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## Creator

[Ryo Toyama](https://orcid.org/0000-0002-7398-5803), [Keisuke Masuda](https://orcid.org/0000-0002-6884-6390), [Kodchakorn Simalaotao](https://orcid.org/0000-0002-6098-4422), [Weinan Zhou](https://orcid.org/0000-0003-2946-9913), [Varun K Kushwaha](https://orcid.org/0000-0001-6344-4264), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550)

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This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics D: Applied Physics.  IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it.  The Version of Record is available online at https://dx.doi.org/10.1088/1361-6463/ad460e[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Large anomalous Nernst conductivity of L1<sub>0</sub>-ordered CoPt in CoPt composition-spread thin films](https://mdr.nims.go.jp/datasets/93e98403-e6c9-42ba-80b3-9ebbc58ff9ef)

## Fulltext

1 Large anomalous Nernst conductivity of L10-ordered CoPt in CoPt composition-spread thin films  Ryo Toyama1,*, Keisuke Masuda1, Kodchakorn Simalaotao1,2, Weinan Zhou3, Varun K. Kushwaha1 and Yuya Sakuraba1,*  1 Research Center for Magnetic and Spintronic Materials (CMSM), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan 2 Graduate School of Pure and Applied Sciences, University of Tsukuba, Tenodai 1-1-1, Tsukuba, Ibaraki 305-8571, Japan 3 International Center for Young Scientists (ICYS), National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan  E-mail: TOYAMA.Ryo@nims.go.jp and SAKURABA.Yuya@nims.go.jp  Abstract We demonstrate a high-throughput experimental characterization of anomalous Nernst conductivity (𝛼!"# ) of L10-ordered CoPt using Co1–xPtx composition-spread thin films on MgO(100) substrates. The compositional dependence of the anomalous Nernst effect (ANE), anomalous Hall effect (AHE) and Seebeck effect is systematically measured. As increasing the Pt concentration, the crystal structure in the composition-spread film grown at 500 °C changes from fcc Co, A1-disordered CoPt, L10-ordered CoPt, A1-CoPt to fcc Pt. The largest 𝛼!"#  of 2.52 A m–1 K–1 is obtained in L10-CoPt for Pt-rich composition of x = 70%, which is larger than that for an additionally fabricated nearly stoichiometric L10-Co48Pt52 reference uniform film. The contribution from direct conversion of a temperature gradient to a transverse charge current through 𝛼!"#  is dominant to the total anomalous Nernst coefficient compared to the AHE-related contribution. From a scaling analysis of the AHE, the intrinsic contribution is found to be dominant for x = 70%. A theoretical calculation for 𝛼!"#  of L10-Co50Pt50 agrees with the experimental 𝛼!"#  value for the nearly stoichiometric reference film by considering on-site Coulomb interaction for Co atoms. We also point out the possible electron doping effect by the addition of Pt in L10-CoPt, which could explain the larger 𝛼!"#  for the off-stoichiometric Pt-rich composition than that for the nearly stoichiometric one. Our experimental and theoretical results suggest the potential of L10-CoPt with a large 𝛼!"#  originating from the intrinsic mechanism for future thermoelectric applications.  Keywords: anomalous Nernst conductivity, anomalous Nernst effect, L10-ordered alloys, CoPt, anomalous Hall effect, composition-spread films    2 1. Introduction The anomalous Nernst effect (ANE) has received growing attention owing to its transverse electric field generation [1, 2]. The transverse electric field can be generated in magnetic materials with spontaneous magnetization even in the absence of external magnetic field, which is different from the ordinary Nernst effect that requires a large external magnetic field [1, 2]. Although conventional thermoelectric devices based on the Seebeck effect (SE) exhibit relatively higher output signals than existing ANE-based devices, the SE-based devices have a more complex structure because a charge current is generated in the same direction as a temperature gradient [1, 2]. However, owing to the transverse electric field generation, the ANE is beneficial for realizing advanced thermoelectric devices with simpler device structures such as anomalous Nernst thermopiles [3] and heat flux sensors [4]. The transverse electric field (𝑬$%&) is expressed as 𝑬$%& = 𝑆$%& %∇𝑇 ×'|'|),                            (1) where 𝑆$%&  is the anomalous Nernst coefficient, ∇𝑇  is the temperature gradient and M is the magnetization [1]. The ANE stems from two different origins; one is the direct conversion of ∇𝑇 to a transverse charge current and the other is the conversion of an SE-induced charge current by the anomalous Hall effect (AHE) [1]. Thus, the 𝑆$%& can be expressed as 𝑆$%& = 𝛼!"