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[Andres Martin-Cid](https://orcid.org/0000-0002-9711-288X), [Babu Madavali](https://orcid.org/0000-0002-8486-701X), [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Nikita Kulesh](https://orcid.org/0000-0001-7046-2671), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897)

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[Effect of Cr substitution for Mn on magnetic and transverse thermoelectric properties of isotropic Mn1-Cr AlGe magnets](https://mdr.nims.go.jp/datasets/12428cf9-4823-4cfe-af4c-70e67bcf5aa8)

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Effect of Cr substitution for Mn on magnetic and transverse thermoelectric properties of isotropic Mn1-xCrxAlGe magnets Andres Martin-Cid1†, Babu Madavali1†, Fuyuki Ando1, Nikita Kulesh1, Ken-ichi Uchida1,2, Hossein Sepehri-Amin1*1National Institute for Materials Science, Tsukuba 305-0047, Japan2Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, JapanE-mail: *Corresponding author: h.sepehriamin@nims.go.jp†These authors contributed equally to this work.Transverse thermoelectric generators (TTEGs) based on the anomalous Nernst effect can operate without the need for an external magnetic field by incorporating permanent magnets. Utilizing permanent magnets with a large anomalous Nernst coefficient is needed to enhance power density, thereby improving the efficiency of electricity generation from waste heat. Several commercially available permanent magnets have been considered for demonstration of the zero magnetic field operation of TTEGs, including SmCo5, Sm2Co17, and Nd2Fe14B-based magnets. However, there are limited studies on transverse thermoelectric properties of the bulk permanent magnets without the use of rare earth element as potential candidates for the TTEGs. In this work, we have systematically studied the evolution of the magnetic and transverse thermoelectric properties of isotropic MnAlGe-based permanent magnets upon Cr substitution for Mn. A maximum coercivity of 1.14 T with a remanence of 0.22 T is achieved for a composition of Mn0.8Cr0.2AlGe. The anomalous Nernst coefficient (SANE) is found to be negative regardless of the composition, with a maximum absolute value of 0.74 μVK-1 for the Mn0.9Cr0.1AlGe, representing a 3-fold enhancement compared to the pristine MnAlGe sample. On the other hand, the Seebeck coefficient is found to be positive for all compositions, with a maximum value of 18.5 μVK-1 for the Mn0.8Cr0.2AlGe composition. The synergistic enhancement of transverse thermoelectric conductivity and Seebeck coefficient contributes to the high SANE of developed rare-earth free permanent magnets, reaching comparable to that SANE of Nd2Fe14B-type commercial magnets.Keywords: anomalous Nernst effect, permanent magnets, transverse thermoelectrics1. IntroductionMaterials with thermoelectric  properties can directly convert heat into electricity and vice versa, offering a promising solution for the growing need for sustainable energy. Current thermoelectric devices rely on longitudinal effects, specifically the Seebeck and Peltier effects, where heat and electric currents flow in the same direction. This alignment, however, leads to several drawbacks. These devices require complex structures and need electrical contacts on the hot side, which increases both electrical and thermal resistance. Additionally, these hot-side contacts are prone to thermal damage, reducing the device's lifespan and performance [1–3]. Transverse thermoelectric systems offer several advantages over traditional longitudinal designs. In these systems, heat and electric currents flow perpendicular to each other, eliminating many of the drawbacks of conventional designs and enabling simpler device geometries [1,4–8].Transverse thermoelectric phenomena can be divided into two main groups; the time-reversal symmetry breaking phenomena, where the anomalous Nernst effect (ANE) is included, and the structural symmetry breaking phenomena, including the off-diagonal Seebeck effect (ODSE) due to macroscale and microscale anisotropic structure [1,6,9–20]. Among these effects, the ANE is an interesting phenomenon due to its ability to produce a transverse electric field in the magnetic materials at the cross product of temperature grant and spontaneous magnetization. However, an external magnetic field is needed for