Sm-Co-based amorphous alloy films for zero-field operation of transverse thermoelectric generation

ABSTRACT

Transverse thermoelectric generation using magnetic materials is essential to develop active thermal engineering technologies, for which the improvements of not only the thermoelectric output but also applicability and versatility are required. In this study, using combinatorial material science and lock-in thermography technique, we have systematically investigated the transverse thermoelectric performance of Sm-Co-based alloy films. The high-throughput material investigation revealed the best Sm-Co-based alloys with the large anomalous Nernst effect (ANE) as well as the anomalous Ettingshausen effect (AEE). In addition to ANE/AEE, we discovered unique and superior material properties in these alloys: the amorphous structure, low thermal conductivity, and large in-plane coercivity and remanent magnetization. These properties make it advantageous over conventional materials to realize heat flux sensing applications based on ANE, as our Sm-Co-based films can generate thermoelectric output without an external magnetic field. Importantly, the amorphous nature enables the fabrication of these films on various substrates including flexible sheets, making the large-scale and low-cost manufacturing easier. Our demonstration will provide a pathway to develop flexible transverse thermoelectric devices for smart thermal management.

GRAPHICAL abstract

KEYWORDS:

• Transverse thermoelectric conversion
• magnetic thin films
• rare-earth magnet
• amorphous alloy
• heat flux sensor

1. Introduction

In recent years, the research on spin caloritronics is showing a new direction with the demonstration of many magneto-thermoelectric effects by advanced heat detection techniques [1–5]. The magneto-thermoelectric effects that provide interconversion between heat and charge currents in magnetic materials exhibit unique thermoelectric conversion functionalities, which potentially enable versatile thermal energy harvesting and active thermal management for electronic and spintronic devices. Among the magneto-thermoelectric effects, the anomalous Nernst effect (ANE) and its Onsager reciprocal called anomalous Ettingshausen effect (AEE) are of particular interest due to their unique heat-charge current conversion symmetry [6–12]. ANE (AEE) generates a charge (heat) current in the direction perpendicular to an applied temperature gradient $\mathrm{\nabla }\mathit{T}$ (charge current) and magnetization M:

(1) ${\mathbf{j}}_{\mathrm{c},\mathrm{ANE}}=\mathit{\sigma }{S}_{\mathrm{ANE}}\left(\hat{\mathbf{m}}\mathit{\hspace{0.17em}}\times \mathrm{\nabla T}\right),$(1)

(2) ${\mathbf{j}}_{\mathrm{q},\mathrm{AEE}}={\mathrm{\Pi }}_{\mathrm{AEE}}\left(\hat{\mathbf{m}}\times {\mathbf{j}}_{\mathrm{c}}\right),$(2)

where ${\mathbf{j}}_{\mathrm{c},\mathrm{ANE}}({\mathbf{j}}_{\mathrm{q},\mathrm{AEE}})$ is the charge (heat) current density driven by ANE (AEE), ${\mathbf{j}}_{\mathrm{c}}$ is the charge current density applied to a magnetic material, $\hat{\mathbf{m}}$ is the unit vector along M, $S_{\mathrm{ANE}}$ (${\mathrm{\Pi }}_{\mathrm{AEE}}$) is the ANE (AEE) coefficient, and $\mathit{\sigma }$ is the electrical conductivity. The above relations provide various advantages for ANE/AEE-based devices. For example, the symmetry of ANE enables thermoelectric generation simply by forming a magnetic material on a heat source surface. This simple and effective structure makes it possible to construct thermoelectric modules with high flexibility, high mechanical endurance, and low cost and to reduce efficiency losses in contact resistances [13]. The output voltage and power induced by ANE can be increased by increasing the length and area of the magnetic material in a lateral direction, respectively. Since it is easy to increase the length and area of such lateral devices, ANE is suitable for harvesting thermal energy distributed over a large area. In contrast, AEE enables active control of heat current directions and distributions by controlling the M direction [14]. These strong potentials of ANE/AEE have stimulated innumerable studies in fundamental and materials science in these effects.

Despite these technological advantages, practical applications of ANE/AEE-based thermoelectric converters require systematic device engineering and introduction of new materials as most of the conventional ANE/AEE materials till date have low thermoelectric conversion performance. To overcome this situation, researchers around the globe are investigating ANE/AEE systematically and many ANE/AEE materials have been discovered. Recently, large S_ANE of 6 ~ 8 × 10⁻⁶ VK⁻¹ was observed in ferromagnetic Heusler compound Co₂MnGa, which is the record-high value at room temperature [15–18]. In 2021, Asaba et al. found giant S_ANE of 23 × 10⁻⁶ VK⁻¹ at 40 K in UCo_0.8Ru_0.2Al [19]. Large ANE was also observed in single-crystalline noncollinear antiferromagnet YbMnBi₂, where S_ANE ~6 × 10⁻⁶ VK⁻¹ at 160 K [20]. However, most of ANE/AEE materials require an application of external magnetic fields to align the magnetization; this situation significantly compensates the advantages of ANE/AEE-based devices and limits the practical applications. Therefore, ANE/AEE materials with large remanent magnetization and coercive force are desired. In this context, Miura et al. found that SmCo₅-type bulk permanent magnets exhibit large AEE and their figure of merit above room temperature is comparable to that in Co₂MnGa [8,11]. This finding suggests that the investigation of ANE/AEE in rare-earth magnets is important to realize zero-field operation of transverse-thermoelectric conversion. Although bulk ANE/AEE materials are suitable for energy harvesting and temperature control, thin films are advantageous for smart applications including wearable thermoelectric converters and heat flux sensors due to high flexibility and low heat resistance.

In this paper, we show that Sm-Co-based amorphous thin films enable zero-field operation of ANE/AEE. Using combinatorial thin-film deposition and thermoelectric imaging techniques, we systematically investigated the composition dependence of AEE for Sm_pCo_100-p (0 ≤ p ≤ 100) amorphous films and confirmed that Sm₂₀Co₈₀ shows largest AEE-induced temperature modulation. We demonstrated that AEE can further be improved by partially replacing Co with Fe by preparing Sm₂₀(Co_100-qFe_q)₈₀ (0 ≤ q ≤ 100) composition-spread films and found that Sm₂₀(Co₇₇Fe₂₃)₈₀ exhibits largest AEE in these alloys. Despite their amorphous nature, the Sm-Co-based films exhibit large in-plane remanent magnetization and coercive force; these films are advantageous over conventional materials for applications including heat flux sensors, as they can generate thermoelectric output in the absence of external magnetic fields. Importantly, the Sm-Co-based amorphous films can be fabricated on any surface including flexible substrates, which improves the versatility of the ANE/AEE devices.

