.1 μV K −1 .This value is almost the same magnitude as the difference of the SE coefficient ΔS xx (= 19.6 μV K −1 ) for Fe 79 Ga 21 (100 nm) and Fe 79 Ga 21 (100 nm)/Cu (100 nm) as shown in Figure 3e, indicating that the offset voltage comes from the difference ΔS xx between the magnetic metal and electrode lines.Moreover, a comparison of|V SE | and |V ANE | reveals that the sensitivity to ∇T y is much larger than that to ∇T z .This is due to the larger value of ΔS xx than S yx for the magnetic metals, making it difficult to selectively measure the perpendicular heat flux.Notably, the SE-free ANE thermopile shows a negligibly small offset-voltage V SE compared to the hysteresis loops originating from ANE.The sensitivities for ∇T y and ∇T z evaluated from the slopes are 0.8 and 3.1 μV K −1 m, respectively.Their ratio ≈ 4 shows a good agreement with the ratio ≈5 of S yx of the magnetic metal to ΔS xx .These results indi-cate that the contribution from ∇T z is dominant, as designed for the SE-free ANE thermopile.The same analysis for the inplane temperature gradient yields S xx ≈ 0.56 μV K −1 , which reasonably reproduces ΔS xx ≈ 0.41 μV K −1 of the magnet and electrode.

Conclusion
We have succeeded in fabricating the first flexible ANE-based heat flux sensor that directly measures the heat flux flowing perpendicular to the sensor plane.By adjusting the Seebeck coefficient S xx of the magnetic metal lines and the electrode lines in the thermopiles, we demonstrate that the signal due to the inplane heat flux can be made negligibly small compared to the signal originating from the perpendicular heat flux by making the difference ΔS xx sufficiently smaller than the ANE signal S yx of the magnetic metal.By enabling the direct measurement of the perpendicular heat flux, our design of the ANE-based heat flux sensor eliminates the complicated calibration process of the offset signal due to the in-plane Seebeck effect by taking hysteresis loops of the electromotive force in the magnetic field under various heat fluxes, which has been essential in measuring the perpendicular heat flux with the ANE-type sensor.In addition, our method employs sputtering and R2R methods popular for mass production and can be easily applied to the fabrication of flexible and large-in-area heat flux sensors.Our work will advance the social implementation of the ANE-based heat flux sensors that are much less expensive than the SE-based counterparts and will contribute to the future development of heat management technology as well as of digital transformation of our society.Sensor Device Fabrication: For ANE measurements in the heat flux sensor, the bilayer films were patterned into meander shapes by photolithography with wet etching.The process was carried out in two steps to form the thermopile, and the structure shown in Figure 3c  Transport Measurements: Both longitudinal and Hall resistivities ( xx and  yx ) were measured by a standard four-terminal method using a commercial physical property measurement system (PPMS, Quantum Design).The bar-shaped samples with electrical contacts made by Au wires were used. yx was estimated as ( yx (+H) −  yx (−H))∕2 to remove offsets derived from the longitudinal resistivity.ANE and SE were measured by the thermal transport option in the commercial PPMS (Quantum Design).Samples were cut into small pieces.A heater and electrodes were attached to the samples (Figure S1, Supporting Information).In the solid films, S yx was estimated as (S yx (+H) − S yx (−H))∕2 to remove offsets derived from SE.

Experimental Section
Measurements for the Sensor with the Perpendicular Heat Flux q z : The measurement for the sensor devices under the perpendicular heat flux was performed using a variable temperature insert with a superconductor magnet (Teslatron PT, Oxford Instruments) and a homemade measurement system with electromagnets.The thermopile device was sandwiched between a Cu heat sink (the flat stage for Figure 4 and the bending stage with the curvature radius of 10.5 mm for Figure 5) and a heater assembly. [14]oth interfaces were covered with 0.5 mm-thick thermal interface silicone pads (TC-50HSV-1.4,Shinetsu-Silicone).To evaluate the heat-flux sensitivity, a bilayer heater and Cu sheet heat spreaders were employed to obtain uniform heat flux.The bilayer heater was constructed with the upper/sub resistance heater, thermal insulation sheet, lower/main resistance heater, and Cu heat spreader.The main heater acted as a heat flux supplier.The sub-heater acted as a backup heater that prevented a leak of heat flux from the main heater to the opposite direction of the sensor devices.To reduce the heat flux leakage, the output of the sub-heater was adjusted so that the output voltage of the differential thermocouples on both sides of the thermal insulation sheet was zero.Here the heater power of the main heater was used to estimate the perpendicular heat flux q z .
Measurements for the Sensor with the Temperature Gradient Applied in an Oblique Direction: A dedicated heater was used in the setup to provide ∇T y and ∇T z .The heater consisted of resistor chips arranged parallel to the x-axis on a Cu plate.The space without a resistor was filled with epoxy resin, and the heater consisted of a sandwiched structure with Cu plates.(Figure S2, Supporting Information).A heater power (Q heater ) was controlled by the current value.V was an experimentally obtained signal.The voltage derived from ∇T z (V ANE ) and ∇T y (V SE ) were estimated as (V( 0 H = +0T) − V( 0 H = −0T))∕2 and (V( 0 H = +0T) + V( 0 H = −0T))∕2, respectively.∇T y was quantified by the in-plane temperature gradient sensor (Note S1, Supporting Information).∇T z was obtained from V ANE and several parameters of the magnetic metal wires (wire length L = 1.425 m and S yx = −2.1 μV K −1 ) as described by ∇T z = V ANE ∕(S yx × L) .