operation of most of the ANE materials. Recent studies show that permanent magnets with finite remanent magnetization can enable the operation of ANE-based thermoelectric generation devices without requiring an external magnetic field [21–25]. Among the available commercial permanent magnets at room temperature, SmCo5-type magnets present the highest positive anomalous Nernst coefficient (SANE) of 4.1 μVK-1 , while Nd-Fe-B based magnets present a moderate negative value of the SANE of -0.87 μVK-1 [6,23]. These values of SANE translate into a very small thermoelectric figure of merit zxyT for ANE (< 10-3), making these materials ineffective for application as transverse thermoelectric generators (TTEGs) with permanent magnet functionality. ANE can also contribute to enhancing transverse thermoelectric conversion by incorporating it within an artificially tilted multilayer (ATML). Recently, Lee et al. [26] directly observed temperature modulation via transverse thermoelectric conversion and were able to separately identify the contributions from the ODSE and the ANE in SmCo5/Bi0.2Sb1.8Te3 ATMLs under zero magnetic field, successfully hybridizing the ODSE and ANE to obtain a high zxyT of 0.30 at room temperature, improving the value of previously reported permanent magnet-based ATMLs [27,28].This result paves the way for exploring new couplings between permanent magnets and thermoelectric materials in ATML devices, with the goal of further enhancing transverse thermoelectric performance in “thermoelectric permanent magnets”. However, one drawback is the limited permanent magnet material of choice with large SANE, especially permanent magnet materials free of rare-earth elements. Among non-commercial hard ferromagnetic materials, only three systems have been reported to have a negative SANE, including the Mn-Ga system [29], the MnBi system [30–32], and the MnAlGe system [33], while it has also been reported in compensated ferrimagnetic CoxGd1-x films [34] and in soft ferromagnetic iron in bulk [35] and thin films [36].Among these systems, MnAlGe based intermetallic with the tetragonal Cu2Sb-type structure exhibits a relatively large anisotropy constant of 5.2 × 105 J/m3 and a moderate saturation magnetization of 50 Am2/kg at room temperature [37]. These properties allowed the development of a coercivity of up to 0.64 T in ball-milled and annealed powder, and up to 0.5 T in compacted powders [38]. Furthermore, substitution of Mn for Cr leads to an enhancement of the magnetic properties, increasing the magnetization up to ~60 Am2/kg. and the anisotropy constant up to 7.3 × 105 J/m3 [39–42]. Recent studies report that Cr substitution for Mn can enhance the SANE from -0.13 μV/K to -0.5 μV/K, while also doubling the Seebeck coefficient (Sxx) from 10 μVK-1 for MnAlGe to 20 μVK-1 in (Mn,Cr)AlGe thin films, respectively [33]. The key question, however, is whether comparable properties can be achieved in bulk (Mn,Cr)AlGe materials by optimizing the Mn/Cr ratio, while still maintaining sufficiently large coercivity and a finite remanent magnetization. In this study, we systematically investigated the effect of substituting Cr for Mn on the magnetic and transverse thermoelectric properties of bulk Mn1-xCrxAlGe (x=0, 0.1, 0.2, 0.3, 0.4, and 0.5) systems. This intermetallic compound is explored as a potential permanent magnet material for TTEGs  with a negative anomalous Nernst coefficient.2. Experimental SectionSample Preparation: Mn1-xCrxAlGe (where x = 0, 0.1, 0.2, 0.3, 0.4, and 0.5) alloys were fabricated through induction melting and casting into a water-cooled steel die of high-purity elements (purity of 99.9% or higher) in an argon atmosphere. To compensate for Mn loss during alloy melting and processing, an additional 5 wt.