Combinatorial tuning of electronic structure and thermoelectric properties in Co$_2$MnAl$_{1-x}$Si$_x$ Weyl semimetals

A tuning of Fermi level (E$_F$) near Weyl points is one of the promising approaches to realize large anomalous Nernst effect (ANE). In this work, we introduce an efficient approach to tune E$_F$ for the Co$_2$MnAl Weyl semimetal through a layer-by-layer combinatorial deposition of Co$_2$MnAl$_{1-x}$Si$_x$ (CMAS) thin film. A single-crystalline composition-spread film with x varied from 0 to 1 was fabricated. The structural characterization reveals the formation of single-phase CMAS alloy throughout the composition range with a gradual improvement of L2$_1$ order with x similar to the co-sputtered single layered film, which validates the present fabrication technique. Hard X-ray photoemission spectroscopy for the CMAS composition-spread film directly confirmed the rigid band-like E$_F$ shift of approximately 0.40 eV towards the composition gradient direction from x = 0 to 1. The anomalous Ettingshausen effect (AEE), the reciprocal of ANE, has been measured for whole x range using a single strip along the composition gradient using the lock-in thermography technique. The similarity of the x dependence of observed AEE and ANE signals clearly demonstrates that the AEE measurement on the composition spread film is an effective approach to investigate the composition dependence of ANE of Weyl semimetal thin films and realize the highest performance without fabricating several films, which will accelerate the research for ANE-based energy harvesting


INTRODUCTION
A thermoelectric generator (TEG) using the Seebeck effect (SE) is one of the promising energy harvesting technologies which can generate electricity from everyday waste heat. During past many decades, researches on developing TEG using SE has been extensively conducted, but till now various remaining problems have to be solved. 1,2 One of the major drawbacks in SE is the direction of thermoelectric voltage which appears in parallel to the temperature gradient. Thus, SE-based module usually has a complicated structure in which the multiple thermopiles must be placed and connected at bottom and top alternatively in serial, causing 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 perpendicular direction to a temperature gradient and a 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 ANE not only for gaining a fundamental understanding of the phenomenon but also for practical thermoelectric applications. [6][7][8][9][10][11][12][13][14][15][16][17][18][19] At present, studies on ANE are still very less as compared to those on SE, and the reported thermopowers of ANE at around room temperature are usually very small to be implemented for practical device applications. Thus, an exploration of the materials showing high thermopower of ANE is clearly needed. Recent theoretical and experimental investigations suggested that the presence of intense Berry curvature (BC) in the vicinity of the Fermi energy (EF) can potentially enhance the intrinsic anomalous Hall effect (AHE) and ANE. [20][21][22][23][24][25] Very recently, the large anomalous Nernst coefficient (SANE) 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 strong BC near EF originating from the Weyl points. 28,29 This SANE value is almost one order of magnitude larger than that for conventional ferromagnetic materials, which opens a new possibility of enhancing ANE in these alloys. Sumida et al. has recently observed spin-polarized Weyl points near EF in Co2MnGa epitaxial films having different composition ratios and found that the magnitude of SANE strongly depends on the position of BC with respect to EF. 30 As an evidence of the importance of EF tuning, the magnitude of SANE of 6.2 V/K observed for EF 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 theoretically predicted intrinsic BC and realize large SANE, tuning the position of EF is essential. Recently, the tuning of EF with atomic substitution has been performed in Co2MnAl1-xSix (CMAS) alloys. [32][33][34] The replacement of Al by Si shifts the EF to higher energy and enhances the spin-polarization, AHE, and ANE for optimal CMAS composition. However, the tuning of EF by making individual specimens and performing systematic measurements for each are time-consuming and also cause a risk missing the best property of the material because of the unavoidable discontinuous change of the EF. Therefore, more facile approach to achieve continuous EF tuning is strongly desired.
Combinatorial deposition is one of the most effective tools which allows 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 EF and other transport and thermoelectric properties with composition. Through the measurement of the anomalous Ettingshausen effect (AEE), which is the reciprocal effect of ANE, we employed a much faster and easier technique to effectively optimize the composition suitable for the transverse thermoelectric conversion.