# 𝜌!! − 𝛼!!𝜌"!# ,                            (2) where 𝛼!"#  is the anomalous Nernst conductivity, 𝜌!!  is the longitudinal resistivity, 𝛼!!  is the longitudinal thermoelectric conductivity and 𝜌"!#  is the anomalous Hall resistivity [1]. The first term on the right-hand side of equation (2) gives a direct conversion through 𝛼!"#  [1]. Thus, materials possessing a large 𝛼!"#  has been explored intensively [1].      Towards the applications to energy harvesters and heat flux sensors, because of large 𝛼!"#  as well as 𝑆$%& , ferromagnets such as Co2MnGa [5–10], Fe–Ga [11, 12] and Fe–Al [4, 11] alloys can be potential candidates. However, these materials are ferromagnetically soft that show weak magnetocrystalline anisotropy and small coercivity. These magnetic properties would not be suitable for the practical device applications. The strong magnetocrystalline anisotropy is another key factor to realize those advanced thermoelectric devices.      In this regard, L10-ordered alloys are the promising group of ferromagnets that exhibits a large 𝛼!"#  while possessing strong magnetocrystalline anisotropy and large coercivity. The ANE in L10-ordered alloys such as FePt [3, 13–16], FePd [14, 16] and MnGa [14, 17] has been reported. Although CoPt also shows the L10-ordered phase and has been the basis for magnetic devices such as next-generation high-density magnetic recording media [18–24], the study of ANE in L10-CoPt has been lacking despite its potentially large 𝛼!"# . It has been reported that CoPt crystallizes in the L10-ordered phase for a relatively wide range of Pt concentration from ≈ 42 to 63% [25]. Thus, a large 𝛼!"#  might be found in L10-CoPt for not only stoichiometric composition but also off-stoichiometric one. To search a wide range of composition, combinatorial techniques such as using composition-spread films can be adopted [26–31], which are  3 beneficial for high-throughput and systematic characterization for 𝛼!"# . In this study, we demonstrate a high-throughput experimental characterization for 𝛼!"#  of L10-CoPt using CoPt composition-spread thin films. We systematically measure the ANE, AHE and SE and obtain a large 𝛼!"#  within the composition-spread films. We also perform a theoretical calculation for 𝛼!"#  of L10-CoPt to explain the experimentally obtained large 𝛼!"#  originating from the intrinsic contribution.  2. Method 2.1 Fabrication and characterization Co1–xPtx composition-spread thin films were fabricated on single-crystal MgO(100) substrates (Furuuchi Chemical Corp.) with a size of 10 × 10 mm2 (figures 1(a) and (b)) using a combinatorial sputtering system (CMS-A6250X2, Comet Inc.). The deposition process of composition-spread films has been reported elsewhere [29–31]. Briefly, a wedge-shaped Co layer with a maximum thickness of 0.4 nm, which is close to the lattice constant of CoPt alloys, was deposited on the cleaned substrates with a composition gradient width of 7 mm using a linear moving mask. Subsequently, the substrates were rotated by 180° and a wedge-shaped Pt layer with the same maximum thickness and composition gradient width was deposited on the wedge-shaped Co layer. The deposition process for one-unit layer of 0.4 nm with a flat surface was repeated 75 times to obtain 30-nm-thick films. The deposition was performed with a substrate temperature of room temperature (RT) or 500 °C and Ar process gas pressure of 0.6 Pa. After the deposition, the films were capped with Ta (2 nm) at RT to prevent oxidization. The positional dependence on the actual film thickness and composition of the composition-spread films was measured using x-ray reflectometry (SmartLab, Rigaku) and x-ray fluorescence (XRF; ZSX Primus Ⅱ, Rigaku), respectively. The compositional dependence of crystal structures of the composition-spread films was measured using x-ray diffraction (XRD; SmartLab, Rigaku) at an interval of 1 mm with a collimated Cu-Kα radiation using a 0.5 mm incident slit. Additionally, as a reference sample, a (Co/Pt)100 multilayer film with a nominal thickness of 40 nm was deposited on an MgO(100) substrate at RT, followed by post-annealing at 600 °C. The composition of the reference film after annealing was determined to be Co48Pt52 by XRF, which was nearly stoichiometric composition. Hereafter, this film is referred to as reference uniform film, where the term uniform is used here as a contrast to the term composition-spread.   