Combinatorial tuning of electronic structure and thermoelectric properties in Co₂MnAl_1−xSi_x Weyl semimetals

A thermoelectric generator (TEG) using the Seebeck effect (SE) is one of the promising energy harvesting technologies that can generate electricity from everyday waste heat. In the past few decades, research on developing TEGs using the SE has been extensively conducted, but until now, various problems have arisen, which need to be solved.^1,2 One of the major drawbacks in the SE is the direction of thermoelectric voltage, which appears in parallel to the temperature gradient. Thus, the SE-based module usually has a complicated structure in which multiple thermopiles must be placed and connected at the bottom and top alternatively in series, resulting in high cost, low flexibility, and poor mechanical endurance. One possible solution to overcome these issues is developing a TEG based on the anomalous Nernst effect (ANE), which generates thermoelectric voltage in the direction perpendicular to the temperature gradient and magnetization.³ This transverse thermoelectric generation enables us to realize a much simpler laterally connected thermopile structure to increase the output thermoelectric voltage in a TEG.^4,5 These unique advantages have stimulated studies on the ANE not only for gaining a fundamental understanding of the phenomenon but also for practical thermoelectric applications.^6–19 

At present, studies on the ANE are still very few compared to those on the SE, and the reported thermopowers of the ANE at around room temperature are usually very small to be implemented for practical device applications. Thus, exploration of materials showing high thermopower of the ANE is clearly needed. Recent theoretical and experimental investigations have suggested that the presence of an intense Berry curvature (BC) in the vicinity of the Fermi energy (E_F) can potentially enhance the intrinsic anomalous Hall effect (AHE) and ANE.^20–25 Very recently, a large anomalous Nernst coefficient (S_ANE) of ∼6 µV/K was reported in Co₂MnGa at room temperature,^26,27 which is a member of the Co₂YZ-based full Heusler family having a strong BC near E_F originating from the Weyl points.^28,29 This S_ANE value is almost one order of magnitude larger than that for conventional ferromagnetic materials, which opens a new possibility of enhancing the ANE in these alloys. Sumida et al. recently observed spin-polarized Weyl cones near E_F in Co₂MnGa epitaxial films having different composition ratios and found that the magnitude of S_ANE strongly depends on the position of the BC with respect to E_F.³⁰ As evidence of the importance of E_F tuning, the magnitude of S_ANE of 6.2 µV/K observed for the E_F tuned Co₂MnGa film by Sumida et al. is nearly three times larger than that for the similar Co₂MnGa epitaxial film reported earlier.³¹ Therefore, to investigate the effect of the theoretically predicted intrinsic BC and realize large S_ANE, tuning the position of E_F is essential. Recently, tuning of E_F with atomic substitution has been performed in Co₂MnAl_1−xSi_x (CMAS) alloys.^32–34 The replacement of Al by Si shifts E_F to higher energy and enhances the spin-polarization, AHE, and ANE for optimal CMAS composition. However, tuning of E_F by making individual specimens and performing systematic measurements for each specimen are time-consuming and also cause a risk, missing the best property of the material because of the unavoidable discontinuous change in E_F. Therefore, a more facile approach to achieve continuous E_F tuning is strongly desired. Combinatorial deposition is one of the most effective tools that allows us to fabricate composition-spread films with single atom substitution from 0% to 100% on a single film. In this study, we fabricated a CMAS composition-spread thin film using the combinatorial deposition technique and experimentally demonstrated the systematic tuning of E_F and other transport and thermoelectric properties with composition. Through the measurement of the anomalous Ettingshausen effect (AEE), which is the reciprocal effect of the ANE, we employed a much faster and easier technique to effectively optimize the composition suitable for transverse thermoelectric conversion.