% Mn was included in the target composition.The ingots were further processed by rapid solidification using a single-roller melt-spinning machine. The melt-spinning conditions were set the same for all samples at 3 kPa Ar overpressure, 0.6 mm nozzle diameter, and a tangential wheel speed of 40 m/s. This enables the reduction of the grain size of the ingots, and to develop coercivity in the magnets through microstructure modifications. The produced ribbons were pulverized and hot-pressed in steel dies with 10 mm diameter at 320 MPa and 650 °C for 10 to 30 minutes to obtain nearly fully dense isotropic magnets. Densified magnets were cut into different shapes for characterization with a diamond-wire cutting machine.Sample Characterization: The magnetic hysteresis loops were measured for 1 mm side cubic samples using a 7 T Superconducting Quantum Interference Device vibrating sample magnetometer (SQUID-VSM). A scanning electron microscope with energy-dispersive X-ray spectroscopy (SEM-EDS),  Carl-Zeiss 1540EsB Crossbeam, was used to study the overall microstructure of the hot-compacted samples. Powder X-ray diffraction patterns were obtained using a Rigaku MiniFlex X-ray diffractometer with Cr-Kα radiation and analyzed using the Rietveld method implemented in the FullProf Suite software [43].The lock-in thermography (LIT), a technique based on infrared thermometry, was used to measure the anomalous Ettingshausen effect (AEE), which is the Onsager reciprocal to ANE. This technique enables observation of temporal response of the AEE-induced temperature modulation with exceptional sensitivity (<< 1 mK) and spatial resolution (~10 µm), which depends on the IR lens used [23,24,44,45]. Rectangular-shaped samples with a width and thickness of approximately 2 mm and a length of about 15 mm were employed for AEE measurements. The samples were mounted on a Bakelite slab to reduce heat loss via thermal conduction. For enhanced and uniform infrared emissivity, the samples' top surface was coated with high-emissivity black ink (>0.94). In LIT measurements, a square-wave modulated AC charge current was applied with amplitude Jc=1.0 A, frequency f=1-10Hz, and zero offset to the slabs along the longitudinal direction of the sample’s long side. We extracted the first harmonic component from the thermal images and performed Fourier analysis to obtain the lock-in amplitude (A) and phase (ϕ) of the AEE-induced temperature modulation, where the A image represents the distribution of the magnitude of temperature modulation signals, while the ϕ image indicates the sign of temperature modulation and time delay caused by thermal diffusion. This approach enabled selective detection of the thermoelectric response (AEE and Peltier effect) while eliminating Joule heating contributions, and allowing to obtain the isothermal SANE value of the bulk material, comparable to that measured in thin film systems [6,46].Samples with dimensions of about 2 mm × 2 mm × 15 mm were prepared and magnetized using a pulse magnetizer (3T) to ensure a finite remanence state with Mr being the remanent magnetization, and LIT measurements were conducted without applying an external magnetic field. Given that the AEE-generated temperature modulation displays odd dependence on magnetization (M-odd), we extracted and analyzed the corresponding M-odd components of the lock-in amplitude (Aodd) and phase (ϕodd) through the following expressions [21,45,47]:     (1) (2)where A(+Mr) [ϕ(+Mr)] and A(–Mr) [ϕ(–Mr)] show the A (ϕ) value measured at the sample magnetization of +Mr and –Mr, respectively. The magnetization M reversal was done by applying a 3 T magnetic field in the opposite direction to the sample slabs. The values of σ and Sxx were simultaneously measured using the Seebeck Coefficient/Electric Resistance Measurement System (ZEM-3, ADVANCE RIKO, Inc.). Thermal diffusivity D was measured using the laser flash method. Specific heat capacity (cp) was determined from differential scanning calorimetry (DSC, Rigaku Thermo Plus EV02), then the thermal conductivity κ was estimated by multiplying the D and cp values with the density determined using the Archimedes method. The anomalous Hall effect (AHE) was measured using a Physical Property Measurement System (PPMS, Quantum Design). A Hall-bar–type sample with dimensions of approximately 2 × 2 × 0.5 mm³ was used. A DC current (100 mA) was applied along the length direction of the Hall bar, and the transverse Hall voltage was recorded across the width direction. An external magnetic field was applied perpendicular to the current (out-of-plane) and swept between −3 and +3 T.3. Results and Discussion3.1. Structural and Magnetic Properties of Mn1-xCrxAlGeX-ray diffraction spectra of hot-compacted Mn1-xCrxAlGe magnets are shown in Figure 1(a). The main phase corresponds to the C38-MnAlGe phase with the tetragonal P4/nmm (space group 129). Figure S1 shows the fitted spectra and the fitting residuals obtained by Rietveld refinement