4  Figure 1. Schematic diagrams of Co1–xPtx composition-spread thin films and Hall bar devices on MgO(100) substrates. (a) Cross-sectional view and (b) top-view of the film. (c) Top-view of the Hall bar devices.  2.2 Transport measurements To evaluate the compositional dependence of the AHE, ANE and SE, the composition-spread films were patterned into 21 Hall bar devices (figure 1(c)), which were aligned to the composition gradient, using conventional photolithography and Ar-ion milling techniques. Additionally, one horizontal bar parallel to the composition gradient was fabricated on one side of the Hall bar devices, which will be utilized to estimate actual ∇𝑇 during the ANE measurement. The detail of the device structures can be found in Ref. [31]. For the AHE measurement, a Hall voltage was measured using Physical Property Measurement System (PPMS DynaCool, Versalab; Quantum Design) by sweeping an external perpendicular magnetic field (H). For the ANE measurement, the sample was placed between two Cu blocks that are connected by a Peltier module of a customized sample holder [32]. The anomalous Nernst voltage (𝑉$%&) was measured at 300 K by sweeping H under ∇𝑇 that was in-plane direction of the substrate surface and perpendicular to the long-axis of the Hall bar devices. Four different ∇𝑇 were generated by applying different constant currents to the Peltier module to heat up one side of the substrate. The actual ∇𝑇 generated during the ANE measurement was estimated using a Seebeck voltage of the horizontal bar and an infrared camera. 𝑆$%& was obtained by a linear fitting of four data points in 𝐸$%& vs ∇𝑇 plots for each device. For the SE measurement, the same sample used for the ANE measurement was placed between the two Cu blocks by rotating it 90° in order to  5 generate a temperature difference (∆𝑇) along the long-axis of the Hall bar devices. The Seebeck voltage (𝑉)&) was measured at room temperature by applying four different constant currents to the Peltier module. Simultaneously, the temperature of the sample was measured using the infrared camera. It is noted that Au bonding wires were used to connect between the contact pads of the devices and terminals of the sample holder. The total Seebeck coefficient comprising of the Hall bar device and Au wires was obtained by a linear fitting of four data points in 𝑉)&  vs ∆𝑇 plots for each device. To obtain the Seebeck coefficient originating only from the devices (𝑆)&), the contribution of the SE from the Au bonding wires was subtracted from the total Seebeck coefficient using the Seebeck coefficient for Au. The detail method for the measurement and data analysis can also be found in Ref. [31].  2.3 Theoretical calculations The theoretical anomalous Hall conductivity (𝜎!"# ) and 𝛼!"#  of L10-Co50Pt50 were analyzed by combining the linear response theory and the first-principles calculation. The electronic structure of L10-Co50Pt50 was first calculated employing the first-principles calculation based on the density functional theory (DFT), implemented in the Vienna ab initio simulation program (VASP) [33]. We took into account the spin-orbit interaction to calculate 𝜎!"# . The generalized gradient approximation (GGA) [34] was adopted for the exchange-correlation energy and the projected augmented wave pseudopotential [35, 36] was used to treat the effect of core electrons properly. Using the obtained electronic structure, we calculated the energy-dependent anomalous Hall conductivity (𝜎!"# (𝜀)) expressed as 𝜎!"# (𝜀) = − *!ℏ ∫,"-(/0)"Ω2(𝐤),                            (3) Ω2(𝐤) = −%ℏ3)/∑ 𝑓8𝐸4,𝐤, 𝜀:4 ∑/ 89:𝜓4,𝐤;𝑝!;𝜓4#,𝐤<:𝜓4#,𝐤;𝑝";𝜓4,𝐤<=>$#,𝐤?>$,𝐤@!4#A4 ,         (4) where ℏ is the Planck constant, e is the elementary charge of electron, Ω2(𝐤) is the Berry curvature at the wave vector k, m is the effective mass of electron, n and n’ denote the band indices, 𝑝! (𝑝") is the x (y) component of the momentum operator, 𝜓4,𝐤 is the eigenstate with the eigenenergy 𝐸4,𝐤 and 𝑓8𝐸4,𝐤, 𝜀: is the Fermi distribution function for the band n and the wave vector k at the energy ε relative to the Fermi level (EF). In the calculation of 𝜎!"# (𝜀), the direction of magnetization was set along the [001] direction of the L10-CoPt lattice with experimentally obtained lattice constants of c = 3.714 Å and a = 3.804 Å. The 91 × 91 × 91 k-points were used for the Brillouin zone integration. The on-site Coulomb interaction (U) for Co atoms was varied from 0 to 1.5 eV. From the Boltzmann transport theory, by substituting 𝜎!"# (𝜀) into the following expression, we can obtain 𝛼!"# : 𝛼!"# = − B*C ∫𝑑𝜀 %−DEDF) (𝜀 − 𝜇) 𝜎!"