A 001-oriented epitaxial CMAS composition-spread film with a thickness of 50.4 nm and a composition of 0 ≤ x ≤ 1 was fabricated on a single-crystalline MgO (001) substrate using DC/RF magnetron sputtering with a base pressure of <6.0 × 10⁻⁶ Pa and a process Ar gas pressure of 0.4 Pa. Before deposition, the MgO substrate was flashed at 790 °C, and then the film was deposited at 600 °C substrate temperature. The CMAS composition-spread film with composition variation over a length of 7.0 mm was prepared from Co₂MnAl (CMA) and Co₂MnSi (CMS) alloy targets using the following deposition sequence: (1) deposition of a wedge-shaped CMA layer using a linear moving shutter with a deposition rate of 0.042 nm/s and a shutter speed of 0.53 mm/s, (2) rotation of the substrate by 180°, and (3) deposition of a wedge-shaped CMS layer using the linear moving shutter with a deposition rate of 0.026 nm/s and a shutter speed of 0.33 mm/s, where the total thickness of the CMAS film after completing (1) to (3) was 0.56 nm, which is close to the lattice constant of L2₁- Co₂MnSi and Co₂MnAl. The sequence was repeated 90 times to get a film of around 50.4-nm thickness [see Fig. 1(a)]. The film was capped with a 2-nm-thick Al film to prevent oxidation. The compositions in x = 0 and 1 regions in the CMAS composition-spread film were measured by x-ray fluorescence spectroscopy using standard Co₂MnAl and Co₂MnSi films whose compositions were strictly premeasured by inductively coupled plasma mass spectrometry. The crystal structure and atomic ordering were investigated by x-ray diffraction with a Cu K_α x-ray source. The measurement was performed at different positions on the CMAS film along the composition gradient at an interval of 1.0 mm using a 0.5 mm incident slit. To investigate the variation in electronic structures with composition, hard x-ray photoemission spectroscopy (HAXPES) measurements were performed at BL15XU of SPring-8.³⁵ An excitation x ray of 6 keV with a focal size of 25 µm (vertical) × 35 µm (horizontal) in the FWHM at the sample position was irradiated at different places on the CMAS film to probe the different compositions. The composition gradient of the film was along the vertical direction. Thus, the vertical x-ray size is sufficiently small for composition dependent measurements. The incidence angle of the x ray was set to 88°, which expands the footprint of the x ray on the film in the horizontal direction. An additional film with 10.0 mm composition variation length was fabricated under identical conditions for HAXPES measurements. A horizontal linearly polarized x ray was used to excite photoelectrons, and excited photoelectrons were detected by using a hemispherical analyzer (VG Scienta R4000). The pass energy of the analyzer was set to 100 eV, and the total energy resolution was ∼150 meV. All measurements were performed at room temperature in nearly normal emission geometry.³⁶ 

We performed the first-principles calculation to analyze the observed valence band spectra by HAXPES. The first-principles electronic structure calculations were performed with the Vienna ab initio simulation package.^37,38 The spin-polarized generalized gradient approximation is adopted for the exchange and correlation terms.³⁹ The atomic core potential is described by the pseudopotential with the projector augmented wave method.^40,41 In the calculation of photoemission spectra for CMS and CMA, we take into account the effects of the photoionization cross sections for constituent elements and the electron life time by Lorentzian smearing.

To investigate the dependence of AHE and ANE on the composition ratio of Al to Si efficiently, the composition-spread CMAS film was patterned into parallel aligned Hall bars, as shown in Fig. 1(b), by photolithography and Ar ion etching processes. The width of each bars is designed to be 200 µm; thus, the composition variation of Al:Si in one Hall bar is estimated to be about 2.8%. The AHE was measured by applying a charge current of 1 mA in the y direction, the external magnetic field in the z direction, and the measured anomalous Hall voltage along the x direction [see Fig. 1(b)]. The ANE was measured by applying a temperature gradient ∇T of 0.3 K/mm in the x direction, the external field in the z direction, and the measured anomalous Nernst voltage in the y direction [see Fig. 1(c)]. It should be mentioned that ∇T must be equal in all Hall bars with different CMAS compositions because ∇T in the CMAS film is determined by the thermal conductance of the thick (0.5 mm) MgO substrate. The ∇T distribution was precisely evaluated using an infrared camera with a blackbody coating on the sample to correct emissivity, which is a technique established in earlier studies.^18,19,30,34 The SE was measured by applying ∇T in the y direction and measured voltage in the same direction [see Fig. 1(d)]. AEE measurement was performed for the CMAS film using the lock-in thermography (LIT) technique.^42–46 To measure the AEE, the film was patterned in a strip shape of 8.0 mm length and 0.4 mm width, where the length direction is along the composition gradient [see Fig. 1(e)]. During the AEE measurement, a square-wave-modulated AC charge current with a square-wave amplitude of 10 mA, frequency f = 25 Hz, and zero DC offset was applied along the strip, and an external magnetic field with a magnitude μ₀H = ±0.1 T was applied along the y direction (see Sec. I in the supplementary material). Pure AEE contribution was extracted using the previously established procedures from the raw LIT images.^47–53 Note that all patterns shown in Fig. 1 were made from the identical CMAS composition-spread film.