performed using the FullProf Suite software [43]. Figure 1(b) shows the trend of the lattice constants of the structure obtained from the Rietveld refinement. Both lattice constants, a and c, increase with Cr addition in the composition, in agreement with previous literature [39,41,48], with a total increase between MnAlGe and Mn0.5Cr0.5AlGe of 0.52 % and 0.22 %, respectively, increasing the unit cell volume linearly by 1.28 % for x = 0.5. This asymmetric increase of the lattice constants results in a linear decrease of the tetragonality, c/a, of the unit cell by 0.30 % for x = 0.5. Figure 1. (a) Cr-kα x-ray diffraction (XRD) patterns of the Mn1-xCrxAlGe alloys for different amounts of Cr with the C38 phase indexed reflections. (b) Linear evolution of the lattice constants with Cr content obtained by Rietveld refinement.Analysis of the microstructure of the compacted magnets by SEM reveals a wide distribution of grain sizes, ranging from 0.5 μm to 8 μm, as shown in the backscattered electron (BSE)-SEM images in Figure S2-S7. The grain size distribution, calculated over ~25000 μm², presented in Figure S8, shows that both the average grain size and the standard deviation decrease for the composition with x = 0.2, followed by a gradual increase in samples with higher Cr content. In the case of the samples with Cr content of x = 0.2 and 0.1, some regions with larger grain size can be found, which can be seen in BSE-SEM image of Figure S4 and Figure S5, although the grain size distribution is narrower compared to the other samples, showing that these large grain size regions are not predominant. SEM-EDS mapping was carried out in all samples, as shown in Figure S10, indicating no compositional heterogeneity in the samples. As shown in Figure 2, the main C38-MnAlGe phase in all samples exhibits a (Mn, Cr)-rich composition, ranging from 37.7 at.% to 39.4 at.%. Considering the objective elemental ratio of 1:1:1, the different samples show the following composition: Mn1.18Al0.93Ge0.89, (Mn0.89Cr0.11)1.14Al0.95Ge0.91, (Mn0.79Cr0.21)1.15Al0.94Ge0.91, (Mn0.69Cr0.31)1.13Al0.96Ge0.91, (Mn0.59Cr0.41)1.13Al0.97Ge0.90, and (Mn0.49Cr0.51)1.14Al0.95Ge0.91. Notably, by adding just an extra 5 wt.% of Mn during the initial melting to compensate for evaporation during processing, the targeted Mn-Cr ratio was successfully achieved in all samples.Figure 2. (a) BSE-SEM image and SEM-EDS maps, (b) high resolution high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) and STEM-EDS maps of constituent elements obtained from the Mn0.8Cr0.2AlGe isotropic magnet, confirming the same cite occupancy of Cr and Mn  as well as Al and Ge, and (c) the compositional evolution of the different Mn1-xCrxAlGe hot-compacted magnets obtained from SEM-EDS. The dashed line at 33 at. % serves as a visual reference for the target 1:1:1 MnAlGe alloy composition.Figure 3 presents the hysteresis loops of the magnets, measured under a maximum applied magnetic field of 7 T. The magnetization curves were corrected for the demagnetizing field corresponding to a cubic sample [49,50]. The initial magnetization curves of the MnAlGe and Mn0.9Cr0.1AlGesamples exhibit high susceptibility at low magnetic fields. For the samples with higher Cr content (Figure 3(c–f)), a two-step behavior is observed in the initial magnetization curves. This feature can be attributed to variations in grain size, with grains approaching or below single domain size, and to intrinsic pinning due to changes in crystallographic orientation between adjacent grains in isotropic magnets. A larger fraction of single domain-sized grains (estimated to be ~2.5 μm for MnAlGe [51]) can enhance domain wall pinning at grain boundaries as magnetic domain walls propagate into neighboring misaligned grains [52] As the Cr content increases, the magnetocrystalline anisotropy constant also increases, reaching a maximum of ~1.5 MJ/m3 near x = 0.2 [40], and gradually decreases with further Cr substitution, reaching a similar value for x = 0.45 and x = 0.1. A larger magnetocrystalline anisotropy constant increases the single-domain size. Combined with the smaller average grain size observed for samples with x = 0.2, 0.3, 0.4, and 0.5, this can lead to a larger fraction of grains remaining below the single domain size [53]. This also explains the reduced step observed in the initial magnetization curve at high Cr