2. Experimental details

2.1. Sample preparation

The Sm_pCo_100-p and Sm₂₀(Co_100-qFe_q)₈₀ composition-spread films with a thickness of 100 nm were fabricated on a single-crystalline MgO (001) substrate using a magnetron sputtering system (Comet, Inc., CMS-3200), where direct current power sources were used for Sm and Co depositions and a radio frequency power source was used for Fe deposition. Before sputtering the films, the chamber was evacuated at a base pressure of < 6.0 × 10⁻⁶ Pa and then deposited at a process Ar gas pressure of 0.4 Pa at ambient temperature. To achieve a composition variation of 0 ≤ p ≤ 100 at.% over a length of 7.0 mm on a single substrate, the films were prepared from Sm and Co targets using a layer-by-layer wedge-shaped deposition process established in earlier studies [21,22]. Here, (I) we first deposited a wedge-shaped Co layer using a linear moving shutter over a length of 7.0 mm, (II) then rotated the substrate by 180º, (III) followed by the deposition of a wedge-shaped Sm layer using the linear moving shutter over a length of 7.0 mm, where the total thickness of the Sm_pCo_100-p films after completing (I)-(III) were designed to be 1.0 nm. This sequence was repeated 100 times to get the 100-nm-thick composition-spread film (see Figure 1 (a)). The Sm₂₀(Co_100-qFe_q)₈₀ composition-spread films with q varying from 0 to 100 at.% were prepared using the similar approach, where first a uniform layer of Sm was deposited and then wedge shaped Co and Fe layers with an opposite thickness gradient were deposited on top of the Sm layer (see Figure 7 (a)). The combination of the uniform Sm layer and the Co/Fe wedge layer forms the 1-nm-thick Sm₂₀(Co_100-qFe_q)₈₀ film. The processes were repeated 100 times to get the 100-nm-thick film. In addition to the composition-spread films, we also fabricated uniform 100-nm-thick Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films by the repeating Sm/Co and Sm/Co/Fe layers for 100 times, respectively (see Figure 5 (a) and 9 (a)). All the films were capped with a 2-nm-thick Al film to prevent oxidation.

Figure 1. (a) Schematic of the Sm_pCo_100-p composition-spread film structure, where the wedge-shaped Sm and Co layers were alternatively deposited using the linear moving shutter on a MgO substrate. (b) XRD profiles for the Sm_pCo_100-p composition-spread film measured at 1-mm interval along the x direction. (c) Corresponding 2D XRD profile. The compositions written on the 2D profile are estimated from the x-dependent composition data measured by thermal emission EPMA. Here x = 0 corresponds to the substrate edge at pure Co side.

2.2. Composition, structural, and magnetic characterization

The Sm, Co, and Fe concentrations of the Sm_pCo_100-p and Sm₂₀(Co_100-qFe_q)₈₀ composition-spread films were measured by the thermal emission electron probe microanalyzer (EPMA) (JEOL, JXA-8530F). The crystal structures of the composition-spread films were investigated by the X-ray diffraction (XRD) method (Rigaku, SmartLab) with a Cu K_α X-ray source (λ = 0.15406 nm). The X-ray was incident on the sample in the Bragg-Brentano geometry as a parallel beam through a length limit slit of 0.5 mm in the direction perpendicular to the composition gradient and detected with a 2D detector (Rigaku, PILATUS100K/R). The measurements were performed at different positions on the Sm_pCo_100-p and Sm₂₀(Co_100-qFe_q)₈₀ composition-spread films along the composition gradient at an interval of 1.0 mm. The microstructures of the films were investigated using scanning transmission electron microscope (STEM) (FEI, Titan G2 80–200) equipped with a probe aberration corrector. Energy-dispersive-spectroscopy (EDS) data was collected using a Super-X EDX detector. The STEM specimens were prepared by a FEI Helios G4 dual beam machine using the lift-out process. The composition dependence of the magnetic property of the Sm_pCo_100-p and Sm₂₀(Co_100-qFe_q)₈₀ composition-spread films was evaluated by performing position-dependent in-plane micro-magneto-optical Kerr effect (MOKE) (NEOARK Co., BH-PI920BU-TKT) measurement at an interval of 0.25 mm along the composition gradient direction using a green laser with spot size of 2 μm diameter in minimum. The magnetization curve of the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films were characterized using the vibrating sample magnetometer (Quantum Design, MPMS3) at room temperature.

2.3. Transport properties measurement

The composition dependence of the electrical resistivity (${\rho }_{\mathit{xx}}$) for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film was measured by means of the four-probe method, where the distance between the voltage probes is 100 μm and the local resistivity measurements were performed at an interval of 0.25 mm. The ${\rho }_{\mathit{xx}}$ and Seebeck coefficient S_SE values for the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films were measured using the Seebeck Coefficient/Electric Resistance Measurement System (ADVANCE RIKO, ZEM-3). To measure ANE and AHE for the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films, Hall-bar-shaped patterns were prepared using photolithography and Ar-ion milling. The ANE voltage was measured by applying a temperature gradient and magnetic field in the in-plane and out-of-plane directions, respectively (see the inset to Figure 5 (c)). The temperature distribution was precisely evaluated by an infrared camera while coating the sample surface with the black ink to correct an emissivity, which is a technique established in earlier studies [17,23–25]. To evaluate AHE, the Hall voltage along the width direction of the Hall bar was measured by applying a charge current of 1 mA in the length direction of the sample and the external magnetic field in the out-of-plane direction.

2.4. Lock-in thermography (LIT) measurement

For the AEE measurement using the LIT technique, the Sm_pCo_100-p and Sm₂₀(Co_100-qFe_q)₈₀ composition-spread films were patterned into a device consisting of two wires with a width of 0.4 mm and length of 8.0 mm, where the composition gradient was along the length direction. During the LIT measurements, one end of the wires was electrically connected, such that the two wires were connected in series with the charge current flowing along the opposite directions (see Figure 4 (a)). The magnetic field was applied along the y direction (width direction of the wires); thus, the temperature modulation is generated on the sample surface due to the AEE-induced heat current along the thickness direction. The infrared radiation thermally emitted from the sample surface was detected while applying a square-wave-modulated AC charge current with the square-wave amplitude of 15 mA, frequency f = 25 Hz, and zero DC offset along the wires and an external magnetic field with the magnitude μ₀H = ± 0.8 T. To extract the pure AEE contribution from other thermoelectric background signals, we employed the previously established procedure [6–10,26,27]; we extracted lock-in amplitude A_odd and phase ϕ_odd images showing the distribution of the current-induced temperature modulation with the H-odd dependence, which were obtained by subtracting the raw LIT images for M || +y from those for M || -y and dividing the subtracted images by 2.