Figure 2(a) shows the out-of-plane X-ray diffraction (XRD) pattern for the CMAS epitaxial film grown on the MgO (001) substrate at 600 °C. The only presence of 002 and 004 peaks for θ–2θ scan confirms the 001-oriented growth of the CMAS alloy on MgO (001) for all the composition range. In order to measure the 111 superlattice peak, the sample stage was tilted to 54.7° from the normal direction. As shown in the inset of Fig. 2(a), the 111 peak is absent in the CMA side and gradually appears with increasing intensity while moving to the CMS side. The 002 and 111 superlattice peaks give information about the B2 and L2₁ atomic ordering in these alloys, respectively. B2 is the ordering between Co and the (Mn, Al/Si) site [see Fig. 2(b)], and L2₁ is the structure having the ordering between Mn and the Al/Si site [see Fig. 2(c)]. The presence of the 002 peak in the XRD patterns indicates B2 ordering structure for all the composition range. Similarly, the absence of the 111 peak at the CMA side signifies the absence of L2₁ ordering, which is in accordance with previous results for CMA.³⁴ With the introduction of Si at the Al site, the 111 peak appears and gradually increases when moved toward the CMS side, which signifies the formation of L2₁ ordering. The degree of order for B2 and L2₁ structures, defined as S_B2 and $SL21$⁠, has been evaluated using the following equations:⁵⁴ 

where I₀₀₂, I₀₀₄, and I₁₁₁ represent the integrated intensities of the 002, 004, and 111 peaks, respectively. The subscripts expt. and cal. represent the values obtained from the experimental XRD pattern and simulated XRD pattern for an ideal L2₁ structure, respectively. For the present analysis, we performed XRD pattern simulation for L2₁-ordered CMAS alloys using the visualization for electronic and structural analysis (VESTA) (the parameters of the simulation are given in Sec. II in the supplementary material), where we used the actual compositions measured for pure CMA and CMS regions and estimated a linear variation in composition from the CMA side to the CMS side, as shown in Fig. 2(d). The obtained B2 and L2₁ ordering parameters are summarized in Fig. 2(e). It is observed that the degree of S_B2 is nearly 1 in the whole range of x, indicating that nearly perfect B2 ordering exists throughout the CMAS composition-spread film. In contrast, $SL21$ is zero for CMA and rapidly increases from zero to 0.8 with x when x is changed from 0.1 to 0.4. The alloy with x > 0.4 has strong L2₁, which slowly improves with Si enrichment, and a maximum L2₁ order of 0.9 was observed for CMS. The lattice constant a, as evaluated from the 004 peak position, is plotted as a function of x in Fig. 2(f). The a values for the CMA and CMS ends are found to be 5.726 and 5.646 Å, respectively, which are comparable with the reported values in the literature.^34,54,55 The a almost linearly decreases with increasing Si content following Vegard’s law, indicating that Al atoms were substituted into the Si sites without phase separation and that the single-phase CMAS alloy film was formed in the whole composition range.