content. Furthermore, spatial heterogeneity in grain size can also contribute to the two-step behavior of the initial magnetization. As shown in Figure S9, the sample with x = 0 shows a uniform grain size distribution, while the sample with x = 0.2 exhibits heterogeneity, with regions dominated by smaller grains adjacent to regions dominated by larger grains. For sample with x = 0.5, the spatial distribution becomes uniform again, approaching that of x = 0.Figure 3. Evolution of the magnetization curves for the different amounts of Cr substitution in Mn1-xCrxAlGe hot-compacted magnets.The magnetization at 7 T increases with the partial substitution of Mn by Cr, from 0.37 T for MnAlGe up to a maximum of 0.41 T for Mn0.8Cr0.2AlGe and Mn0.7Cr0.3AlGe. This trend is consistent with previously reported results [39,41,54]. The remanence ratio aligns with the expected value for isotropic magnets, reaching approximately 51% of the magnetization measured at 7 T. Similarly, the coercivity follows the trend reported for the anisotropy field [40], with a maximum of 1.14 T for Mn0.8Cr0.2AlGe, closely followed 1.11 T for Mn0.7Cr0.3AlGe. This coercivity change is also closely related to the average grain size of samples, shown in Figure S8, which suggests that the increase of the coercivity may come from a combination of increased anisotropy field [40] and reduced grain size in the samples. Table 1 summarizes the structural and magnetic properties of all samples. These results demonstrate that the developed magnets have sufficiently high coercivity to allow for the evaluation of their transport properties, particularly the SANE in the remanent state.Table 1. Summary of the structural and magnetic properties of Mn1-xCrxAlGe hot-compacted magnets. Cr content Lattice constant a [Å] Lattice constant c[Å] Tetragonality c/a μ0M@7T[T] μ0Mr[T] Mr/M@7T μ0Hc[T] x = 0 3.9136 5.9527 1.5210 0.37 0.19 0.52 0.37 x = 0.1 3.9164 5.9543 1.5203 0.39 0.20 0.51 0.73 x = 0.2 3.9216 5.9594 1.5196 0.41 0.22 0.52 1.14 x = 0.3 3.9271 5.9618 1.5181 0.41 0.21 0.51 1.11 x = 0.4 3.9324 5.9657 1.5171 0.39 0.20 0.51 0.97 x = 0.5 3.9340 5.9659 1.5165 0.35 0.18 0.51 0.643.2. Transverse and Longitudinal Thermoelectric Properties of Mn1-xCrxAlGeFigure 4. (a) Amplitude Aodd and phase ϕodd images obtained by Lock-in thermography at Jc = 1.0 A, f = 1 Hz, and under remanent state of the Mn1-xCrxAlGe magnets. A schematic of the direction of the applied electrical current, Jc, and the anomalous Ettingshausen effect-induced heat current, jq.AEE is shown in (a). (b) Experimental amplitude, circles, and calculated amplitude, line, and (c) measured phase at different measurement frequencies.Figure 4(a) shows the Aodd and ϕodd images of the Mn1-xCrxAlGe (x = 0-0.5) hot-compacted magnets at a f = 1.0 Hz and Jc  = 1A measured in the remanent state under zero external field. A uniform current-induced temperature modulation was observed on the entire surface of the slabs. To quantitatively estimate SANE from LIT measurements, the frequency dependence of the Aodd per unit charge density i.e., Aodd/jc was measured and is shown in Figure 4(b). The Aodd values at each f were determined by averaging the Aodd values within the marked area (1.2 × 4.5 mm2) as shown in Figure 4(a). The magnitude of Aodd/jc decreased gradually with increasing f, this trend was well reconstructed by solving the one-dimensional heat diffusion equation in the frequency domain as indicated by the solid curves in Figure 4(b) (See supplementary information S12). Based on the fitting curve in Figure 4(b), the steady state values of Aodd/jc, corresponding to f → 0 Hz (i.e., Aodd,0Hz/jc), was calculated. The sign of the AEE-induced temperature modulation on the surface for all slabs is negative (ϕodd ~180°), as plotted in Figure 4(c). This suggests a negative sign for SANE [23].Figure 5. (a) anomalous Nernst coefficient SANE,  (b) electrical conductivity σ, (c) thermal conductivity κ, and (d) the anomalous Nernst coefficient figure of merit zANET as defined in equation (4) obtained from the Mn1-xCrxAlGe magnets. All measurements were performed at 300 K.The anomalous Ettingshausen coefficient ΠAEE is estimated from the steady state as follows;[24]  (3)where t is the thickness. SANE is evaluated using the reciprocal relation as ΠAEE = 𝑆ANE𝑇. Mr is precisely measured to estimate the SANE at the remanent state. Noteworthy that