2.5. Time-domain thermoreflectance (TDTR) measurement

The out-of-plane thermal conductivity for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film was measured by means of a pump-probe optical technique called TDTR [28,29]. For the TDTR measurements, the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film was covered with a 100-nm-thick Al capping layer. The Al layer works as a transducer because the thermoreflectance coefficient of Al is well known [29–31]. The TDTR system used in this study is based on the front-heating front-detection configuration [32], where the pulse duration, optical power, repetition rate, modulation frequency, wavelength, and spot diameters of the pump (probe) laser are 0.5 ps (0.5 ps), 47 mW (<1 mW), 20 MHz (20 MHz), 200 kHz (none), 1550 nm (775 nm), and 90 μm (~30 μm), respectively. Since the diameter of the pump laser spot is much larger than the heat diffusion length in the MgO substrate, $\sqrt{\mathit{\alpha }/\mathit{\pi f}}$ $\cong$5.5 μm, where $\mathit{\alpha }$ is the thermal diffusivity of MgO and f is the modulation frequency, one-dimensional heat diffusion can be presumed. The pump laser was irradiated on the film surface, and then the probe laser was focused at the same spot with the specific delay that is electrically controlled by a function generator [32]. By detecting the reflected probe laser using a Si adjustable balanced photoreceiver connected to a lock-in amplifier, the amplitude and phase components of thermoreflectance signals synchronized with the modulation frequency can be characterized. Finally, the thermal conductivity of the Sm₂₀(Co_100-qFe_q)₈₀ layer was quantified from the measured TDTR signals with a heat conduction model [32], where a one-dimensional heat conduction in the model comprising the MgO substrate and two layers, i.e. Sm₂₀(Co_100-qFe_q)₈₀ and Al, are assumed. Here, the actual thicknesses of the Sm₂₀(Co_100-qFe_q)₈₀ and Al layers are estimated based on cross-sectional STEM measurements.

3. Results and discussion

3.1. Deposition and characterization of Sm_pCo_100-p (0 ≤ p ≤ 100) composition-spread film

The Sm_pCo_100-p composition-spread film was prepared on a MgO (001) substrate using magnetron sputtering, where the Sm concentration (p) is varied from 0 at.% (pure Co) to 100 at.% (pure Sm) on a single film. The wedge-shaped Sm and Co layers were alternately deposited using a linear moving shutter and the thickness gradient direction of the Sm layers was kept opposite to that of the Co layers. The thickest part of each layer has a thickness of 1 nm and one Sm-Co pair forms a uniform 1-nm-thick film, where the Sm and Co atoms are naturally mixed without any heat treatment as a solid solution or binary alloy. By repeating the deposition of such Sm-Co pairs 100 times, a 100-nm-thick Sm_pCo_100-p composition-spread film was obtained (see experimental section for detailed procedures). The systematic change of the Sm_pCo_100-p alloy composition along the composition gradient was confirmed by position-dependent EPMA measurements. A schematic illustration of the deposited film is displayed in Figure 1 (a). Such a composition-spread film is useful for high-throughput material screening over wide composition range without time-consuming experiments using many films. Figure 1 (b-c) respectively represent the XRD line profile and 2D image profile of the as-deposited Sm_pCo_100-p composition-spread film measured at different positions along the composition gradient. The XRD data reveals that the Sm_pCo_100-p alloys are amorphous in nature except the Co-rich and Sm-rich regions. For the Co-rich and Sm-rich regions, the film has polycrystalline nature, where the pure metal phases are dominated and hcp Co and trigonal Sm are formed (see the 2D XRD profiles at x = 1.5 mm, 2.5 mm, and 8.5 mm).

Figure 2 (a-c) shows the cross-sectional bright-field (BF) STEM images with microbeam electron diffraction patterns. The electron diffraction patterns clearly demonstrate no crystalline ordering at the Sm₃₀Co₇₀ composition, while the crystalline ordering was observed for the Co-rich and Sm-rich regions. These results are consistent with the XRD data. Figure 2 (d) shows the STEM-EDS elemental maps obtained at Co-rich, Sm₃₀Co₇₀, and Sm-rich regions of the Sm_pCo_100-p composition-spread film. Figure 2 (e-f) displays the high-magnification STEM-EDS maps of Sm and Co observed from the Sm₃₀Co₇₀ region of the film and composition line profiles of the constituent elements (obtained from selected box shown in Figure 2 (e)), respectively. These data reveal the formation of the Sm_pCo_100-p alloy with mixing of Sm and Co atoms in microstructure level, although the film was fabricated by layer-by-layer deposition.

Figure 2. (a)-(c) Cross-sectional BF-STEM images and microbeam electron diffraction patterns for the Sm_pCo_100-p composition-spread film measured at three different positions corresponding to the compositions (a) Sm₂Co₉₈, (b) Sm₃₀Co₇₀, and (c) Sm₉₇Co₃.(d) The STEM-EDS elemental maps obtained at the same positions of (a)-(c). (e) High magnification STEM-EDS maps of Sm and Co observed from Sm₃₀Co₇₀ composition. (f) The composition line profiles of the constituent elements along the horizontal direction obtained from the selected box region shown in (e).

To investigate the magnetic properties of this amorphous Sm_pCo_100-p alloys, we measured the composition-dependent MOKE loops using the above composition-spread film by applying an in-plane magnetic field. From the hysteresis behavior of the MOKE loops, we estimated the composition dependence of the coercive field (${\mu }_0{H}_{\mathrm{C}}^{\mathrm{Kerr}}$) and plotted as a function of p in Figure 3 (a). We observed that the alloy compositions with 20 ≤ p ≤ 30 at.% have significantly large in-plane coercivity and remanent magnetization. The typical Kerr loops observed at p = 21 at.% and 43 at.% for the film are shown in Figure 3 (b-c), respectively. The absence of the MOKE signal for p > 43 at.% signifies that the Sm_pCo_100-p alloys with p > 43 at.% are nonmagnetic (see the inset to Figure 3 (a)). This magnetic behavior is consistent with previous works on Sm-Co-based amorphous films [33–35]. The magnetic anisotropies originating from short range ordering of SmCo alloys in these amorphous structures are considered to be the origin of such magnetic nature. However, the detailed microscopic origin for this property remains to be investigated. The presence of the large in-plane coercivity and remanent magnetization make these alloys potential candidates for the zero-field operation of the transverse thermoelectric conversion.

Figure 3. (a) Sm concentration p dependence of the coercive field ${\mu }_0{H}_{\mathrm{C}}^{\mathrm{Kerr}}$ estimated from the MOKE loops for the Sm_pCo_100-p composition-spread film, measured with applying an in-plane magnetic field. The inset shows the absence of the Kerr loop at a non-magnetic Sm-rich region of the Sm_pCo_100-p composition-spread film. (b),(c) In-plane Kerr loops observed for the Sm_pCo_100-p composition-spread film at the Sm₂₁Co₇₉ and Sm₄₃Co₅₇ compositions.