Figure 3(a) represents the valence band HAXPES spectra for the CMAS film at different compositional positions defined as P1–P6 [see the inset of Fig. 3(a)]. The observed spectra for the CMS site are in good agreement with the previously reported HAXPES data in bulk and thin films,^56–59 as well as the theoretical prediction based on the density of states (DOS) for the L2₁-ordered CMS alloy [see Figs. 3(c) and 3(d)]. The observed highest intensity at the binding energy (E_B) of ∼1.26 eV just below E_F for CMS is due to flat d bands that belong to minority t_2g states localized in the Co planes as well as localized Mn majority e_g states, as already described in detail for bulk samples.^56–59 The shifting of the peak position toward the higher E_B side signified the shifting of E_F while moving to the CMA side. A total shifting of 0.40 eV was observed from CMA to CMS [see Fig. 3(b)]. This value is consistent with the expectation based on the DOS calculation, as shown in Figs. 3(c) and 3(d), where the Fermi level is predicted to be shifted around 0.45 eV with the composition variation from CMA to CMS. This peak shift can be qualitatively explained by the rigid band picture of Co-based Heusler alloys. The total shifting of 0.45 eV corresponds to the difference in the number of valence electrons between CMA and CMS. The experimental observation clearly demonstrated a systematic shift of E_F with a changing Al/Si ratio for the single CMAS composition-spread film, which clearly established the usefulness of the present combinatorial investigation approach.

The x dependence of the anomalous Hall resistivity (ρ_yx) and the longitudinal resistivity (ρ_xx) has been measured for the CMAS composition-spread film with a 7.0 mm composition variation length by patterning the film into Hall bars, as described in the experimental section. Figure 4(a) shows the out-of-plane magnetic field dependence of ρ_yx for the CMAS film for various values of x. ρ_yx increases with the field and saturates when saturation magnetization is reached, as expected for a ferromagnetic material. Figures 4(b) and 4(c) show the measured ρ_yx and ρ_xx values as a function of x, respectively. ρ_xx has the largest (smallest) value of 480 μΩ cm (40 μΩ cm) for CMA (CMS). Similarly, the CMA film shows the largest ρ_yx value of 22.3 μΩ cm, which monotonically decreases with increasing x and reaches 0.06 μΩ cm for CMS. These tendencies are consistent with the previous report on CMAS films.³⁴ Figure 4(d) presents the estimated anomalous Hall angle (θ_AHE = ρ_yx/ρ_xx) values for the CMAS film as a function of x. The observed θ_AHE gradually decreases with increasing Si percentage; CMA showed the largest magnitude of θ_AHE of 4.8%, while CMS showed nearly zero θ_AHE. The observed difference in the composition dependence of ρ_xx, ρ_yx, and θ_AHE between the present CMAS film and the previous co-sputtered CMAS films in Ref. 34 can be roughly explained by a difference in composition and the total valence electron number N_v of the CMA in these two films. Namely, N_v is 27.9 in the x = 0 region of the present CMAS film and 27.5 in the CMA film in the previous study because the compositions of the former and latter are Co_52.1Mn_21.1Al_26.8 and Co_48.4Mn_24.5Al_27.1, respectively. Recent investigation on Co₂MnGa Weyl semimetal thin films having various off-stoichiometric compositions clearly demonstrates that the transport properties strongly depend on N_v calculated from their compositions.³⁰ A similar effect can also be expected in CMAS films. Since the CMA of the current CMAS film has larger N_V by 0.4 than the previous CMA film, we can see a closer matching between the data in two CMAS films by shifting of ρ_xx, ρ_yx, and θ_AHE vs x for the present film toward the +x direction by ∼0.4 (see Fig. S2 in the supplementary material) although there is still a certain amount of disagreement, which originates from the factors that do not scale with only N_V but each composition ratio of Co, Mn, and Al/Si. For example, the obtainable degree of L2₁ order depends not on N_v but the Al/Si composition ratio, which might be a reason for much larger ρ_xx for the CMA with no L2₁-order in the present CMAS film than Co₂MnAl_0.6Si_0.4 with a partial L2₁-order in the previous study, regardless of the same N_V (∼27.9) in these films.