Figure 1 .
Figure 1.a-c) Schematic illustrations of the measurement geometry of the anomalous Nernst effect (ANE) and Seebeck effect (SE) voltages (V ANE , V SE ) under the temperature gradients: a) ∇T along the z-axis, b) ∇T along the y-axis, and c) ∇T along an oblique direction in the yz-plane.The magnetization (M) is aligned along the x-direction.V is the output voltage obtained in the experimental setup.E ANE and E SE are the electric fields generated by ANE and SE, respectively.E ANE(y) (E SE(y) ) and E ANE(z) (E SE(z) ) are the y-and z-components of E ANE (E SE ), respectively.d) Schematic illustrations of the transverse geometry of the heat flux sensor using ANE.V ANE and V SE are induced by the temperature gradients in the perpendicular direction (∇T z ) and in the in-plane direction (∇T y ), respectively.The sensor signal is the sum of V ANE induced in magnetic metal lines and V SE induced in electrode lines.e,f) Magnetic field dependence of V for the ANE-type thermopile under various heater power at 300 K. g,h) Zero-field sensor signal as a function of ∇T z (blue circles) and ∇T y (red circles) for the thermopiles at 300 K.The pairs of the Fe 79 Ga 21 magnetic metal line and the Fe 79 Ga 21 /Cu electrode line (ΔS xx > 0) and the pairs of the Fe 79 Ga 21 magnetic metal line and the Fe 79 Ga 21 /Ni 10 Cu 90 electrode line (ΔS xx ≈ 0) are used in (e,g) and (f,h), respectively.ΔS xx is the difference in the Seebeck coefficient between the magnetic metal line and the electrode line.

Figure 2 .
Figure 2. a) XRD pattern for Fe 79 Ga 21 and Fe thin films on PET.b,c) Anomalous Nernst effect S yx (b) and Hall resistivity  yx (c) plotted as a function of the magnetic field H along the z-axis in the Fe 79 Ga 21 (blue lines) and Fe (black lines) thin films on PET at 300 K. d) Cu composition x dependence of the Seebeck coefficient S xx (orange circles) and conductivity  xx (open black circles) of the Ni 100−x Cu x films on PET at 300 K.

Figure 3 .
Figure 3. a) Schematic illustration of the fabricating process employing the R2R sputtering system and photo showing the 340 mm wide R2R fabricated thin films.b) Schematics of the fabrication process for the ANE-based heat flux sensor.c) Schematic illustration of the cross-sectional view of the heat flux sensor.The Fe 79 Ga 21 and (Fe 79 Ga 21 /(Ni 10 Cu 90 or Cu)) lines have a size of 15 mm-length × 100 μm-width (15 mm-length × 40 μm-width) with a distance of 10 μm, and the sensor consisted of 95 pairs of these elements.d) Photo of the ANE-type flexible heat flux sensor on the PET substrate.The spots on the film are due to the anti-blocking layer on the film surface.e) Temperature dependence of the Seebeck coefficient S xx for each component of the heat flux sensor.
shows the x dependence of S xx of the Ni 100−x Cu x films on the PET substrates obtained by Ni and Cu co-sputtering methods at room temperature (Experimental Section).In the range of x = 45-100, S xx increases monotonically and changes in S xx = −35-3 μV K −1 .The x dependence of S xx (orange circles) of Ni 100−x Cu x reaches S xx of the Fe 79 Ga 21 films (blue dashed line) at x = 90.Therefore, in this study, we use Ni 10 Cu 90 as the electrode material corresponding to the ANE material Fe 79 Ga 21 .Note that the electrical conductivity  xx of the Ni 10 Cu 90 film is about one order of magnitude larger than that of the Fe 79 Ga 21 film ( xx ≈ 6.3 × 10 3 S cm −1 ) (Figure 2d).