3.2. Transverse thermoelectric conversion performance of Sm_pCo_100-p films

Now we are in a position to evaluate the composition dependence of the transverse thermoelectric effects, i.e. ANE and AEE, in the Sm_pCo_100-p alloys. The direct one-by-one measurements of ANE and other transport properties using conventional Hall-bar-shaped samples for a composition-spread film involve complicated device design and time-consuming experiments. Also, the limitation of the number of the Hall bars along the composition gradient lowers the composition resolution. To solve such hurdles, we employed the LIT technique which enables imaging measurements of the temperature modulations due to thermoelectric effects [1–3,36,37]. In the LIT measurements, the thermal images recorded with applying a charge current to a sample are Fourier transformed to obtain the lock-in amplitude A and phase ϕ images, where A and ϕ represent the magnitude and sign of temperature modulation due to the thermoelectric effects. As can be seen from Equation 2(2) ${\mathbf{j}}_{\mathrm{q},\mathrm{AEE}}={\mathrm{\Pi }}_{\mathrm{AEE}}\left(\hat{\mathbf{m}}\times {\mathbf{j}}_{\mathrm{c}}\right),$(2) and Figure 1 (a), if a charge current is applied along the x direction (along the composition gradient) and magnetic field is applied along the y direction, the AEE-induced heat current is generated along the z direction (perpendicular to the film plane). Thus, the LIT image recorded in this configuration contains the spatial distribution of temperature modulation signals reflecting the composition dependence of AEE. Therefore, the AEE measurements using LIT require only a simple strip along the composition gradient, thus enabling easy and efficient scanning to find the suitable composition region with largest AEE in a composition-spread film. Importantly, the magnitude of the AEE-induced temperature modulation obtained by extracting the line profile of the LIT image is continuous along the composition gradient. This gives much accurate estimation of the composition dependence of AEE [6]. Based on the reciprocal relation between AEE and ANE, the combination of composition-spread film and LIT enables high-throughput screening of ANE materials.

Figure 4 (a-d) represent the lock-in A and ϕ images for the Sm_pCo_100-p composition-spread film at the charge current amplitude J_c = 15 mA and frequency f = 25 Hz for various magnitudes of an external magnetic field μ₀H. The images were recorded while applying the magnetic field in the order of μ₀H = 0.8 T (Figure 4 (a)), 0.0 T (Figure 4 (b)), −0.8 T (Figure 4 (c)), and 0.0 T (Figure 4 (d)) (note that our MOKE measurements confirm that the in-plane magnetization saturates at |μ₀H| = 0.8 T for any compositions). Thus, by subtracting the LIT images in Figure 4 (c,d) from those in Figure 4 (a,b), we can obtain the A_AEE and ϕ_AEE images showing the pure AEE-induced temperature modulation for the saturation magnetization (remanent magnetization) state, as shown in Figure 4 (e,f). The ϕ_AEE image in Figure 4 (e) shows that the sign of the temperature modulation for the top wire is opposite to that of the bottom wire because of the phase difference of ⁓180°. The result indicates that ${\mathbf{j}}_{\mathrm{q},\mathrm{AEE}}$ is generated along the +z (-z) direction when M and J_c are along the +y and -x (+x) directions, respectively, which is consistent with the symmetry of AEE in Equation 2.(2) ${\mathbf{j}}_{\mathrm{q},\mathrm{AEE}}={\mathrm{\Pi }}_{\mathrm{AEE}}\left(\hat{\mathbf{m}}\times {\mathbf{j}}_{\mathrm{c}}\right),$(2) Figure 4 (f) shows that similar A_AEE and ϕ_AEE signals appear in the Sm_pCo_100-p composition-spread film even in the remanent magnetization state, confirming the zero-field operation of AEE in our film.

Figure 4. (a)-(d) Lock-in amplitude A and phase ϕ images for the Sm_pCo_100-p composition-spread film recorded by applying a square-wave-modulated AC charge current with the amplitude J_c = 15 mA and frequency f = 25 Hz for various values of the in-plane external magnetic field μ₀H. J_c and M represent the charge current and magnetization directions, respectively. (e) A_AEE and ϕ_AEE images showing the pure AEE-induced temperature modulation for the Sm_pCo_100-p composition-spread film at $\left|{\mu }_0\mathit{H}\right|=0.8\mathrm{T},$ obtained by subtracting the images in (c) from those in (a). (f) A_AEE and ϕ_AEE images at $\left|{\mu }_0\mathit{H}\right|=0.0\mathrm{T}$ , obtained by subtracting the images in (d) from those in (b). (g) Line profile of A_AEE normalized by the charge current density j_c at $\left|{\mu }_0\mathit{H}\right|=0.8\mathrm{T}$ and 0.0 T as a function of the Sm concentration p.

Figure 4 (g) shows the x-directional line profile of A_AEE normalized by the charge current density j_c for the Sm_pCo_100-p composition-spread film both in the saturation magnetization (|μ₀H| = 0.8 T) and remanent magnetization (|μ₀H| = 0.0 T) states, extracted from the images in Figure 4 (e-f), respectively. Here, the position dependence of A_AEE/j_c is converted into the p dependence by using the x dependence of the alloy composition. We found that the AEE-induced temperature modulation is very small for pure Co and gradually increases with increasing p in the Sm_pCo_100-p alloy for the 0 ≤ p ≤ 20 at.% region. At p = 20 at.%, the alloy shows the maximum AEE signal which remains nearly constant for 20 ≤ p ≤ 30 at.%. Then, the magnitude of the AEE signal gradually decreases for 30 ≤ p ≤ 43 at.% and vanishes for p > 43 at.%. The similar tendency was also observed in the remanent magnetization state. Here, it should be noted that the maximum value of A_AEE/j_c in the remanent magnetization state is nearly 30% reduced from that in the saturation magnetization state. This behavior can be explained by the fact that the magnetic field dependence of the AEE signal follows the magnetization curve (see the MOKE signal in Figure 3 (b)).

3.3. Measurement of anomalous Nernst coefficient for Sm₂₀Co₈₀ film

Through the LIT measurements using the Sm_pCo_100-p composition-spread films, we have successfully determined the compositions showing largest AEE among the present amorphous alloys. It is also important to quantitatively determine S_ANE and Π_AEE to evaluate the transverse thermoelectric performance of the amorphous Sm_pCo_100-p alloys. For this purpose, we fabricated a uniform Sm₂₀Co₈₀ film with the optimized composition by alternately depositing Sm and Co thin layers (see Figure 5 (a)). The thicknesses of each layer were determined from the layer thicknesses of the composition-spread film used for the aforementioned experiment. The Sm₂₀Co₈₀ film is amorphous in nature as confirmed by a microbeam electron diffraction pattern (see supplementary material Figure S1), which is consistent with the structural property of the composition-spread film at this composition. To investigate the magnetic property of the uniform film, we measured in-plane magnetization curve. As represented in Figure 5 (b), the film exhibits hysteresis behaviors with large in-plane coercivity and remanent magnetization. These results suggest that the uniform Sm₂₀Co₈₀ film has structural and magnetic behaviors similar to the composition-spread film at the same composition region.

Figure 5. (a) Schematic of the uniform Sm₂₀Co₈₀ film structure, where the Sm/Co layers were alternatively deposited on a MgO substrate. The thickness of each layer was optimized from the composition-spread film to get the desired compositions. The composition of the deposited uniform films was verified by EPMA measurements. (b) H dependence of the magnetization M for the film at room temperature. (c) H dependence of the transverse voltage V normalized by the width of the Hall bar w for various values of the temperature gradient $\mathrm{\nabla }\mathit{T}$. (d) $\mathrm{\nabla T}$ dependence of the ANE-induced electric field E_ANE for the uniform Sm₂₀Co₈₀ film, extracted by the field-odd component of the voltage at μ₀H = 5.0 T.