To investigate the thermoelectric property of the CMAS film, the SE and ANE were measured. The x dependence of the Seebeck coefficient (S_SE) for the film is shown in Fig. 5(b). S_SE is found to be −14 µV/K for CMA and reaches a maximum value of −22 µV/K at around x = 0.3. With a further increase in x, S_SE decreases and remains almost invariant for x > 0.65. Figure 5(a) presents the measured ANE voltage (V_ANE) as a function of the applied magnetic field measured at different positions of the CMAS film. The ANE voltage saturates around 1 T, which signifies that the signal is dominated by the ANE. The anomalous Nernst coefficient (S_ANE) is evaluated using the relation E_ANE = −S_ANEm × ∇T, where m is the normal vector along the magnetization. The x dependence of S_ANE is summarized in Fig. 5(c). The S_ANE value is +1.3 µV/K for CMA and increased to a maximum value of +2.7 µV/K for x ≈ 0.08. S_ANE then gradually decreases with increasing x. Interestingly, the observed trends of S_SE and S_ANE with respect to x are similar to those observed in the previous study based on the individual CMAS films but shifts to the less x (Si-poor) direction.³⁴ This shift can be explained by a difference in N_v, in a similar manner to the above-mentioned ρ_xx, ρ_yx, and θ_AHE. One can see the closer matching of S_SE vs x and S_ANE vs x in the two films by shifting the data for the present film toward the +x direction by ∼0.4 (see Fig. S2 in the supplementary material). However, the maximum S_ANE of +2.7 µV/K is smaller than that in the previous report (+3.9 µV/K).³⁴ Here, we would like to explain a reason for small S_ANE in the present CMAS film. One can see from the band dispersion on the high symmetry line (Fig. S3 of the supplementary material) that the energetical position of the Weyl cones giving a large Berry curvature is very close to E_F in L2₁-Co₂MnAl (0–0.2 eV below E_F) whereas far below E_F (0.5–0.7 eV) in Co₂MnSi. That is the origin of the giant AHE observed in L2₁-ordered single-crystalline Co₂MnAl.⁶⁰ However, it is usually difficult to obtain L2₁-atomic order in Co₂MnAl, especially in a thin film form, because of the much less energetical stability of L2₁-structure than Co₂MnSi, as we found in this study. The previous study reported that B2-disordered structure smears the band dispersion forming Weyl cones and reduces the AHE and ANE.³⁴ Therefore, one promising approach for getting the effect of a large Berry curvature on the AHE and ANE in CMAS is to make a Co₂MnAl having an off-stoichiometric composition that shifts E_F toward a lower energy level by hole doping (N_V < 28.0) and replace Al with Si to not only shift E_F toward a higher level but also improve L2₁-ordering. The CMA in the present CMAS film has a composition ratio that results in less hole doping (N_V = 27.9) than the previous report (N_V = 27.5), which results in small S_ANE, because the optimum Si composition for maximum ANE is close to the CMA side where the degree of L2₁-ordering is small.