# (𝜀),                      (5) where T is the temperature and 𝑓 = 1 {exp[(𝜀 − 𝜇) 𝑘G⁄ 𝑇] + 1}⁄  is the Fermi distribution function with μ being the chemical potential. Here, T is fixed at 300 K and μ = 0 corresponds to the EF. The density of states (DOS) of L10-CoPt with different Pt concentration were calculated on the basis of the DFT and the Korringa-Kohn-Rostoker (KKR) method [37, 38], implemented in the AkaiKKR code [39]. The exchange-correlation energy was treated within the GGA [34]. To describe the  6 chemical disorder between Co and Pt atoms in the L10-ordered structure, the coherent potential approximation was utilized [40, 41]. The lattice constant of L10-CoPt was set to c = 3.722 Å and a = 3.859 Å, which were optimized within the calculation, corresponding to the c/a ratio of 0.964. The Brillouin zone integration was performed with 20 × 20 × 20 k-points and the imaginary energy component was set to 0.001 Ry.  3. Results and discussion 3.1 Crystal structures      The out-of-plane (χ = 0°) XRD patterns of the films grown at RT and 500 °C are shown in figures 2(a) and (b), respectively. It is noted that each diffraction pattern except for x = 0% and 100% should contain the neighboring composition region with a maximum of ≈ +/–6% due to the collimator width of 0.5 mm. For the film grown at RT (figure 2(a)), when x = 0% (pure Co), a diffraction peak was observed at 2θ ≈ 75.5°. This peak can be originated from face-centered cubic (fcc) Co 220 or hexagonal close-packed (hcp) Co 110, whose diffraction angles are very similar. To distinguish the phase of Co, tilted-plane XRD was performed with χ = 40.191°, and a peak at 2θ ≈ 47° was observed, which corresponds to hcp Co 101 (figure S1 in the Supplementary Material). Thus, the peak at 2θ ≈ 75.5° with χ = 0° in figure 2(a) should correspond to hcp Co 110, and the phase of Co was determined to be hcp. The formation of hcp Co on MgO substrates at low deposition temperature agrees with the previous reports [42, 43]. The peak from hcp phase shifted to the lower diffraction angles for x up to 13%. From x = 28%, an A1-CoPt 002 peak was observed at 2θ ≈ 48.7°, which indicates the intermixing of ultrathin Co and Pt layers in the composition-spread films even without any heating process. The A1-CoPt 002 peak shifted to the lower diffraction angles for x up to 97%, which was due to the incorporation of Pt atoms with larger atomic radius into the CoPt lattice, and thus, the lattice constant increased as shown in figure 2(c). From x = 87%, an additional peak of fcc Pt 111 was observed together with the A1-CoPt 002 peak. The peak intensity of fcc Pt 111 became stronger as increasing x. For x = 100% (pure Pt), only fcc Pt 111 was observed at 2θ ≈ 39.6°. As a result, the crystal structure of the RT-grown film changed from hcp Co, hcp CoPt, A1-CoPt to fcc Pt as increasing x. On the other hand, for the film grown at 500 °C (figure 2(b)), when x = 0% (pure Co), a peak from fcc Co 002 was observed at 2θ ≈ 51.5°, which is different from the case of RT-grown film. As increasing x from 0% to 100%, the 002 peak shifted to the lower diffraction angles from 2θ ≈ 51.5° to 46.1°, and the phase changed from fcc Co (x = 0%), CoPt (x = 3–98%) to fcc Pt (x = 100%). Additionally, for x = 24% to 68%, a superlattice peak of CoPt 001 was observed at 2θ ≈ 24°, indicating the formation of L10-ordered phase. Especially from x = 49% and 68%, L10-CoPt 003 peak also appeared at 2θ ≈ 77°. Thus, the L10-ordered phase was confirmed for a relatively wide range of Pt concentration from 24% to 68% in the composition-spread film. Although the other ordered phases such as L12-Co3Pt and L12-CoPt3 exist in the bulk phase diagram of Co–Pt, those region should be L10-ordered because the AHE properties derived from strong perpendicular magnetocrystalline anisotropy (PMA) and large coercivity were observed, which will be described in the next section. From x = 86%, the superlattice peaks disappeared and only the CoPt 002 peak was observed, indicating the disappearance of L10-ordered  7 phase. Finally, for x = 100% (pure Pt), an fcc Pt 002 peak was observed at 2θ ≈ 46.1° together with the weak peak of fcc Pt 111. The (002) orientation of fcc Pt was dominant in the 500 °C-grown film, which is also different from the case of RT-grown film. The lattice constant of the 500 °C-grown film is summarized in figure 2(d). The lattice constant of L10-CoPt agrees with the previous reports [44–48]. As a result, the crystal structure of the 500 °C-grown film changed from fcc Co, A1-CoPt, L10-CoPt, A1-CoPt to fcc Pt as increasing x. The degree of L10 order (𝑆HB' ) is estimated by 