To determine S_ANE, the uniform Sm₂₀Co₈₀ film was patterned into a Hall-bar structure (see the inset to Figure 5 (c) and experimental section). ANE was measured by applying a magnetic field along the film thickness direction because the estimation of S_ANE requires the accurate determination of the applied temperature gradient $\mathrm{\nabla }$T and thus $\mathrm{\nabla }$T must be applied along the in-plane direction [12]. Figure 5 (c) shows the out-of-plane H dependence of the transverse voltage V normalized by the Hall bar width w for various values of $\mathrm{\nabla }$T. The electric field generated by ANE E_ANE (=V_ANE/w) was extracted from the field-odd-dependent component of V at the field magnitude of μ₀H = 5.0 T. The S_ANE value was evaluated by linear fitting to the $\mathrm{\nabla }$T dependence of E_ANE, as shown in Figure 5 (d). The S_ANE value for the uniform Sm₂₀Co₈₀ film was estimated to be 1.07 ± 0.08 × 10⁻⁶ VK⁻¹. Although this S_ANE value is three times smaller than S_ANE for SmCo₅-type bulk permanent magnets [8,11], it is much larger than that for pure Co (S_ANE = 0.32 × 10⁻⁶ VK⁻¹) [12,38] and comparable to that for Sm₁₂Co₁₇-type and Nd₂Fe₁₄B-type bulk magnets [8]. Despite the moderate S_ANE, our demonstration shown in the next section reveals the usefulness of our amorphous films for ANE-based applications.

3.4. Demonstration of heat flux sensor using Sm₂₀Co₈₀ film

Here, we demonstrate the performance of the SmCo-based amorphous films as a flexible heat flux sensor based on ANE. The heat flux sensor is a device enabling quick and simultaneous detection of the magnitude and direction of a heat flow, which can be an essential component for smart thermal management systems. However, till now, the commercial applications of heat flux sensors are confined due to several limitations. The commercially available sensors are based on the Seebeck effect and constructed from a serially connected three-dimensional matrix of two different thermoelectric materials. Therefore, the Seebeck-effect-based heat flux sensors require a durable substrate or thick plate to provide mechanical stability. Hence, the conventional sensors are mainly applicable to flat surfaces and the flexibility is limited. Due to the presence of thick substrates, these sensors have large thermal resistance that disturbs the heat flow. Although the sensibility of the Seebeck-effect-based heat flux sensors is proportional to the number of the thermoelectric material junctions and to the sensor size, the complex structure and low mechanical durability make it difficult to enlarge the sensor size. As an alternative to the Seebeck-effect-based heat flux sensors having these limitations, researchers proposed thin-film-based heat flux sensors driven by ANE [24,39,40]. In the ANE-based sensor, a lateral thermopile structure consisting of alternately arranged and serially connected two different conductor wires with different ANE coefficients is used. Owing to this simple thermopile structure and the symmetry of ANE, the device can be thin, making it easy to reduce the thermal resistance. If magnetic materials showing large ANE can be formed on thin flexible sheets, flexible heat flux sensors can be constructed. These features of the ANE-based heat flux sensors are advantageous over the Seebeck-effect-based heat flux sensors.

Figure 6 (a) represents a schematic view of the prototypical ANE-based heat flux sensor having a thermopile structure where the one end of a magnetic wire is electrically connected to the opposite end of an adjacent magnetic wire. In this thermopile structure, when the magnetization (heat flux) is along the width (thickness) direction of the wires, the ANE voltage is generated along the length of the wires and the total output voltage gets multiplied by the number of magnetic wires. However, when we pattern the magnetic film into a wire structure, the strong in-plane demagnetization field reduces the remanent magnetization which causes the reduction of the sensitivity of the device at zero field [24]. For wide applications of heat-flux sensors, the zero-field operation is necessary, and the present SmCo-based amorphous films with strong out-of-plane anisotropy (see Figure 5 (c)) are promising candidates.

Figure 6. (a) Schematic of the ANE-based heat flux sensor. The sensor consists of the Sm₂₀Co₈₀ and Au wires arranged alternately and connected in series on a flexible polyethylene naphthalate substrate. (b) Schematic of the experimental setup to evaluate the sensitivity of the ANE-based heat flux sensor. (c) H dependence of V from the Sm₂₀Co₈₀/Au-based sensor for various values of the heat flow j_q. (d) j_q dependence of V_ANE at |μ₀H| = 0.2 and 0.0 T. V_ANE is extracted by the field-odd component of V at μ₀H = 0.2 T. V_ANE at zero field was extracted from the zero field V values for the positive-to-negative and negative-to-positive sweep of H. The solid lines show the results of the linear fitting.

For the demonstration, we deposited the 100-nm-thick Sm₂₀Co₈₀ amorphous film on a 50-μm-thick flexible polyethylene naphthalate (PEN) sheet. We formed 50 Sm₂₀Co₈₀ wires with a width of 50 μm and a length of 10 mm arranged in a parallel configuration at an interval of 150 μm over a region of 10 mm. The wires are then connected in series using 50-μm-thick gold wires to make the total device area of 10 $\times$ 10 mm². The total length of the Sm₂₀Co₈₀ wires for this configuration reaches 500 mm. To evaluate the performance of the heat flux sensor, we made an experimental configuration shown in Figure 6 (b). Here, the ANE-based heat flux sensor and a commercially available Seebeck-effect-based heat flux sensor (Energy Eye, model D0001, Denso corporation) were sandwiched by two Cu blocks. To apply an out-of-plane heat current, the bottom Cu block was heated using a ceramic heater, while the top Cu block acts as a heat bath. After the setup reached thermal equilibrium, the voltage (V) between the ends of the thermopile structure was measured by applying an in-plane external magnetic field along the width direction of the wires.

As shown in Figure 6 (c), clear ANE signals with a hysteresis behavior were observed in the magnetic field dependence of V and their magnitude increases with increasing the heater power. Figure 6 (d) represents V_ANE as a function of the heat flux (j_q) across the device, where V_ANE was obtained by extracting the field-odd component of V at |μ₀H| = 0.2 T and 0.0 T and j_q was obtained from the output of the commercial heat flux sensor (Figure 6 (b)). Using the data, the sensitivity of the ANE-based heat flux sensor, V_ANE/j_q, was estimated to be 1.12 ± 0.02 × 10⁻⁷ VW⁻¹m² and 0.89 ± 0.02 × 10⁻⁷ VW⁻¹m² in the saturation magnetization (|μ₀H| = 0.2 T) and remanent magnetization (0.0 T) states, respectively. The experimentally obtained sensitivity is consistent with the V_ANE/j_q value of 0.94 ± 0.16 × 10⁻⁷ VW⁻¹m², determined considering the measured S_ANE value for the uniform Sm₂₀Co₈₀ film based on the relation [24]:

(3) $\frac{{\mathit{V}}_{\mathrm{ANE}}}{j_{\mathrm{q}}}=\frac{{\mathit{S}}_{\mathrm{ANE}}{L}_1{L}_2}{\mathit{\kappa }(l_1+l_2)},$(3)

where L₁L₂ is the area of the zigzag pattern (Figure 6 (a)), l₁ is the width of each magnetic wire, l₂ is the interval between the adjacent wires, and κ is the thermal conductivity of the magnetic material in the out-of-plane direction for the in-plane magnetization configuration. The obtained sensitivity of the present heat flux sensor at the saturation magnetization state is much larger than that in the prototypical PEN//Fe₈₁Al₁₉-Au [24] thermopile and comparable to the current best results for the MgO//Co₂MnGa-Au [12] and Si/SiO₂//Mn₃Sn-Au [41] thermopiles. Importantly, the present amorphous-Sm₂₀Co₈₀-based heat flux sensor has 5.6 times higher sensitivity at zero field as compared to the Co₂MnGa-based sensor [12]. The comparable V_ANE/j_q values for the devices on the MgO and PEN substrates suggest that the AEE/ANE performance of the present SmCo-based amorphous films is preserved even on flexible substrates.

Here, we have demonstrated heat flux sensing using a prototypical ANE-based heat flux sensor comprising the amorphous Sm₂₀Co₈₀ thin film on a flexible substrate. Although till now the sensitivity of this sensor is lower than that of Seebeck-effect-based sensors, ANE has strong advantages in flexibility and low thermal resistance, extending applications of heat flux sensors. In the ANE-based sensors, there is a plenty of room to improve the sensitivity with proper optimization of materials and device structures. As can be seen from Equation 3(3) $\frac{{\mathit{V}}_{\mathrm{ANE}}}{j_{\mathrm{q}}}=\frac{{\mathit{S}}_{\mathrm{ANE}}{L}_1{L}_2}{\mathit{\kappa }(l_1+l_2)},$(3) , the higher sensitivity can be achieved by using materials with larger S_ANE, reducing $\mathit{\kappa }$ of ANE materials, increasing the density of the wires (by reducing l₁ and l₂), replacing Au with a different magnetic material having S_ANE with opposite sign, and increasing the area of the sensor. As shown later, amorphous materials are also beneficial for reducing $\mathit{\kappa }$. Since amorphous materials can be fabricated on any surfaces, they enable large-scale manufacturing and reduce the device cost. Therefore, the investigation of amorphous materials with large ANE is one of the most promising approaches towards the development of ANE-based heat flux sensors and our demonstration showcases a guideline for that.

3.5. Effect of Fe substitution for Co in Sm₂₀Co₈₀ film

To explore the possibility of further enhancement of ANE/AEE in the Sm_pCo_100-p amorphous films, we systematically replaced Co with Fe by fabricating Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film with the Fe concentration (q) varying from 0 at.% (Sm₂₀Co₈₀) to 100 at.% (Sm₂₀Fe₈₀) (see Figure 7 (a)). Here, Sm₂₀Co₈₀ was chosen as the base alloy composition to tune Co concentration due to the presence of the maximum AEE signal and large coercivity. In a similar manner to Sm₂₀Co₈₀, the Sm₂₀(Co_100-qFe_q)₈₀ alloys are amorphous in nature for the whole composition range, as confirmed by the position-dependent XRD measurement (see Figure 7 (b)). The XRD data suggest that the introduction of Fe in Sm₂₀(Co_100-qFe_q)₈₀ alloys does not affect their structural configuration. To investigate the microstructures, we performed the cross-sectional STEM analysis. Figure 7 (c-d) respectively show the cross-sectional BF-STEM image with the microbeam electron diffraction pattern and STEM-EDS maps of Sm, Co, and Fe obtained from the Sm₂₀(Co₇₇Fe₂₃)₈₀ composition in the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film. The microbeam electron diffraction pattern clearly confirms the amorphous nature of the film, as determined by XRD. The composition line profiles obtained from a dotted rectangle in STEM-EDS map (Figure 7 (d)) are shown in Figure 7 (e). Figure 8 (a) represents the q dependence of in-plane ${\mu }_0{H}_{\mathrm{C}}^{\mathrm{Kerr}}$ values for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film, estimated from the MOKE measurements. The Sm₂₀(Co_100-qFe_q)₈₀ alloys show typical ferromagnetic nature with finite coercivity, although the ${\mu }_0{H}_{\mathrm{C}}^{\mathrm{Kerr}}$value was observed to decrease monotonically with increasing the Fe concentration. The origin of such magnetization behavior is yet to be understood and future investigations on microstructural and magnetic evaluations of these films are required.

Figure 7. (a) Schematic of the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film structure, where the uniform Sm layer and wedge-shaped Co and Fe layers were alternatively deposited using the linear moving shutter on a MgO substrate. (b) XRD profiles for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film measured at the 1-mm interval along the x direction. The inset shows 2D XRD profile at x = 3.5 mm. Here x = 0 corresponds to the substrate edge at pure Sm₂₀Co₈₀ side. (c) Cross-sectional BF-STEM image and microbeam electron diffraction pattern for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film measured near the Sm₂₀(Co₇₇Fe₂₃)₈₀ composition. (d) High magnification STEM-EDS maps for the Sm₂₀(Co₇₇Fe₂₃)₈₀ composition. (e) The composition line profiles of the constituent elements along the horizontal direction obtained from the dotted rectangle region shown in (d).

Figure 8. (a) Fe concentration q dependence of ${\mu }_0{H}_{\mathrm{C}}^{\mathrm{Kerr}}$ estimated from the MOKE loops for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film, measured with applying an in-plane magnetic field. (b) A_AEE and ϕ_AEE images showing the pure AEE-induced temperature modulation for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film at J_c = 15 mA, f = 25 Hz, and |μ₀H| = 0.8 T and 0.0 T. (c) Line profile of A_AEE/j_c at $\left|{\mu }_0\mathit{H}\right|=0.8\mathrm{T}$ and 0.0 T as a function of q. (d) q dependence of the electrical resistivity (ρ_xx) measured the using Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film. (e) Out-of-plane thermal conductivity κ measured by the time-domain thermoreflectance method using the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film. (f) ANE coefficient S_ANE and AEE coefficient Π_AEE for the Sm₂₀(Co_100-qFe_q)₈₀ alloys at different values of q, estimated from the AEE data using Equations (4)(4) ${\mathrm{\Pi }}_{\mathrm{AEE}}=S_{\mathrm{ANE}}\mathit{T}$(4) and (5(5) ${\mathrm{\Pi }}_{\mathrm{AEE}}=\frac{\mathit{\pi \kappa }\mathrm{\Delta }\mathit{T}}{4j_c\mathit{L}},$(5) ).