We have successfully demonstrated the advantage of preparing a single composition-spread film fabricated using the combinatorial sputtering technique over preparing several uniform films of different compositions to investigate the composition dependence of the ANE. However, the direct measurement of the ANE and other transport properties for such a composition-spread film requires complicated design, which makes high-throughput and systematic investigations difficult. For example, there is a limitation of the number of Hall bars made along the composition gradient, as shown in Figs. 1(c) and 1(d), which limits the minimum composition difference between two successive bars, and measuring thermopower one-by-one takes a long time. This limitation can be overcome by the combination of the combinatorial sputtering method and the LIT technique. The LIT imaging detection enables high-throughput material screening for the ANE through the measurement of its Onsager reciprocal: the AEE. The AEE measurement using LIT requires only a simple strip along the composition gradient, as shown in Fig. 1(e), thus enabling easy and efficient scanning for the best composition region in a composition-spread film. Importantly, the AEE data are continuous along the composition gradient, which gives much accurate composition dependence of the ANE/AEE. To demonstrate this, the AEE for the CMAS composition-spread film was measured along the composition gradient using the LIT technique.^42–46 Figures 6(a) and 6(b) show the lock-in amplitude (A) and phase (ϕ) images of the temperature modulation due to the Joule heating (defined as A_Joule and ϕ_Joule) and AEE (defined as A_AEE and ϕ_AEE), respectively. The A_Joule value is proportional to the local resistivity in our configuration because the charge current density j_c is uniform and the heat loss from the film to the substrate is independent of the position.⁶¹ The A_Joule image clearly demonstrates the higher resistance value at the CMA side, as shown in the x dependence of the A_Joule/j_c² in Fig. 6(c) (note that A_Joule is proportional to j_c²). In fact, the tendency is consistent with the ρ_xx variation, as shown in Fig. 6(c) [the ρ_xx value is taken from Fig. 4(c)]. The A_AEE image, obtained by extracting the H-odd component of the detected LIT images,^47–53 clearly shows that the AEE is intense at the CMA side and nearly vanishes at the CMS side. A_AEE/j_c as a function of x is shown in Fig. 6(d) along with the measured S_ANE value for the current film from Fig. 5(c). The result shows that A_AEE/j_c first increases with x and then gradually decreases in a similar manner to S_ANE. A large AEE was observed between n = 0.06 and 0.12, which is consistent with the ANE result, as can be seen in Fig. 6(d). The above-mentioned result clearly shows that the imaging measurement of the temperature modulation due to the AEE is an effective method to find the best composition for the ANE in a composition-spread film. Here, one should note that it is possible to quantitatively estimate S_ANE from the AEE-induced temperature modulation based on the Onsager reciprocal relation, Π_AEE = S_ANET, where the anomalous Ettingshausen coefficient Π_AEE is proportional to A_AEE · κ/j_c, with κ being the thermal conductivity of the ferromagnetic material. The detailed procedure of extracting Π_AEE from the observed AEE data can be seen in the previous reports.^48,51 The very close overlap between the AEE and ANE results in Fig. 6(d) suggests that the variation in κ with the composition in our CMAS film is very small, although we did not perform direct measurement of κ. This work demonstrates the usefulness of the combination of the combinatorial sputtering method and the LIT technique as high-throughput material screening for finding materials showing a large ANE and AEE. By performing direct measurements of S_ANE as well as κ only for the optimum composition determined by the high-throughput screening, the exploration of materials for the ANE and AEE will be efficient. Importantly, the LIT-based method can be used not only for the ANE but also for other thermoelectric and thermo-spin effects.^61,62

We have successfully fabricated a composition-spread single-crystalline Co₂MnAl_1−xSi_x Heusler alloy film on a MgO substrate using layer-by-layer wedge shape deposition. x is varied from 0 to 1 (0%–100% Si substitution) on a single film. The XRD characterization confirmed the formation of a single phase throughout the composition range with linear variation of the lattice constant, showing the almost linear composition gradient over the film. The systematic tuning of the Fermi energy level for CMA Weyl semimetals has been experimentally verified using HAXPES measurements, and a shift of 0.40 eV was observed for varying CMA to CMS. The electrical resistivity, AHE, ANE, and SE properties for the composition-spread film have been investigated systematically. The composition dependence of the AEE, the reciprocal transverse thermoelectric effect of the ANE, for the composition-spread CMAS film has also been investigated by means of the LIT technique. The AEE result is consistent with the ANE result, which reveals a much easier and accurate approach to study the thermoelectric property of composition-spread films. This research will accelerate the material investigation and optimization of the best composition with a large ANE/AEE, which is essential to realize applications based on transverse thermoelectric effects.

See the supplementary material for the details on the procedure for extracting pure AEE signals, XRD simulation data, and the figure showing correlation of transport and thermoelectric properties of CMAS composition-spread films with Ref. 34 in terms of N_V and band structures for Co₂MnAl and Co₂MnSi alloys.

The authors thank R. Iguchi for valuable discussions and B. Masaoka and N. Kojima for technical support. This work was supported by CREST “Creation of Innovative Core Technologies for Nano-enabled Thermal Management” (Grant No. JPMJCR17I1) and PRESTO “Scientific Innovation for Energy Harvesting Technology” (Grant No. JPMJPR17R5) from the Japan Science and Technology Agency and NEDO “Mitou Challenge 2050” (Grant No. P14004). The HAXPES measurements were performed under the approval of the NIMS Synchrotron X-ray Station (Proposal Nos. 2020A4604 and 2020A4606).

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