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M. Parzer, T. Schmid, F. Garmroudi, A. Riss, [T. Mori](https://orcid.org/0000-0003-2682-1846), E. Bauer

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in M. Parzer, T. Schmid, F. Garmroudi, A. Riss, T. Mori, E. Bauer; Measurement setup for Nernst and Seebeck effect at high temperatures and magnetic fields tested on elemental bismuth and full-Heusler compounds. Rev. Sci. Instrum. 1 April 2024; 95 (4): 043906 and may be found at https://doi.org/10.1063/5.0195486[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Measurement setup for Nernst and Seebeck effect at high temperatures and magnetic fields tested on elemental bismuth and full-Heusler compounds](https://mdr.nims.go.jp/datasets/f27695db-19e2-496a-9953-ed0e82487ae4)

## Fulltext

Measurement setup for Nernst and Seebeck effect at high temperaturesand magnetic fields tested on elemental Bismuth and full-HeuslercompoundsM. Parzer,1, a) T. Schmid,1, b) F. Garmroudi, A. Riss,1 T. Mori,2, 3 and E. Bauer11)Institute of Solid State Physics, Technische Universität Wien, 1040 Vienna,Austria2)International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science(NIMS), Tsukuba, Japan3)Graduate School of Pure and Applied Science, University of Tsukuba, Tsukuba,JapanIn this work, a measurement setup to study the Seebeck and Nernst effect at high temperatures and highmagnetic fields is introduced and discussed. The measurement system allows for simultaneous measurementsof both thermoelectric effects up to 700K and magnetic fields up to 12T. Based on theoretical concepts,measurement equations are derived, that counteract constant spurious offset voltages and and therefore inhibitsystematic errors of the measurement setup. The functionality is demonstrated on polycrystalline samplesof elemental bismuth as well as various full-Heusler materials, exhibiting an anomalous Nernst effect. In allsamples, the measured Seebeck and Nernst coefficient aligns excellently with reported values. This allows forfuture research to substantially extend the measured temperature and field intervals, which are commonlylimited to temperatures below room temperature. For the first time, the thermoelectric and thermomagneticproperties of these materials are reported up to temperatures of 560K.IntroductionResearch on thermoelectric effects constitutes a broadfield of physical sciences today, with topics reachingfrom fundamental studies up to functional prototypesand commercialization of thermoelectric devices.1–3 Foryears, most of the application-based research has beenfocused on the longitudinal thermoelectric effect, namelythe Seebeck effect.4 Only in the last few decades, sig-nificant effort has been made towards the application oftransverse voltage generation, which can be achieved forexample via the Nernst effect.5 Similar to the well-knownHall effect, an electrical voltage emerges perpendicular tothe perpetrating current, if a magnetic field is applied.This is caused by the deflection of the charge carriers bythe Lorentz force. The Nernst effect has only recentlygained a lot of attention due to the discovery of giantanomalous Nernst signals in topological materials.6–8 Formost of these cases the large signal stems from a non-trivial band structure, involving topological bands closeto the Fermi level EF and originates from the result-ing Berry curvature. Moreover, the anomalous contri-bution can be large even at elevated temperatures aboveT = 300K, bringing this effect closer to possible appli-cations. A recent study by Uchida and Heremans out-lined several advantages of energy harvesting based ontransverse voltages compared to the Seebeck effect.9 Toexplore promising materials for application, but also forfundamental research, reliable and precise measurementsof thermoelectric effects are indispensable. While build-ing an experimental setup for Seebeck measurements isa)Electronic mail: michael.parzer@tuwien.ac.atb)Electronic mail: ts.schmid94@gmail.comJe,xB∇Φ∇xT ∇xΦ ∇x T Je,x∇xΦBJe,xJQ,xB∇ΦBz∇xT ∇yΦBz ∇xT ∇yΦBzJQ,x∇ΦSeebeck effectNernst effect Hall effectElectrical current(a) (b)(c) (d)Je,xFigure 1: (Thermo)electric effects Schematic of theunderlying currents and gradients of the four differenteffects: a) Seebeck effect: A