Figure 9. (a) Schematics of the uniform Sm₂₀(Co₇₇Fe₂₃)₈₀ film structure, where the Sm,Co, and Fe layers were alternatively deposited on a MgO substrate. The composition of the deposited uniform films was verified by EPMA measurements. (b) H dependence of M for the film at room temperature. (c) $\mathrm{\nabla }\mathit{T}$ dependence of E_ANE for the uniform Sm₂₀(Co₇₇Fe₂₃)₈₀ film, extracted by the field-odd component of the voltage at $\left|{\mu }_0\mathit{H}\right|=5.0\mathrm{T}$.

To investigate the effect of the Fe substitution in the transverse thermoelectric conversion property, we measured the AEE signals for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film using the LIT technique under the same experimental configuration as described in Section 3.2. Figure 8 (b) shows the A_AEE and ϕ_AEE images for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film in the saturation magnetization (|μ₀H| = 0.8 T) and remanent magnetization (|μ₀H| = 0.0 T) states. Figure 8 (c) shows the extracted line profile of A_AEE/j_c as a function of q. These results indicate that the AEE-induced temperature modulation in Sm₂₀(Co_100-qFe_q)₈₀ can be enhanced by 20% compared to Sm₂₀Co₈₀. The maximum A_AEE/j_c value was observed for the 23 ≤ q ≤ 38 at.% region. It was found that A_AEE/j_c gradually decreases for q > 38 at.% and the finite AEE-induced temperature modulation appears for q > 90 at.%. The ϕ_AEE image in Figure 8 (b) shows the sign reversal of the AEE signals, i.e. the ⁓180° change in ϕ_AEE, around q = 90 at.%. We also checked that the AEE signals in Sm-Fe alloys are opposite in sign to those in the Sm-Co alloys (see supplementary material Figure S2). Figure 8 (d) shows that the electrical resistivity for the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film is almost independent of q. From these results, we determined that the Sm₂₀(Co_100-qFe_q)₈₀ alloys with 23 ≤ q ≤ 38 at.% show enhanced ANE/AEE. We then quantitatively determine S_ANE and Π_AEE based on the LIT results via the following relations:

(4) ${\mathrm{\Pi }}_{\mathrm{AEE}}=S_{\mathrm{ANE}}\mathit{T}$(4)

(5) ${\mathrm{\Pi }}_{\mathrm{AEE}}=\frac{\mathit{\pi \kappa }\mathrm{\Delta }\mathit{T}}{4j_c\mathit{L}},$(5)

where ∆T=A_AEEcosϕ_AEE is the AEE-induced temperature change, and (4/π)j_c is the sinusoidal amplitude of the charge current density applied to the magnetic material during the AEE measurement. The out-of-plane κ for the Sm₂₀(Co_100-qFe_q)₈₀ alloys with different compositions were measured using the TDTR method (see experimental section). As shown in Figure 8 (e), the κ value for Sm₂₀(Co_100-qFe_q)₈₀ is ~ 6 Wm⁻¹K⁻¹ and nearly independent of the Fe concentration, where $\mathit{\kappa }$ of the amorphous alloys is more than 60% smaller than that of the bulk counterpart [8,11]. Therefore, the enhancement in A_AEE/j_c directly leads to the increase in Π_AEE. In Figure 8 (f), we plot the Π_AEE and S_ANE values for various Sm₂₀(Co_100-qFe_q)₈₀ alloys with different Fe concentrations. The highest S_ANE of 1.26 ± 0.20 × 10⁻⁶ (0.86 ± 0.16 × 10⁻⁶) VK⁻¹ was obtained for Sm₂₀(Co₇₇Fe₂₃)₈₀ at |μ₀H| = 0.8 T (|μ₀H| = 0.0 T).

To confirm the consistency of the result, we fabricated a uniform Sm₂₀(Co₇₇Fe₂₃)₈₀ film with the optimized composition by alternately depositing Sm, Co, and Fe thin layers (see Figure 9 (a)). The structural and magnetic behaviors of the Sm₂₀(Co₇₇Fe₂₃)₈₀ film were characterized by microbeam electron diffraction patterns (see supplementary material Figure S1) and in-plane magnetization measurement (see Figure 9 (b)). The results confirm that the film has similar structural and magnetic behavior as the composition-spread film at the same composition region. S_ANE for the uniform Sm₂₀(Co₇₇Fe₂₃)₈₀ film was directly measured and estimated to be 1.55 ± 0.20 × 10⁻⁶ VK⁻¹ as shown in Figure 9 (c). The directly measured S_ANE value for the film is consistent with the value estimated from the AEE measurements using the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film. The maximum S_ANE value for the present alloys is still lower than that for the SmCo₅-type bulk permanent magnets [8,11], magnetic Heusler alloys (e.g. Co₂MnGa and Co₂MnSi_1-xAl_x) [15–17,25], and iron-based binary ferromagnets (e.g. Fe₃Al and Fe₃Ga) [24,42]. However, as shown before, the unique physical properties of present amorphous alloys, e.g. large in-plane coercivity and remanent magnetization, make them advantageous over the conventional alloys, especially, for zero-field operation of thermoelectric generation and application to heat flux sensors on flexible substrates [24].

3.6. Detailed characterization of Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films

Finally, let us discuss the factors determining ANE in our amorphous alloys. S_ANE can be expressed as [23,25],

(6) $S_{\mathrm{ANE}}={\rho }_{\mathit{xx}}{\alpha }_{\mathit{xy}}+{\rho }_{\mathit{xy}}{\alpha }_{\mathit{xx}}\equiv S_{\mathrm{I}}+S_{\mathrm{II}},$(6)