𝑆HB' = L8𝐼IIB*!J 𝐼II/*!JN : 8𝐼IIBKL3 𝐼II/KL3N :N , where 𝐼IIB (II/)*!J  is the experimental integrated intensity of 001 superlattice (002 fundamental) peak and 𝐼IIB (II/)KL3  is the simulated intensity of 001 (002) peak. The 𝐼IIB (II/)KL3  value was calculated using the VESTA software [49] for a stoichiometric composition (L10-Co50Pt50) with theoretical lattice constants of c = 3.7 Å and a = 3.8 Å. The calculated 𝑆HB' is plotted in figure 2(d); it showed a maximum value of 0.54 for x = 49%. The Co48Pt52 reference uniform film post-annealed at 600 °C also showed L10-ordered phase with c = 3.7144 Å and a = 3.8037 Å (figure S2). The 𝑆HB' was estimated to 0.85, which was closer to the ideal L10-ordered structure than the one in the composition-spread film.   Figure 2. Compositional dependence on the out-of-plane x-ray diffraction (XRD) patterns of Co1–xPtx composition-spread films on MgO(100) substrates grown at (a) room temperature (RT) and (b) 500 °C.  8 The diffraction peaks originated from MgO(100) substrates are indicated by the symbol ＊. It is noted that each diffraction pattern except for x = 0% and 100% should contain the neighboring composition region with a maximum of ≈ +/–6% due to the x-ray collimator width of 0.5 mm. The lattice constants of the RT- and 500 °C-grown films are summarized in parts (c) and (d), respectively. The degree of L10 order (𝑆HB') is also plotted in part (d).  3.2 Anomalous Hall effect (AHE)      The H-dependent Hall resistivity (𝜌"!) of the composition-spread films grown at RT and 500 °C measured at 300 K are shown in figures 3(a) and (b), respectively. It should be noted that the transport properties of Co-rich (x < 63%) and Pt-rich (x > 92%) regions in the 500 °C-grown film could not be measured due to high electrical resistance. This might be due to discontinuous grain growth in those regions, which could be caused by the deposition at the elevated substrate temperature under the condition of long target–substrate distance (27 cm) and relatively high process gas pressure. It is also noted that the surface roughness of the 500 °C-grown film for x = 63–92% was smaller than that for the other regions, which was confirmed by XRR. In order to complement the data near the stoichiometric composition, the transport properties of L10-Co48Pt52 reference uniform film post-annealed at 600 °C was also measured. For the RT-grown film (figure 3(a)), 𝜌"! showed a clear compositional dependence and all of the composition region showed a large saturation field. For the 500 °C-grown film (figure 3(b)), the 𝜌"! curves for x = 63% and 70% exhibited a large hysteresis with a remanence at zero field and saturated at a lower H. This behavior can be derived from of the L10-CoPt possessing strong PMA and large coercivity. It is noted that the region for x = 70% should not be L12-ordered structure because L12-CoPt3 shows low coercivity below ≈ 200 Oe [44, 50–53], no PMA [54, 55] and low Curie temperature below ≈ RT [56, 57]. The compositional dependences of 𝜌"!# , 𝜌!!, anomalous Hall angle (AHA; tan 𝜃M = 𝜌"!# 𝜌!!⁄ ), 𝜎!"# , and longitudinal conductivity (𝜎!!) are shown in figures 3(c)–(g), respectively. The 𝜎!"#  and 𝜎!!  values were calculated using the equations 𝜎!"# = N()*=N()*!ON))!@ and 𝜎!! =N))=N()*!ON))!@. From figure 3(c), for the RT-grown film, the 𝜌"!#  value first increased as increasing x, showing a maximum of 1.75 µΩ cm for x = 55%, and decreased towards zero against further Pt addition. For the 500 °C-grown film, a maximum 𝜌"!#  value of 1.08 µΩ cm was observed for x = 70%. The 𝜌"!#  for the RT-grown film was larger than that for the 500 °C-grown film for all x. The smaller 𝜌"!#  value for L10-ordered alloys than disordered ones is consistent with the previous reports [58–61]. The 𝜌!! values for L10-CoPt in the film grown at 500 °C were smaller than those for the disordered CoPt in the film grown at RT (figure 3(d)), which is also consistent with the previous reports [58–61]. From figure 3(g), the 𝜎!! values were in the range of 103–104 µΩ cm, which suggests that the dominant mechanism of the AHE could be intrinsic [62, 63]. To understand the mechanism of the AHE especially for the L10-CoPt, we employ a scaling analysis to the AHE results for x = 70% in the 500 °C-grown film, where the largest 𝜌"!#  value was observed. The Tian-Ye-Jin (TYJ) scaling was used, which is expressed as   9 𝜌"!# = 𝛼𝜌!!I + 𝛽𝜌!!/ ,                               (6) where 𝜌!!I is the residual resistivity (𝜌!! at 10 K in this study) and α and β correspond to extrinsic and intrinsic contribution, respectively [64]. The temperature-dependent 𝜌"! curves for x = 70% in the 500 °C-grown film measured from 10 to 300 K are shown in figure 3(h). From the fitting of the data in the 𝜌"!