gradient in the electricalpotential arising from a temperature gradient; b)Voltage-driven electrical current: The motion ofelectrons due to a potential gradient in the absence of atemperature gradient c) Nernst effect: Perpendicularvoltage gradient arising in the presence of a magneticfield and a temperature gradient orthogonal to eachother. d) Hall effect: Perpendicular voltage arising inthe presence of a magnetic field and an electricalcurrent normal to each other.simple and compact devices are commercially available,measuring the Nernst effect is more challenging. This ismainly due to lower voltage signals and the requirementof a controllable magnet that can reach reasonably highmagnetic fields. Hence, there are significantly less Nernstmeasurement data published than for the Seebeck coef-ficient. For temperatures above 400K there are, to themailto:michael.parzer@tuwien.ac.atmailto:ts.schmid94@gmail.com2best of our knowledge, no published Nernst data so far.This work documents the process of building, optimizingand validating a custom-built measurement setup thatcan perform simultaneous Seebeck and Nernst effect mea-surements at high temperatures and high magnetic fieldsup to 12T. Additionally, the theory of both effects is dis-cussed, the underlying measurement framework is elu-cidated and the underlying measurement principles forhigh temperature measurements and noise reduction arederived. To confirm full functionality of the setup, poly-crystalline samples of constantan, bismuth and multiplefull-Heusler compounds were synthesized, measured andanalyzed. The data are presented and compared with lit-erature data and reference measurements in the resultssection.I. Thermoelectric transportThe electrical current in a given material is defined bythe two conductivity tensors σ̂ and α̂, the electrical field~E and the temperature gradient ~∇T :~Je = σ̂ · ~E − α̂~∇T. (1)In open circuit conditions, hence Je = 0, the equationsimplifies to an expression for the electrical field ~E:~E = σ̂−1 · α̂ · ~∇T. (2)In other words, an electrical field in a material can becaused by a temperature gradient and is proportional tothe ratio of the thermoelectric conductivity to the elec-trical conductivity. It is a materials property closely con-nected to the electronic structure and can be derived fromBoltzmann theory to10σ̂−1α̂ = −π2k2BT3eσ̂−1(∂σ̂(E)∂E)|E=EF. (3)Its magnitude is given by the change of the conductiv-ity at the Fermi energy EF for infinitesimal shifts of thechemical potential divided by the total electrical conduc-tivity.Seebeck coefficientComing back to Equation 2, only considering a tem-perature gradient in the x-direction, the field in the x-direction yields:Ex = αxx/σxx∇xT. (4)This proportionality factor regarding the electrical fieldEx is denoted as Seebeck coefficient S = σ−1xx αxx. Forsmall temperature difference ∆T between the contacts,so that S(Tmax) ≈ S(Tmin), the voltage signal originatingfrom the Seebeck coefficient is given byUx = Sxx∆T , (5)and is independent of any dimensions, as long as the volt-age is measured at the same position as the temperaturegradient.Nernst effectSimilar considerations can be made for the electricalfield in the y-direction Ey. Again, setting the tempera-ture gradient ∇xT and demanding Je,x, Je,y = 0, a resultfor the Nernst signal eN in dependence of ∇xT can bederived:eN = Ey/∇xT =αxyσxx − σxxαxyσ2xx + σ2xy. (6)Using the Hall angle tan (θH) = σxy/σxx, Equation 6 canbe expressed in a more illustrative way:11eN = αxy/σxx + S · tan (θH). (7)Thus, two terms can lead to a finite transverse voltagesignal eN caused by a temperature gradient in x. Oneis proportional to the Seebeck coefficient and the Hall-angle, i.e. the ratio of transverse and lateral electricalconductivity, while the other one is directly proportionalto the off-diagonal matrix element of the thermoelectricconductivity tensor αxy. In isotropic materials the off-diagonal elements of both tensors, α̂ and σ̂ are generallyzero. When applying a magnetic field Hz, however, theLorentz force leads to deviation of the charge carriers,leading to finite values for αxy and σxy, hence to a fi-nite voltage signal eN 6= 0. Consequently, a temperaturedifference in x-direction leads to a thermovoltage eN per-pendicular to it. A sketch