the conversion of AEE into SANE itself does not introduce any additional systematic error; because it is reciprocal relation in the liner-response. Rather, the overall uncertainty is dominated by the quantitative extraction of the AEE amplitude from the calibrated LIT thermal maps (e.g., emissivity/calibration and heat-loss boundary conditions), while the conversion step contributes only standard error propagation. The estimated value of SANE for Mn1-xCrxAlGe (x=0-0.5) magnets is illustrated in Figure 5(a). The absolute value of SANE increases from -0.22 ± 0.02 μVK-1 to -0.74 ± 0.02 μVK-1 for 0.1 at. % of Cr doped in Mn1-xCrxAlGe alloy. However, SANE is gradually decreased for x > 0.1 in Mn1-xCrxAlGe alloys. The dimensionless figure of merit for transverse thermoelectric conversion due to ANE is given by the following expression [23,24,44,47]: (4)where σ, κ, and T are electrical conductivity, thermal conductivity, and absolute temperature respectively. Figure 5(b) shows the σ values, which are likely in between 0.5 to 0.6  106 Sm-1 for all Mn1-xCrxAlGe alloys, with no clear trend with Cr content. However, the κ values are slightly higher for x=0.2 and 0.3 compositions. To understand the total κ, the electronic contribution κe and the phonon contribution κph were estimated using the Wiedemann–Franz law, (5)where L is the Lorenz number (2.4410-8 WΩK-2) [47,55]. Consequently, κph is evaluated as the difference between the total thermal conductivity κ and the electronic contribution κe.  The κe presents a small variation between compositions, influenced by the stability of the electrical conductivity, while the κph increases for the higher Cr content, which dominantly contributes to the total κ values as shown in Figure S11. Finally, zANET is estimated using the measured SANE, σ, and κ values and shown in Figure 5(d). The magnet with a Cr content of x=0.1 shows the highest zANET among the different compositions due to the significant improvement in SANE and lower κ values.It is worth noting that, although the samples used for thermoelectric and magnetic properties measurements differ in dimensions and aspect ratios as described in the experimental section, an appropriate demagnetization correction factor, based on each sample geometry [49,50], was applied to ensure accurate determination of M@7T and Mr ​. 3.3. Evaluation of contribution factors for ANE in Mn1-xCrxAlGe alloysThe primary contribution in ANE/AEE for the Mn1-xCrxAlGe magnets is described as follows.SANE can be divided into two constituents using the linear response equation [23,24,44]: (6)where ρxx is the longitudinal electrical resistivity, αxx (αxy) is the diagonal component (off-diagonal component) of the thermoelectric conductivity tensor and  is the anomalous Hall resistivity. The SI component is often referred to as the intrinsic part of ANE, which directly converts temperature gradient into a transverse electric field through αxy , whereas SII signifies the transverse voltage induced by the Seebeck effect carrier flow bent by the anomalous Hall effect . The SII term can be written as (7)where  (8)with θAHE being the anomalous Hall angle [47][21,44]The Sxx of Mn1-xCrxAlGe alloys are shown in Figure 6(d). All the alloys exhibit positive Sxx values, indicating the p-type semiconductor nature, where holes are the majority charge carriers [56]. The Sxx values increased with Cr substitution up to x = 0.2, then decreased gradually. The maximum Sxx value of 18.5 µVK-1 is obtained for the Mn0.8Cr0.2AlGe hot-compacted magnet, which is comparable to that reported for the same composition in thin films [33].Figure 6. (a) Magnetic field dependence of  ρAHE, (b) the anomalous Hall angle θAHE, (c) the transverse thermoelectric conductivity αxy, (d) the longitudinal Seebeck coefficient Sxx, and (e) contributions of SI and SII to SANE as defined in equation (6) for Mn1-xCrxAlGe (x = 0, 0.1, and 0.2) alloys at 300 K. Figure 6(a) shows ρAHE as a function of H for the Mn1-xCrxAlGe (x = 0, 0.1, and 0.2) alloys. In this study, the contributions from the ordinary Ettingshausen/Nernst effect are assumed to be negligible, since the ρAHE curve closely resembles the hysteresis loop [21,25]. The values of ρAHE at µ0H = 3 T were considered as the AHE contribution, and the corresponding θAHE values were evaluated using equation (7), as shown in Figure 6(b).  