Figure 4 .
Figure 4. a) Schematic illustration of the experimental setup for the anomalous Nernst effect measurement for the ANE-type heat flux sensors.b) Schematic design of the ANE-type heat flux sensors consisting of an alternating array of the Fe 79 Ga 21 lines and the Fe 79 Ga 21 /Ni 10 Cu 90 lines on the PET substrate.c) Magnetic field dependence of the Nernst voltage V ANE for the thermopile made of 95 pairs consisting of the Fe 79 Ga 21 line and the Fe 79 Ga 21 /Ni 10 Cu 90 line under the heat flux for the perpendicular direction q z = 0.56-1.78kW m −2 at 300 K. d) Zero-field V ANE for the Fe 79 Ga 21 and Fe 79 Ga 21 /Ni 10 Cu 90 heat flux sensor as a function of q z obtained at 300 K.

Figure 5 .
Figure 5. a) Schematic illustration of the experimental setup for the anomalous Nernst effect measurement for the ANE-type heat flux sensors on the bending stage with the curvature radius R stage .The magnetic field direction is parallel to the x-direction.b) Schematic illustration of the inward bending heat flux sensor.c) Magnetic field dependence of the Nernst voltage V ANE for the ANE-type heat flux sensors on the bending stage (blue squares) and the flat stage (black circles) at 300 K. V ANE is normalized by the zero field signal of the sensor on the flat stage.The heat flux for the perpendicular direction q z = 1.78 kW m −2 is applied to the sensors.

Figure 6 .
Figure 6.a) Schematic illustration of the experimental setup of the yz-plane temperature gradient measurement for the Fe 79 Ga 21 thermopile devices.b) Schematic design of the measurement device for the temperature gradient in the in-plane (y) direction (∇T y ) consisting of Ni 10 Cu 90 wires on a PET substrate.c) Heater power dependence (Q heater ) of the zero-field Seebeck voltage induced by ∇T y (V SE ) for the Ni 10 Cu 90 wires at 300 K.The error bars indicate 3 of measurements for the 10 wires.

Sample Preparation:
Fe 79 Ga 21 and Ni 10 Cu 90 films were fabricated on PET substrates by the R2R DC magnetron sputtering from Fe 75 Ga 25 and Ni 9.5 Cu 90.5 targets.To fabricate PET/Fe 79 Ga 21 /Ni 10 Cu 90 thin films, the targets were placed in the order of Fe 79 Ga 21 and Ni 9.5 Cu 90.5 with respect to the transport direction, and PET substrates were transferred at 0.53 m min −1 .In the fabrication of PET/Fe 79 Ga 21 /Cu thin films, a pure Cu target was placed instead of the Ni 9.5 Cu 90.5 target.The Fe 79 Ga 21 layer was deposited at 100 °C, 0.1 Pa with Ar gas.The deposition rate was 20.4 nm W −1 estimated by X-ray reflectivity measurements.The compositions of the films were determined by XRF.The Ni 10 Cu 90 and Cu layers were deposited at 100 °C, 0.2 Pa with Ar.The deposition rate was 26.4 and 32.1 nm W −1 , respectively.The deposition rate and the compositions were determined by the same method for the Fe 79 Ga 21 film.The thickness of each film was adjusted to 100 nm.The Ni 100−x Cu x films for the composition dependence measurements were directly fabricated on the PET substrates by the RF magnetron co-sputtering from Ni and Cu targets.The Ni 100−x Cu x layer was deposited at room temperature, and the Ar gas pressure was 0.3 Pa.A Fe-thin film was also fabricated on the PET substrates by the RF magnetron sputtering from the Fe target with the Ar pressure of 0.3 Pa at room temperature.In order to prevent the Fe film from oxidation, a 5 nm-thick Al 2 O 3 capping layer was deposited by the RF magnetron sputtering.
was obtained by removing half of the Cu or Ni 10 Cu 90 layer in the second step, as shown in Figure 3c.The shape of Fe 79 Ga 21 wires was 15 mm × 100 μm in the inplane direction, and the shape of Fe 79 Ga 21 /(Cu or Ni 10 Cu 90 ) wires was 15 mm × 40 μm.The sensor consisted of 95 pairs of these elements.The in-plane temperature gradient sensor made of Ni 10 Cu 90 wires was similarly formed by wet etching.The shape of Ni 10 Cu 90 wires was 15 mm × 100 μm, and the detection area was aligned to be the same as that of ANE sensors.A capping layer (SU-8 3005, KAYAKU Advanced Materials) was additionally fabricated after the sensor fabrication process.