illustrating the various electricand thermoelectric effects is provided in Figure 1. Theproportionality constant in y-direction N = eN/B is de-noted as Nernst coefficient. On the contrary, the Nernstsignal eN = N · B is proportional to the magnetic fluxdensity B and can be derived from Boltzmann transportfor one band to10eN = −Bπ23k2BTm∗∂τ∂E∣∣E=EF, (8)depending on the effective mass m∗ and the energyderivative of the scattering time τ at EF. The mea-surement equation for the Nernst signal in the y-direction originating from a temperature gradient in thex-direction and a given magnetic field in z-direction canbe written as:Uy = NHz∆Tx∆y∆x, (9)with the distances between the Nernst contacts ∆y andbetween the Seebeck contacts ∆x. Since for magneticmaterials B = µ0H+µ0M , the Nernst signal can furtherbe split into two components12eN = µ0HzQo + µ0MzQa, (10)3where µ0 is the vacuum permeability, M is the magneti-zation and Qo, Qa are the proportionality factors for theordinary and the anomalous Nernst signals, respectively.Hence, the term anomalous Nernst signal encompassesall effects that scale with the magnetization M .II. Measurement equationsTo analyze the dynamic voltage signals associated withthe Seebeck and Nernst effects obtained using the mea-surement setup described here, we can modify Equations(5, 9). This involves introducing mathematical modelsand optimizations to eliminate parasitic signals. In thefollowing, the measurement setup and the measured volt-ages will be illustrated with the help of the sketch of themodel setup depicted in Figure 2. As can be seen in Fig-T1T2ColdHotHT4T5T3PtRhPtCu UN1UN2US1US2yxzFigure 2: Model setup for simultaneous Nernst-and Seebeck measurements The sample isconnected to two R-type thermocouples at the bottomand three copper wires are contacted on the top. Thevoltages are measured using two two-channelnanovoltmeters and are denoted as UN1, UN2, US1, UN2.Each wire’s contact point with the sample can beassigned an individual temperature T1, T2, T3, T4, andT5. The magnetic field is applied in z-direction while atemperature gradient is created along the x-direction,indicated by the red and blue surfaces.ure 2, there are in total five electrical contacts to the sam-ple. Two R-type thermocouples are used to measure theSeebeck coefficient and temperature gradient at the bot-tom of the sample in the x-direction. Three copper wiresare contacted onto the top of the sample for the measure-ment of the parallel voltage gradient as well as the volt-age in the y-direction. The measurements are conductedusing two dual-channel Keithley 2182A nanovoltmeterswhich can accurately measure two different voltage sig-nals each, if used in one electrical circuit. The externalmagnetic field is applied in the z-direction while a tem-perature gradient can be applied along the x-directionof the sample. Test measurements have shown that pos-sible spurious temperature gradients in the y-directionare negligible compared to the temperature gradient inx-direction resulting in T3 ≈ T4 and T5−T4 >> T4−T3.Using Equations (5, 9), we can explicitly write down thevoltages US1, US2, UN1 and US2 measured by each channelof the sketched contacts for a given temperature gradient∇xT and magnetic field Hz. Again, ∆x and ∆y denotethe distances between the voltage contacts for the See-beck coefficient (distance between T5 and T4) and theNernst contacts (distance between T4 and T3)US1 = (SX − SPt)(T2 − T1), (11)US2 = (SX − SRhPt)(T2 − T1), (12)UN1 = (SX − SCu)(T5 − T4) +NHz∆y∆x(T5 − T4), (13)UN2 = (SX − SCu)(T5 − T4). (14)US1 and US2 are the Seebeck voltage measured over thePt wires and the PtRh%13 wires respectively.Measuring the Seebeck coefficientIn this configuration, the sample Seebeck coefficientSX, measured using the thermocouple, can be derivedas:SX = SRhPt −SRhPt − SPt1− US1US2, (15)with SA, SB being the Seebeck coefficient of the respec-tive thermocouple wires and US1/US2 being the ratio ofthe measured voltages.Measuring the Nernst coefficientA similar equation can also be derived for the measure-ment of the Nernst coefficient:UN1UN2= 1 +∆y∆x(NHzSCu − SX). (16)Possible systematic measurement errors from non-parallel contacts can then be eliminated by comparingEquation 16 for two measurements at different values ofHz. By choosing Hz = 0 for one of them, which cor-responds to a reference measurement without magneticfield, the equation is changed to:UN1UN2(Hz)− UN1UN2(0) =∆y∆x(NHzSCu(Hz)− SX(Hz)).