The θAHE values are positive for all Mn1-xCrxAlGe (x = 0, 0.1, and 0.2) alloys. Figure 6(c) shows  estimated by substituting SANE, ρxx, Sxx, and θAHE into equation (6). The αxy values are negative, showing the maximum absolute value for the Mn0.9Cr0.1AlGe sample (Figure 6(d)). Finally, the SI and SII contributions to ANE are depicted in Figure 6(e). Along with SI, SII component also shows a negative sign, attributed to the positive Sxx, and together they collectively contribute to the overall SANE. The magnitude of SI is higher than SII in all samples, showing that the ANE is dominantly governed by the SI component due to a moderately domination of αxy. The substitution of Cr can enhance  not only through enhancement of  but also , which could include intrinsic (Berry-curvature-related) and extrinsic (skew/side-jump) contributions. Prior studies on MnAlGe and (Mn–Cr)AlGe films reported that Cr substitution increases the positive and simultaneously induces a sign reversal of (from positive to negative), so that the two terms contribute with the same (negative) sign, leading to an enhanced negative  [33]. A plausible microscopic origin for the sign reversal is provided by the Mott relation , which links to the energy derivative of the transverse electrical conductivity [57]. In MnAlGe, exhibits a sharp peak structure near , and Cr substitution effectively reduces the valence electron number, shifting toward lower energies and decreasing ; consequently, crossing a region where changes sign can naturally yield a sign change in , consistent with experiment [33,58]. Furthermore, the conductivity scaling behavior reported for MnAlGe-based films is consistent with the “moderately dirty” regime where intrinsic Berry-curvature and/or side-jump mechanisms are expected to dominate over skew scattering, suggesting that the Cr-induced change in is primarily governed by electronic-structure tuning with possible additional disorder-related contributions [33,59].It is worth noting that all samples exhibit an interesting phenomenon of a negative value SANE with a large and positive value of Sxx in bulk permanent magnets, while still maintaining finite remanence and sufficiently large coercivity. In contrast, earlier reports [22,26–28] on permanent magnets, including SmCo5, Sm2Co17, and Nd2Fe14B-type magnets, have shown negative Sxx values, which limited the choice of counterpart materials to p-type thermoelectric materials for constructing ATML device. The present results, however, demonstrate the possibility of using n-type thermoelectric materials as counterparts to permanent magnets in ATML devices, thereby broadening the research scope and opening new opportunities for achieving high transverse thermoelectric power devices.4. ConclusionIn summary, the extrinsic magnetic properties and transverse thermoelectric properties of (Mn,Cr)AlGe isotropic bulk magnets have been assessed. By basic control of grain size and avoiding secondary soft magnetic phases, it was possible to achieve a maximum coercivity of 1.15 T for a composition of Mn0.8Cr0.2GeAl, while keeping a remanence of 0.22 T, accounting for 54% of the saturation magnetization. Electrical conductivity does not show a clear trend with Cr substitution, while the thermal conductivity shows a similar behavior as that of coercivity, with a maximum for a Cr substitution of x = 0.2 and 0.3. The evaluation of the SANE by LIT shows more than a 3-fold increase from -0.22 ± 0.02 μVK-1 for the pristine MnAlGe alloy up to -0.74 ± 0.02 μVK-1 for the Mn0.9Cr0.1AlGe alloy, followed by a progressive decrease for higher Cr content. On the other hand, the Sxx exhibits an increasing trend with rising Cr content, reaching a maximum value of 18.5 μVK-1 for the Mn0.8Cr0.2AlGe composition, followed by a decline upon further Cr addition. These results exceed those previously reported in thin films and can compete with those of commercial Nd-Fe-B based sintered magnets, paving the way to the development of rare-earth-free permanent magnet materials with unique combinations of Seebeck and anomalous Nernst coefficients values for “thermoelectric permanent magnet” applications.Supporting InformationSupporting Information is available from the Wiley Online Library or from the author.AcknowledgementsThe authors thank Y. Sakuraba and N. K. Gupta for valuable discussions. 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