#  vs 𝜌!!/  plots as shown in figure 3(i), we obtained α = –7.90 × 10–3 and β = 763 S cm–1. At 300 K, the intrinsic term (𝛽𝜌!!/ ) of 1.326 µΩ cm was much larger than the extrinsic term (𝛼𝜌!!I) of –0.233 µΩ cm, indicating that the intrinsic contribution was the dominant mechanism. The β value of 763 S cm–1 was close to the experimental 𝜎!"#  value of 628 S cm–1 (figure 3(f)). As a result, the AHE of the L10-CoPt was found to be dominated by the intrinsic mechanism.   Figure 3. External perpendicular magnetic field (H)-dependent Hall resistivity (𝜌"! ) of Co1–xPtx composition-spread films grown at (a) RT and (b) 500 °C measured at 300 K. Compositional dependence of (c) anomalous Hall resistivity (𝜌"!# ), (d) longitudinal resistivity (𝜌!!), (e) anomalous Hall angle (AHA; tan 𝜃M = 𝜌"!# 𝜌!!⁄ ), (f) anomalous Hall conductivity (𝜎!"# ) and (g) longitudinal conductivity (𝜎!!). The data for L10-Co48Pt52 reference uniform film post-annealed at 600 °C are also plotted in parts (b)–(g). (h) Temperature-dependent 𝜌"! for x = 70% in the 500 °C-grown film measured from 10 to  10 300 K. (i) 𝜌"!#  vs 𝜌!!/  plots for x = 70% in the 500 °C-grown film. The data were analyzed by the scaling relationship 𝜌"!# = 𝛼𝜌!!I + 𝛽𝜌!!/ , where 𝜌!!I  is the residual resistivity and α and β correspond to extrinsic and intrinsic contribution, respectively, which is indicated by red solid line.  3.3 Anomalous Nernst effect (ANE) and Seebeck effect (SE) The H-dependent 𝐸$%& curves of the films grown at RT and 500 °C measured at 300 K are shown in figures 4(a) and (b), respectively. The tendency of the 𝐸$%& curves were similar to those of the 𝜌"! curves in figures 3(a) and (b); all of the composition region showed a large saturation field for the RT-grown film (figure 4(a)), while the 500 °C-grown film showed a larger hysteresis with a remanence at zero field and saturated at a lower H (figure 4(b)). The compositional dependence of the Seebeck coefficient (𝑆)&) is shown in figure 4(c). Here, we denote the first term on the right-hand side of equation (2) (𝛼!"# 𝜌!!) as 𝑆8 and the second term (−𝛼!!𝜌"!# ) as 𝑆88. Because 𝛼!! can be expressed as 𝛼!! =𝑆)& 𝜌!!⁄ , 𝑆88  term is rewritten as 𝑆88 = −𝑆)&𝜌"!# 𝜌!!⁄ = −𝑆)& tan 𝜃M  [1]. From those transport measurements, we calculate 𝑆$%&, 𝑆8, and 𝑆88, which are plotted in figure 4(d). The 𝑆$%& showed the largest value of 1.18 µV K–1 for x = 70% in the 500 °C-grown film, which is larger than that of L10-ordered FePt (0.698–0.821 µV K–1), FePd (0.408–0.468 µV K–1) and MnGa (–0.358 µV K–1) at 300 K in the previous reports [14, 16]. The 𝑆88 term of the 500 °C-grown film was small and almost the same as that of the RT-grown film. Thus, the direct conversion of ∇𝑇 to a transverse charge current through 𝛼!"#  was dominant. From the 𝑆8 term, compositional dependence of 𝛼!"#  is also calculated, as shown in figure 4(e). A large 𝛼!"#  value of 2.52 A m–1 K–1 was obtained for x = 70% in the 500 °C-grown film. In contrast, the 𝛼!"#  of L10-Co48Pt52 reference uniform film was 1.72 A m–1 K–1, which was smaller than that for x = 70%. These values are much larger than that of L10-ordered FePt (0.783 A m–1 K–1) and FePd (0.321 A m–1 K–1) [16]. Therefore, a large 𝛼!"#  of L10-CoPt was demonstrated experimentally using the Co1–xPtx composition-spread films. The experimental values obtained in this study are summarized in table 1.   11  Figure 4. H-dependent anomalous Nernst electric field (𝐸$%&) of Co1–xPtx composition-spread films grown at (a) RT and (b) 500 °C measured at 300 K with ∇𝑇 ≈ 0.68 K mm–1. Compositional dependence of (c) Seebeck coefficient (𝑆P>) measured at 300 K, (d) anomalous Nernst coefficient (𝑆$%&), 𝑆8 (=𝛼!"# 𝜌!!) and 𝑆88 (= −𝑆)& tan 𝜃M) terms and (e) anomalous Nernst conductivity (𝛼!"# ). The data for L10-Co48Pt52 reference uniform film post-annealed at 600 °C are also plotted in parts (b)–(e). In part (b), the curve for 600 °C was obtained with ∇𝑇 ≈ 0.56 K mm–1.  Table 1. Summary for experimental values of 𝜌"!# , 𝜌!! , AHA, 𝜎!"# , 𝜎!! , 𝑆)& , 𝑆$%&  and 𝛼!"#  measured at 300 K of Co1–xPtx composition-spread films (x = 0% and 70%) and reference uniform film (x = 52%). Composition Phase 𝜌!"#  (µΩ cm) 𝜌"" (µΩ cm) AHA (%) 𝜎"!#  (S cm–1) 𝜎"" (103 S cm–1) 𝑆$% (µV K–1) 𝑆&'% (µV K–1) 𝛼"!#  (A m–1 K–1) Co hcp 0.207 17.7 1.16 656 56.3 –7.11 0.121 0.215 Co48Pt52 L10 0.501 30.2 1.66 549 33.1 –8.45 0.659 1.72 Co30Pt70 A1 1.61 49.1 3.28 668 20.4 –4.48 0.728 1.18 Co30Pt70 L10 1.08 41.4 2.60 628 24.1 –5.07 1.18 2.52  3.4 Theoretical analysis for AHE and ANE We performed a theoretical calculation for 𝜎!"