(17)Solving for N yields:N =∆x∆y(SCu(Hz)− SX(Hz)Hz)(UN1UN2(Hz)− UN1UN2(0)).(18)SX(Hz) is calculated by using Equation 15 in presenceof a magnetic field Hz, while SCu(Hz) is calculated by4using a fit of experimental data for 70K< T < 1500Kreported in Ref.13, under the reasonable assumption thatits dependence on magnetic field is negligible, SCu(Hz) ≈SCu(0).Elimination of spurious offset voltagesIn real conditions, Equation 16 and Equation 18 tendto be error-prone when applied to singular measurements,resulting in measurement errors due to spurious offsetvoltages that can affect each measured signal differentlyand independently. These spurious voltages likely stemfrom temperature differences at any electrical connectionbetween different materials or from atmospheric noisealong the connectors and can usually not be completelyavoided at elevated temperatures.14 To eliminate the ef-fect of spurious offset voltages, US1 and US2 are measuredat multiple temperature gradients. This way, the slopeof ∂Ui/∂∆T is obtained, which is independent of anyoffsets. Ultimately this allows to express Equation 15 as:SX = SRhPt −SRhPt − SPt1− ∂US1∂US2(19)This transition mathematically eradicates systematic er-rors caused by offset voltages of any source as longas they remain constant during each measurementand is especially important for measurements at hightemperatures.15–18Similar considerations can be made for the measurementof the Nernst coefficient. Proceeding from Equation 18,it is again possible to replace the ratios of UN1 and UN2with their respective derivatives, yielding the followingimproved measurement equation for the Nernst effect:N =∆x∆y(SCu(Hz)− SX(Hz)Hz)(∂UN1∂UN2(Hz)− ∂UN1∂UN2(0)).(20)With these equations, a dynamic measurement methodfor the simultaneous measurement of N and S can berealized to measure the quantities not only faster butespecially more accurate than with conventional steady-state measurement methods.5III. Experimental setupTo measure the Nernst and Seebeck effects of a givenmaterial above room temperature and high fields, themeasurement setup must meet the following require-ments:i) High-field (superconducting) magnet for consistenthigh magnetic fields as regular electromagnets canonly reach fields up to 1.6− 2T.19ii) Stable, variable temperature control and control oftemperature gradients and high-temperature resis-tanceiii) Reliable and accurate measurements of the temper-ature, voltages and temperature gradientsTo accomplish those preconditions, extraordinary tem-perature isolation of the sample space from the super-conducting coil must be assured. To keep the coil in itssuperconducting state below Tc, a reliable cooling sys-tem is needed. Our experiment is designed in a way tofulfill these requirements, while still allowing for a simplemeasurement routine and relatively easy exchange of thesample holder and the samples. A photo, as well as a 2D-sketch of the cut of our measurement setup are presentedin Figure 3 a, b.Measurement environmentThe large magnetic field is achieved using a commer-cially available 4He refrigeration system from CryogenicsLtd containing a superconducting Nb-Ti coil that canreach fields up to 12T. The setup has a 65mm hole thatis accessible from the outside and can be readily used.The homogeneity of the magnetic field was tested usingnuclear magnetic resonance on 63Cu and is above 99.5%of the set value around the center 0 ± 1.5 cm. To reachhigh temperatures inside the coil, without warming it upabove its critical temperature Tc ≈ 9.5K, we employ highvacuum to the sample chamber down to 10−6 mbar andfixed the chamber so that an air gap remains between thechamber and the cryostat. Moreover, thermal decouplingis further facilitated by water cooling at the ends of thesample chamber combined with forced air-flow throughthe space between the sample chamber and the surround-ing cryostat containing the coil.Sample holderAs sketched in Figure 3 b, the measurement setup in-sert is designed as a rod that can be inserted into thesample chamber surrounded by the superconducting coil.To reduce thermal conductivity from