EXPERIMENTAL DETAILS
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 deposition rate 0.042 nm/sec and shutter speed 0.53 mm/sec, (2) rotation of the substrate by 180º, and (3) deposition of a wedge-shaped CMS layer using the linear moving shutter with deposition rate 0.026 nm/sec and shutter speed 0.33 mm/sec, where the total thickness of the CMAS film after completing (1) to (3) was designed to be 0.56 nm corresponding to the lattice constant of L21-ordered Co2MnSi. The sequence was repeated 90 times to get around 50.4-nm-thick film [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 the 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 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 Excitation X-ray of 6 keV with the focal size of 25 m (vertical)  35 m (horizontal) in 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 X-ray was set to 88º deg, which expands the footprint of X-ray on the film in the horizontal direction. An additional film with 10.0 mm composition variation length was fabricated at the identical condition for the HAXPES measurements.
Horizontal linearly polarized X-ray was used to excite photoelectron and excited photoelectrons were detected by a hemispherical analyzer (VG Scienta R4000). The pass energy of the analyzer was set to 100 eV, and the total energy resolution was approximately geometry. 36 We performed the first-principles calculation to analyze the observed valance 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 the parallel aligned Hall bars as shown in Fig. 1 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 the 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 the magnitude μ0H = 1 T was applied along the y direction (see section I in supplementary material). The pure AEE contribution was extracted using the previously established procedures from the raw LIT images. [47][48][49][50][51][52][53] Note that all patterns shown in Fig.1 were made from the identical CMAS composition spread film. 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 towards the CMS side which signifies the formation of L21 ordering.   The SANE value is +1.3 μV/K for CMA and increased to a maximum value of +2.7 μV/K for x ≈ 0.08. SANE then gradually decreases with increasing x. Interestingly, the observed trends of SSE and SANE with respect to x are similar to the previous study based on the individual CMAS films but shifts to less x (Si-poor) direction. 34 This shift can be explained by a difference in Nv in a similar manner to the above-mentioned ρxx, ρyx and AHE. One can see the closer matching of SSE vs x and SANE vs x in the two films by shifting the data for the present film towards the +x direction by ~0.4 (see Fig. S2 in supplementary material).

RESULTS AND DISCUSSION
However, the maximum SANE 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 SANE in the present CMAS film.
One can see from the band dispersion on the high symmetry line (Fig. S3  respectively. The AJoule value is proportional to the local resistivity in our configuration because the charge current density jc is uniform and the heat loss from the film to the substrate is independent of the position. 61 The AJoule image clearly demonstrates the higher resistance value at the CMA side, as shown in the x dependence of the AJoule/ jc 2 in Fig. 6(c) (note that AJoule is proportional to jc 2 ). In fact, the tendency is consistent with the ρxx variation as shown in Fig. 6(c) (ρxx value is taken from Fig. 4(c)). The AAEE image, obtained by extracting the Hodd component of the detected LIT images, [47][48][49][50][51][52][53] clearly shows that AEE is intense at the CMA side and nearly vanishes at the CMS side. The AAEE/jc as a function of x is shown in Fig. 6(d) along with the measured SANE value for the current film from Fig. 5(c). The result shows that AAEE/jc first increases with x, and then gradually decreases in a similar manner to SANE. Large AEE was observed between n = 0.06 to 0.12, which is consistent with the ANE result as can be seen in Fig. 6(d). The above result clearly shows that the imaging measurement of the temperature modulation due to AEE is an effective method to find the best composition for ANE in a composition spread film. Here one should note that it is possible to quantitatively estimate SANE from the AEE-induced temperature modulation based on the Onsager reciprocal relation: ΠAEE = SANET, where the anomalous Ettingshausen coefficient ΠAEE is proportional to AAEE·κ/jc with κ being the thermal conductivity of the ferromagnetic material.
The detailed procedure of extracting ΠAEE 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 of κ with the composition in our CMAS film is very small, although we did not perform the direct measurement of κ. This work demonstrates the usefulness of the combination of the combinatorial sputtering method and LIT technique as high-throughput material screening for finding materials showing large ANE and AEE. By performing the direct measurements of SANE as well as κ only for the optimum composition determined by the high-throughput screening, the materials exploration for ANE and AEE will be efficient. Importantly, the LIT-based method can be used not only for ANE but also for other thermoelectric and thermo-spin effects. 61,62

CONCLUSION
We have successfully fabricated a composition-spread single-crystalline Co2MnAl1-xSix Heusler alloy film on a MgO substrate using layer-by-layer wedge shape deposition. The along the x-direction and the magnetic field of 0.1 T was applied along the −y or +y-directions.
Here, A represents the magnitude of the current-induced temperature modulation, while represents the sign of the temperature modulation at the top surface of the sample when the time delay of the temperature modulation due to thermal diffusion is negligible. 6 In this configuration, the temperature gradient ∇T is generated along the z-direction following the symmetry of AEE: [6][7][8][9][10][11][12] ∇T  Jc  M where Jc is the charge current and M is the magnetization direction in a ferromagnet. The

II. Procedure of XRD pattern simulation:
x