#  and 𝛼!"#  of L10-CoPt to explain the experimentally obtained 𝜎!"#  and 𝛼!"# . The theoretical energy-dependent 𝜎!"#  and 𝛼!"#  curves of L10-Co50Pt50 are shown in figures 5(a) and (b), respectively. Without incorporating U, the theoretical 𝜎!"#  showed a small positive value of 57 S cm–1 at µ = 0 eV, which is largely different from the experiment value of 549 S cm–1 for x = 52%. The theoretical 𝛼!"#  without U was as large as 4.43 A m– 12 1 K–1, which is also largely different from the experimental value of 1.72 A m–1 K–1 for x = 52%. After considering U, the local maximum position of the curves closest to µ = 0 eV for both 𝜎!"#  and 𝛼!"#  shifted toward the higher energies as increasing U. This shift of peak position, which is equivalent to the shift of EF, results in a change in 𝜎!"#  from 510 to 542 S cm–1 and 𝛼!"#  from 3.07 to 1.22 A m–1 K–1 as increasing U from 0.5 to 1.5 eV, respectively. Thus, the experimentally obtained 𝜎!"#  and 𝛼!"#  values for nearly stoichiometric L10-Co48Pt52 can be explained by incorporating U. The validity of incorporation of U into first-principles calculation has been discussed mainly for fundamental 3d ferromagnets [65, 66] and Heusler alloys [67–69]. Our results would show that U must also be considered in the theoretical calculation to explain experimental 𝜎!"#  and 𝛼!"#  values of L10-ordered alloys.   Figure 5. Theoretical energy-dependent 𝜎!"#  and 𝛼!"#  curves of L10-Co50Pt50 with on-site Coulomb interaction (U) for Co atoms of 0.0, 0.5, 1.0 and 1.5 eV.  From the experiment, a maximum 𝛼!"#  value of 2.52 A m–1 K–1 was obtained in the L10-CoPt for off-stoichiometric Pt-rich composition of x = 70%, which was larger than that for the nearly  13 stoichiometric composition of x = 52% (figure 4(e)). To explain this, we also calculate the DOS of L10-CoPt with different Pt concentration. The Pt concentration dependence on the DOS of L10-CoPt is shown in figure 6. As increasing the Pt concentration, although the peaks of DOS at E – EF = 0 remained almost unchanged, the DOS peaks at E – EF < 0 clearly moved away from E – EF = 0, which could possibly be interpreted as the electron doping effect by the addition of Pt in L10-CoPt. From the theoretical 𝛼!"#  curves by incorporating U (figure 5(b)), because the positions of local maximum of the curves closest to EF are located at the positive µ, the 𝛼!"#  value tends to increase as increasing the µ. Thus, an excess amount of Pt atoms in the L10-CoPt for x = 70% could work as electron doping that shifts the EF towards the higher energies in the theoretical 𝛼!"#  curves (figure 5(b)), which would result in a larger 𝛼!"#  value for the off-stoichiometric Pt-rich composition than the stoichiometric one.      An increase in 𝜎!"#  of L10-CoPt as increasing x from 52% to 70% in our experiment could also be explained by the electron doping effect of the excess Pt atoms. From the theoretical 𝜎!"#  curves (figure 5(a)), the peak closest to EF is located at the positive µ for U = 1.0–1.5 eV. Therefore, the increase in 𝜎!"#  from 549 to 628 S cm–1 as increasing x from 52% to 70% could be due to the shift of EF towards the higher energies by the increase in Pt atoms. In addition, the change in theoretical 𝜎!"#  value (figure 5(a)) was more gradual than that in 𝛼!"#  (figure 5(b)). Thus, a small increase in the experimental 𝜎!"#  value by 14% as well as a larger increase in 𝛼!"#  by 47% from 1.72 to 2.52 A m–1 K–1 as increasing x from 52% to 70% qualitatively agree with the theoretical results. Our theoretical calculation suggests that a large 𝛼!"#  over 4 A m–1 K–1 could be achieved in L10-CoPt by adjusting the electron doping. This theoretical 𝛼!"#  value in L10-CoPt is much larger than that of L10-ordered FePt (0.8658 A m–1 K–1) and FePd (0.2412 A m–1 K–1) at 300 K [16], which also indicates a superiority of L10-CoPt compared to the other L10-ordered alloys.   Figure 6. The density of states (DOS) of L10-CoPt with different Pt concentration.   14      We would like to point out the dependence of calculation code on the theoretical 𝜎!"#  values. In Ref. [70], theoretical 𝜎!"#  for L10-CoPt was calculated by the DFT using the PHASE/0 code [71]; the theoretical 𝜎!"#  value at EF was 481 S cm–1 even without considering U, where the value agrees well with our experimental value of 549 S cm–1 for L10-Co48Pt52 (figure 3(c)). In our calculation using the VASP code, the theoretical 𝜎!"