the connectors andwires, the sample rod has a total length of around 1.2mand the connection to the sample holder is made withfour thin steel studding, with a diameter of 2mm. Therod is a hollow cylinder made of brass and the signal wiresare managed inside the rod to give additional shieldingand mechanical stability. A schematic of the upper partwater coolingair hosevacuum600 Kforced airflow4 Kself-coolingsc-coil system(a)(b)Figure 3: Experimental setup a) Image of theexperimental setup and b) sketch of the longitudinalsection of the same. The high temperature differencebetween the superconducting coil ( 4K) and the sampleholder (up to 700K) is achieved by a high vacuum of upto 10−6 mbar in the sample space, extrinsic watercooling of the sample space and forced airflow at theboundary.of the sample holder is depicted in Figure 4. Its coreis a solid copper block, accommodating the sensors andheaters, the thermocouples as well as the sample. It as-sures good heat anchoring of all parts, as elemental cop-per features a very high thermal conductivity of up toκCu = 400W/mK above room temperature.20 The basetemperature is established with two heating cartridges(1), heated with a maximum output power of 5W, whichare inserted into the copper block. To measure the basetemperature, a resistive PT-100 temperature sensor (3) isused, which is inserted into the copper block right belowthe sample. To facilitate a stable temperature gradientand isolate the sample electrically, it is placed on a Macorplate (7), which is screwed onto the copper block. Ma-cor is an electrically insulating ceramic with a very lowthermal conductivity of κMacor = 1.5W/m·K.21 The tem-perature gradient across the sample is established by lo-cally heating on one side using a high-temperature strain-gauge (6) with a resistance of 120Ω. On the other end of6(1) heating cartridge(5) thermocouple holder(2) thermocouples(3) PT-100(7) Macor platesample(6) heater -strain gauge(4) thermal couplingNernst contactsFigure 4: Sample holder 2D-sketch of the sampleholder at the top of the sample rod. The differentcomponents (1-7) are labeled in the figure and describedin more detail in the text.the sample, an extrusion of the copper block (4) is goingthrough the Macor plate, thermally coupling the sampleto the base temperature of the copper block, acting asa heat sink. The temperature difference is measured us-ing two R-type thermocouples (2) which are pressed ontothe sample by the thermocouple holder (5). They areconnected thermally as well as electrically to the sam-ple and the voltages are measured across the wires ofthe same material (Pt-Pt and Pt13%Rh-Pt13%Rh). Thisway, the Seebeck coefficient of the sample can directly beobtained using Equation 19. For type-R thermocouplesthe temperature-dependent Seebeck coefficients of the in-dividual wires (Pt, Pt13%Rh are very well known andreference curves are available.13,22. For the measurementof the Nernst coefficient, three copper wires are attachedto the sample via spot-welding or silver paste. The wiresare placed in a triangular configuration onto the sampleas sketched in Figure 2. Two voltages are measured, oneparallel to the heat current and one diagonal, includingboth the longitudinal as well as the transverse signal.As described earlier, a dynamic measurement method isused for the determination of the Seebeck and Nernst co-efficients. The base temperature of the whole setup is setvia the cartridge heaters. One side of the sample is thenheated until a sufficient and stable temperature gradientis reached. As the heater is turned off, the nanovolt-meters measure the signal continuously, determining thevoltage signals for a multitude of different temperaturegradients. Fitting the slope of the voltage US1 versus US2linearly, gives the correct values of S and N at the re-spective temperatures, when plugged in the correspond-ing equation. The dynamic measurement at a certain Tand H can be repeated to average of the coefficient andachieve a reduction of the noise. Figure 5 shows a sketchof the time-dependent measurement parameters during ameasurement cycle.base temperaturetemperature gradientmagnetic fieldtimeFigure 5: Sketch of the measurement process Thethree graphs show a sketch of the time dependence ofthe base