where ${\rho }_{\mathit{xx}}$ (${\rho }_{\mathit{xy}}$) are the diagonal (off-diagonal) component of the electrical resistivity tensor and ${\alpha }_{\mathit{xx}}$ (${\alpha }_{\mathit{xy}}$) are the diagonal (off-diagonal) component of the thermoelectric conductivity tensor. Equation (6)(6) $S_{\mathrm{ANE}}={\rho }_{\mathit{xx}}{\alpha }_{\mathit{xy}}+{\rho }_{\mathit{xy}}{\alpha }_{\mathit{xx}}\equiv S_{\mathrm{I}}+S_{\mathrm{II}},$(6) shows that there are two different phenomenological sources in S_ANE, and we denote them as $S_{\mathrm{I}}={\rho }_{\mathit{xx}}{\alpha }_{\mathit{xy}}$ and $S_{\mathrm{II}}={\rho }_{\mathit{xy}}{\alpha }_{\mathit{xx}}$ for simplicity. The contribution of S_I is often regarded as an intrinsic part of ANE. The origin of S_I is the direct generation of the transverse electric field originating from the transverse thermoelectric conductivity ${\alpha }_{\mathit{xy}}$ [43]. The second term, S_II, is the contribution of the anomalous Hall effect (AHE) to ANE induced by a longitudinal current due to the Seebeck effect [23,25]. The term can be also expressed as $S_{\mathrm{II}}={\rho }_{\mathit{xy}}{\alpha }_{\mathit{xx}}=S_{\mathrm{SE}}{\rho }_{\mathit{xy}}/{\rho }_{\mathit{xx}}$, where S_SE = ${\rho }_{\mathit{xx}}{\alpha }_{\mathit{xx}}$. Therefore, by measuring $S_{\mathrm{ANE}}$, ${\rho }_{\mathit{xx}},{\rho }_{\mathit{xy}}$, and S_SE, the ${\alpha }_{\mathit{xy}}$ value can be estimated experimentally using Equation (6).(6) $S_{\mathrm{ANE}}={\rho }_{\mathit{xx}}{\alpha }_{\mathit{xy}}+{\rho }_{\mathit{xy}}{\alpha }_{\mathit{xx}}\equiv S_{\mathrm{I}}+S_{\mathrm{II}},$(6) Figure 10 (a) shows the out-of-plane magnetic field dependence of the Hall resistivity ${\rho }_{\mathrm{Hall}}$ for the Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films. The Hall resistivity was observed to increase with the field and saturate when the magnetization saturates, indicating the dominant contribution from AHE. The ${\rho }_{\mathit{xy}}$ values were estimated from the ${\rho }_{\mathrm{Hall}}$ data by finding the zero-field intercept of the linear-fitted line for the saturation region. We observed that the ${\rho }_{\mathit{xy}}$ value is enhanced by 114% for the Fe-substituted alloy (see the inset to Figure 10 (a)). Figure 10 (b) shows the ${\rho }_{\mathit{xx}}$ and S_SE values for the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films. The anomalous Hall angle (${\theta }_{\mathrm{AHE}}=-{\rho }_{\mathit{xy}}/{\rho }_{\mathit{xx}}$) and ${\sigma }_{\mathit{xy}}$ $\left(=-\frac{{\mathit{\rho }}_{\mathit{xy}}}{{\rho }_{xx}^2+{\rho }_{xy}^2}\right)$ were estimated from the ${\rho }_{\mathit{xx}}$ and ${\rho }_{\mathit{xy}}$ data. Figure 10 (c) shows a huge enhancement in the ${\theta }_{\mathrm{AHE}}$ and ${\sigma }_{\mathit{xy}}$ values for Sm₂₀(Co₇₇Fe₂₃)₈₀ as compared to Sm₂₀Co₈₀. Using the experimentally observed values, we estimated the $S_{\mathrm{I}}$, $S_{\mathrm{II}}$, and ${\alpha }_{\mathit{xy}}$ values using Equation (6).(6) $S_{\mathrm{ANE}}={\rho }_{\mathit{xx}}{\alpha }_{\mathit{xy}}+{\rho }_{\mathit{xy}}{\alpha }_{\mathit{xx}}\equiv S_{\mathrm{I}}+S_{\mathrm{II}},$(6) Figure 10 (d) shows that, for both the Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ alloys, the major contribution to ANE comes from the $S_{\mathrm{I}}$ term and the $S_{\mathrm{II}}$ term is very small due to small S_SE. We found that the enhancement in $S_{\mathrm{ANE}}$ for the Sm₂₀(Co₇₇Fe₂₃)₈₀ alloy is attributed to the $S_{\mathrm{I}}$ enhancement. Although ${\alpha }_{\mathit{xy}}$ for Sm₂₀(Co₇₇Fe₂₃)₈₀ is 73% larger than that for Sm₂₀Co₈₀, the value is an order of magnitude smaller than that for the SmCo₅-type bulk permanent magnets [8,11], resulting in smaller S_ANE in our amorphous films. Further improvement of S_ANE and ${\alpha }_{\mathit{xy}}$ in magnetic amorphous films is one of the future tasks.

Figure 10. (a) H dependence of the Hall resistivity ρ_Hall for the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films. The inset shows the anomalous Hall resistivity ρ_xy estimated from the ${\rho }_{\mathrm{Hall}}$ data by extracting the zero-field intercept of the linear-fitted line for the saturation region. (b) Electrical resistivity ρ_xx and Seebeck coefficient S_SE for the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films. (c) The anomalous Hall angle θ_AHE and anomalous Hall conductivity σ_xy. (d) Extracted S_ANE, S_I, S_II, and transverse thermoelectric conductivity α_xy for the uniform Sm₂₀Co₈₀ and Sm₂₀(Co₇₇Fe₂₃)₈₀ films.

4. Conclusions

In this study, we have demonstrated that Sm-Co-based amorphous alloy films exhibit large in-plane remanent magnetization and coercive force and enable zero-field operation of transverse thermoelectric generation, i.e. ANE and AEE. First, we systematically investigated the composition dependence of AEE for the Sm_pCo_100-p composition-spread film with p varying from 0 to 100 at.% by the combinatorial sputtering technique. The experiments revealed that Sm₂₀Co₈₀ exhibits the largest AEE-induced temperature modulation among the Sm_pCo_100-p amorphous alloys. By directly measuring ANE, the ANE coefficient of the Sm₂₀Co₈₀ amorphous alloy was estimated to be 1.07 ± 0.08 × 10⁻⁶ VK⁻¹. To explore the usability of our films, we constructed a prototypical ANE-based heat flux sensing device using the Sm₂₀Co₈₀ amorphous film fabricated on a flexible PEN substrate. The obtained sensitivity for this prototypical ANE-based thermopile at zero field is comparable to the previously reported best results on ANE-based thermopiles. The demonstration opens the door to exploring amorphous ANE/AEE materials for flexible thermoelectric applications.

To explore the possibility of further enhancement of ANE/AEE for the Sm-Co-based amorphous films, we systematically replaced Co with Fe by fabricating the Sm₂₀(Co_100-qFe_q)₈₀ composition-spread film with q varying from 0 to 100 at.%. Significant enhancement in the AEE-induced temperature modulation was observed in the alloy with 23 at.% Fe substitution. The ANE coefficient of the Sm₂₀(Co₇₇Fe₂₃)₈₀ amorphous film was estimated to be 1.55 ± 0.20 × 10⁻⁶ VK⁻¹. Despite of the smaller S_ANE values, the presence of large in-plane remanent magnetization and coercive force in our films makes it advantageous over conventional materials for applications including ANE-based heat flux sensors, as these materials can generate thermoelectric output without an external magnetic field. Importantly, owing to the amorphous nature, the films can be fabricated on any surfaces, increasing the versatility of ANE/AEE devices. Exploring the possibility of hybrid films consisting of the present films and other magnetic materials will be important to realize the zero-field operation of large ANE/AEE.

Acknowledgements

The authors thank R. Iguchi for valuable discussions and I. Narita for technical support to do the composition analysis.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability statement

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/14686996.2022.2138538

Additional information

Funding

This work was supported by CREST “Creation of Innovative Core Technologies for Nano-enabled Thermal Management” [JPMJCR17I1 and JPMJCR17I2] and PRESTO “Scientific Innovation for Energy Harvesting Technology” [JPMJPR17R5] from Japan Science and Technology Agency, Japan; Grant-in-Aid for Scientific Research (S) [18H05246] from Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; “Mitou challenge 2050” [P14004] from NEDO, Japan; and the NEC Corporation. R.M. is supported by JSPS through the “JSPS Postdoctoral Fellowship for Research in Japan (Standard)” [P21064].