#  was as small as 57 S cm–1 unless U is taken into account (black curve in figure 5(a)), which was largely different from our experimental value of 𝜎!"#  (figure 3(c)). On the other hand, in Refs. [72, 73], theoretical 𝜎!"#  for L10-CoPt was calculated using full-potential linearized augmented-plane-wave (FLAPW) method [74, 75], which results in small negative 𝜎!"#  values. These discrepancy could be caused by the calculation code dependence on the position of EF. However, the tendency of the µ-dependent curve for 𝜎!"#  without U calculated using the VASP code in this study (black curve in figure 5(a)) qualitatively agrees with the one calculated using the PHASE/0 code as shown in the blue curve in figure 2(a) in Ref. [70]. Both calculation methods exhibit a drastic change in the 𝜎!"#  curve at the vicinity of EF, which corresponds to a large 𝛼!"#  value at the vicinity of EF. Thus, we could consider the calculation results using the VASP code in this study can be reliable, although the code dependence as well as the necessity of U need to be carefully investigated as a future work.  4. Conclusion We demonstrated a high-throughput experimental characterization for 𝛼!"#  of L10-CoPt using Co1–xPtx composition-spread thin films. The largest 𝛼!"#  of 2.52 A m–1 K–1 and 𝑆$%& of 1.18 µV K–1 were obtained in L10-CoPt for Pt-rich composition of x = 70%, which were larger than that for the nearly stoichiometric L10-Co48Pt52 reference uniform film. The contribution from direct conversion of ∇𝑇 to a transverse charge current through 𝛼!"#  was dominant to the total 𝑆$%& compared to the AHE-related contribution. From a scaling analysis of the AHE, the intrinsic contribution was dominant for x = 70%. A theoretical calculation showed that the experimentally obtained 𝜎!"#  and 𝛼!"#  values for the nearly stoichiometric L10-Co48Pt52 reference uniform film can be explained by incorporating U. We also pointed out the possible electron doping effect by the addition of Pt in L10-CoPt, which could explain the lager 𝛼!"#  for the off-stoichiometric Pt-rich composition than that for the stoichiometric one. Our experimental and theoretical results suggest the potential of L10-CoPt with a large 𝛼!"#  originating from the intrinsic mechanism while possessing strong magnetocrystalline anisotropy, which would be beneficial for future applications to energy harvesters and heat flux sensors.  Supplementary material See the supplementary material for detail on the tilted-plane XRD of Co-rich regions in the composition-spread film grown at RT and the XRD result of the nearly stoichiometric L10-Co48Pt52 reference uniform film.  Data availability statement The data cannot be made publicly available upon publication because no suitable repository exists for hosting data in this field of study. The data that support the findings of this study are available upon  15 reasonable request from the authors.  Acknowledgements The authors thank T T Sasaki and N Suwannaharn for fruitful discussion. The authors thank T Hiroto for the technical support with the XRD measurement. This work was supported by JST CREST (Grant No. JPMJCR21O1), JST ERATO “Magnetic Thermal Management Materials” (Grant No. JPMJER2201), MEXT Program: Data Creation and Utilization-Type Material Research and Development Project (Digital Transformation Initiative Center for Magnetic Materials; Grant No. JPMXP1122715503), JSPS KAKENHI Grants-in-Aid for Scientific Research (B) (Grant No. JP21H01608) and JSPS KAKENHI Grants-in-Aid for Research Activity Start-up (Grant No. JP22K20494).  Conflict of interest The authors have no conflicts to disclose.  ORCID iDs R Toyama https://orcid.org/0000-0002-7398-5803 K Masuda https://orcid.org/0000-0002-6884-6390 K Simalaotao https://orcid.org/0000-0002-6098-4422 W Zhou https://orcid.org/0000-0003-2946-9913 V K Kushwaha https://orcid.org/0000-0001-6344-4264 Y Sakuraba https://orcid.org/0000-0003-4618-9550   https://orcid.org/0000-0002-7398-5803https://orcid.org/0000-0002-6884-6390https://orcid.org/0000-0002-6098-4422https://orcid.org/0000-0003-2946-9913https://orcid.org/0000-0001-6344-4264https://orcid.org/0000-0003-4618-9550 16 References 1 Uchida K, Zhou W and Sakuraba Y 2021 Appl. Phys. Lett. 118 140504 2 Uchida K and Heremans J P 2022 Joule 6 2240–5 3 Sakuraba Y, Hasegawa K, Mizuguchi M, Kubota T, Mizukami S, Miyazaki T and Takanashi K 2013 Appl. Phys. Express 6 033003 4 Zhou W and Sakuraba Y 2020 Appl. Phys. Express 13 043001 5 Sakai A, Mizuta Y P, Nugroho A A, Sihombing R, Koretsune T, Suzuki M-T, Takemori N, Ishii R, Nishio-Hamane D, Arita R, Goswami P and Nakatsuji S 2018 Nat. 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