temperature, the applied temperaturedifference on the sample and the magnetic field,respectively. The yellow lines in the middle panelrepresent the time-intervals in which the thermoelectricvoltages are measured.Measurement softwareA measurement software including a user interface wasdesigned to control and automate the measurement pro-cess introduced above. The communication with themeasurement devices is managed via individual socketservers for each device, respectively. The main programis written in Python3 and reads the starting parametersand measurement program from the user input and thencontrols the whole measurement process. The software isdiscussed in more detail in Ref.23, including snapshots ofthe user interface.7IV. Experimental resultsTo ensure the functionality of the here-presented mea-surement setup, different samples were synthesized, mea-sured and compared with available data in literature.Insert discussion of measurement error here All samplespresented here were prepared as polycrystalline ingots us-ing high-frequency induction melting. For this process,the samples were weighed in using high-purity bulk ele-ments and a scale with an accuracy of 10µg and meltedwith a mass loss below 0.1%. The samples were con-firmed to be single-phase and in the correct crystal struc-ture by X-ray diffraction measurements.ConstantanThe material constantan is most commonly used as ref-erence material for high-temperature Seebeck measure-ment setups.13,24–27 Therefore, it was also chosen as ref-erence material for the Seebeck coefficient here becausereliable reference data of this material exist. Constan-tan is the commercial name for a metallic Cu-Ni alloyconsisting of roughly 55% Copper and 45% Nickel.28 Itis well-known and named after its constant temperature-dependent resistivity, but also exhibits a sizeable See-beck coefficient for a metal, due to strong interbandscattering.29 In Figure 6 the comparison of the mea-surement data for constantan obtained at our lab withreference curves from two different round robin studiesis given.24,25 The measurement data obtained from thenewly built setup are in excellent agreement with thereference data as well as with the data from the ZEM-3measurement on the same sample piece.BismuthElemental bismuth displays the highest measuredvalue of the absolute Nernst coefficient of all materi-als and is therefore an optimal candidate for first testmeasurements.30 Already in their original publication,Nernst and Ettinghausen noted the extraordinary highNernst coefficient of Bi compared to other elemental ma-terials such as nickel, cobalt, iron and antimony.31 It fea-tures a semi-metallic electronic density of states with veryhigh-mobility charge carriers and exhibits a relativelyhigh thermoelectric performance and a strong magnetic-field-dependence of the Seebeck coefficient S(B).Figure 7 a,b shows our measured values of the field-dependent Seebeck and Nernst coefficients of polycrys-talline Bi for different temperatures. For comparison,the measurement results from Hamabe et al.32 at 290Kare plotted as grey crosses. As they report the magneticfield dependence of the thermoelectric effects in polycrys-talline bismuth up to 290K, their data can be best com-pared with our measurement results. Taking into accountthe temperature dependence of S, N for Bismuth andalso the fact that different samples from different labswere measured, very good agreement between the twodata sets was found.Seebeck coefficient (µV/K)-55-50-45-40-35 Lowhorn et al. 2009Z. Lu et al. 2009ULVAC ZEM-3Nernst effect setupTemperature (K)300 350 400 450 500ρ (µΩcm)404550Figure 6: Seebeck coefficient and resistivity ofConstantan The upper panel shows the measuredSeebeck coefficient results of Constantan as function oftemperature compared with reference data of Z. Lu etal. 200924 and N. Lowhorn 2009 et al.25. The solid linesdepict the common curve (expectation value), while thedashed lines visualize the standard deviation derivedfrom the round-robin measurements. The lower paneldepicts temperature-dependent resistivity ρ(T )measured with the ULVAC ZEM-3.Heusler compoundsTo verify the capability of the measurement systemto measure smaller values of the Nernst coefficient ac-curately, we studied different full-Heusler compounds,which have been reported to exhibit anomalous Nernstsignals.Co2MnAl0.63Si0.37Co2MnZ (Z=Al,Ga) compounds have been predictedto exhibit Weyl points near EF, expected to give riseto a large anomalous Nernst effect due to the Berrycurvature.33–35 Sakuraba et al. experimentally validatedthat for Co2MnAl the substitution of Al with Si leads toa shift of the position of the Fermi level EF and improvedL21 atomic ordering. This leads to a significant enhance-ment of the anomalous Nernst effect.35 The highest valueof the Nernst signal, 5.7µV/K at 300K was reportedfor 30 nm single crystal films of Co2MnAl0.63Si0.37 an-nealed at 700 C and measured at room temperature andsaturates at around 1T. As crystalline order is pivotalfor the Nernst coefficient in this system, they found aclear correlation between annealing temperature and themagnitude of the Nernst signal eN . As the crystallineordering process might occur differently in our bulk sam-ples, the samples were heat-treated at 900C to ensuregood chemical ordering. The polycrystalline bulk sam-ple shows very similar Nernst signals, indicating that the8Seebeck coefficient (µV/K)-140-120-100-80-60300 K320 K340 K361 K381 K401 KBismuthMagnetic field (T)-10 -5 0 5 10Nernst signal (µV/K)-200-1000100200300 K320 K340 K361 K381 K401 KBismuthHamabe et al.290 KHamabe et al.290 K(a)(b)Figure 7: Measurement results for elementalBismuth: The upper panel depicts the measuredNernst signal of Bismuth as a function of magnetic fieldfor different temperatures. Panel b) shows themeasurement results for the Seebeck coefficient ofBismuth as a function of magnetic field.higher annealing temperatures had no further effect onthe Nernst coefficient. Furthermore, different from liter-ature, the Nernst coefficient of this sample was measuredup to 560K.Fe2 based Heusler compoundsAn anomalous Nernst effect has also recently beenobserved for various Fe-based Heusler compoundsFe2YZ (Y = Co, Ni; Z = Al/Ga)36. Similar toCo2MnAl0.63Si0.37, a large intrinsic Berry curvature isresponsible for the sizable anomalous Nernst effect inthese compounds. Hence, we prepared and measuredFe2CoAl and Fe2NiAl for comparison with the publishedresults. Notably, while Mende et al. investigated singlecrystals synthesized via the Bridgeman method36, ourmeasured values on polycrystalline samples are in excel-lent agreement with the published results. Comparedto Co2MnAl0.63Si0.37, the Nernst coefficients are consid-erably lower but still a characteristic data-set could beobtained using our measurement setup. For both sam-ples, an increase of N(T ) with rising temperature wasobserved in agreement with the prediction of Mende etal..36Nernst signal (µV/K)-6-4-20246300 K320 K340 K360 K380 K400 K420 K440 K460 K480 K500 K520 K540 K560 KMagnetic field (T)-2 -1 0 1 2Seebeck coefficient (µV/K)-55-50-45-40-35Co2MnAl0.63Si0.37Co2MnAl0.63Si0.37(a)(b)Figure 8: Measurement results forCo2MnAl0.63Si0.37 Panel a) depicts thefield-dependent Nernst effect of of Co2MnAl0.63Si0.37.In panel b) the field-dependent Seebeck coefficient isshown.Fe3Z-based compoundsAnother recent publication8 provided detailed theoret-ical and experimental results for the anomalous Nernsteffect of Fe3Z (Z=Al/Ga).8 It was shown that the 25%substitution of aluminum or gallium in α-Fe dramati-cally increases the anomalous Nernst effect by a factorof more than 10, compared to undoped α-Fe. The re-ported maximum value of the anomalous Nernst effectof Fe3Al is around 4µV/K at room temperature. Dataobtained on our bulk Fe3Al are in good agreement withRef.8 but reach the maximum value at higher fields ofaround 1T, very similar to the other polycrystalline bulksamples discussed above. To corroborate our results onFe3Al, a test measurement of the same sample piece ofFe3Al was conducted at the CNRS in Paris. The compar-ison of our measurement results with the data obtainedat their low temperature measurement setup is depictedin Figure 10. The measurement setup is designed as insetfor a PPMS and is similar to the setup described in thesupplemental information of Ref.37. Excellent agreementbetween the measurement data was achieved, regardlessof the significant differences in the experimental setupand measurement technique.9Magnetic field (T)-2 -1 0 1 2Nernst signal (µV/K)-3-2-10123Fe2NiAl - this workFe2CoAl - this workFe2CoAl - Mende et al.Fe2NiAl - Mende et al.Temperature (K)100 200 300 400 500 600Seebeck coefficient (µV/K)-30-20-100T = 300 K(a)(b)Figure 9: Measurement results for Fe2YAlMeasurement data of the Nernst coefficient of Fe-basedHeusler alloys compared with available data from theliterature.36 b) Measurement results of the Seebeckcoefficient of Fe2-based Heusler alloys as function oftemperature for different values of magnetic field.V. ConclusionSummarizing, the two thermoelectric effects, namelythe Seebeck and the Nernst effect were discussed andthe respective measurement equations were derived. Weexamined the experimental setting required for the mea-surement at high fields and temperatures and the imple-mentation thereof in our setup. The measurement setupincluding the sample chamber, the sample holder andthe measurement principle were discussed in detail. Toconfirm the functionality of the measurement setup, anumber of test measurements were conducted on differ-ent materials and the data obtained were compared toavailable data in the literature. For all measured sam-ples, very good agreement between the different data setswas achieved. Notably, our polycrystalline bulk samplesshow similar Seebeck and Nernst coefficients, comparedwith the data from single-crystal and thin film studies.Reference measurements with established measurementsetups were done on the same sample pieces for constan-tan and Fe3Al for the Seebeck and Nernst coefficients, re-spectively. For both cases, excellent agreement betweenMagnetic field (T)-2 -1 0 1 2Nernst signal (µV/K)-4-2024 300 K - CNRS Paris320 K - CNRS Paris300 K322 K363 K402 K441 K481 K520 K559 KFe3AlFigure 10: Measurement results for Fe3Al Magneticfield-dependence of the Nernst signal of Fe3Al fordifferent measurement temperatures between 300-560Kmeasured with this setup. The measurement at CNRSParis on the same sample piece at T = 300, 320K issuperimposed as green lines for comparison.the data sets was achieved. This nicely demonstrates thefunctionality and applicability of our system to simulta-neously measure magneto-Seebeck and Nernst effects athigh temperatures and high fields. It has been tested upto 600K but the constituting materials can withstandhigher temperatures above 700K. Finally, we want tonote that measurement setups like ours, can be easily ex-tended to additionally measure the resistivity and Hallcoefficient of the sample at the same time.AcknowledgmentThe research in this paper was supported by the JapanScience and Technology Agency (JST) program MIRAI,No. JPMJMI19A1. We acknowledge X-ray center of theTU Wien for providing the means for the X-ray diffrac-tion measurements and analysis. The authors want tothank H. Müller very much for his help with setting upthe experiment as well as as the measurement software.We would like to acknowledge B. Fauqué and K. Behniafrom CNRS Paris for generously providing access to theirNernst measurement device used to validate the built-up device in this study and S. Jiang for his help withpreparing the sample. We appreciate their commitmentto advancing scientific knowledge and their willingness toshare resources.Author contributionM. Parzer, T. Schmid and E. Bauer conceptualized thework and the experiments. M. Parzer and T. Schmid de-signed and built up the measurement setup. T. Schmid10derived the optimized measurement equations and imple-mented them into the setup. T. Schmid and M. Parzersynthesized the samples, did the measurements and wrotethe initial draft. M. Parzer, T. Schmid, F. Garmroudi,A. Riss, T. Mori and E. Bauer discussed the results andedited the final manuscript. E. Bauer and T. Mori orga-nized the funding.Conflict of InterestThe authors have no conflicts to disclose.Data AvailabilityThe data that support the findings of this study areavailable from the corresponding author upon reasonablerequest.References1V. Pecunia, S. R. P. Silva, J. D. Phillips, E. Artegiani,A. Romeo, H. Shim, J. Park, J.-H. Kim, J. S. Yun, andG. C. Welch, Journal of Physics: Materials (2023).2D. Zhao and G. Tan, Applied thermal engineering 66, 15(2014).3G. J. Snyder, A. Pereyra, and R. Gurunathan, AdvancedFunctional Materials 32, 2112772 (2022).4D. 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