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## Creator

[Weinan Zhou](https://orcid.org/0000-0003-2946-9913), [Hirofumi Suto](https://orcid.org/0000-0003-4387-5862), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550)

## Rights

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 Weinan Zhou, Hirofumi Suto, Yuya Sakuraba; Single-material anomalous Nernst heat-flux sensor enabled by heat-assisted magnetization reversal. Appl. Phys. Lett. 11 May 2026; 128 (19): 192401 and may be found at https://doi.org/10.1063/5.0331671.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Single-material anomalous Nernst heat-flux sensor enabled by heat-assisted magnetization reversal](https://mdr.nims.go.jp/datasets/25dbb6e6-dcb1-49b1-88db-f8b9848cc459)

## Fulltext

Single-material anomalous Nernst heat-flux sensor enabled by heat-assisted magnetization reversalSingle-material anomalous Nernst heat-flux sensor enabled by heat-assistedmagnetization reversalWeinan Zhou,a) Hirofumi Suto, and Yuya SakurabaResearch Center for Magnetic and Spintronic Materials,National Institute for Materials Science, Tsukuba 305-0047,JapanHeat-flux sensors based on the transverse thermoelectric phenomenon of anomalousNernst effect have attracted increasing interest in recent years due to the advan-tages stemming from simple and planar sensor structures. However, the difference inSeebeck coefficients of the constituent materials makes the sensors also sensitive toin-plane temperature gradient along the wire direction and can give rise to an unde-sirable offset in the sensor output. In this study, to mitigate this offset, improve struc-tural efficiency, and simplify device fabrication, we propose a single-material anoma-lous Nernst heat-flux sensor with antiparallel magnetization alignment in neighbor-ing wires. Using heat-assisted magnetization reversal through electric-current-drivenJoule heating, we were able to locally control the magnetization and realize such anantiparallel alignment in devices microfabricated from an L10-FePt thin film with anin-plane magnetic easy axis. Systematic measurements on a single FePt wire showedthe conditions of electric current and magnetic field required for heat-assisted magne-tization reversal; these conditions were then applied to a Π-shaped FePt element toselectively reverse one half of its magnetization and achieve antiparallel alignment.As a result, the Π-shaped element with antiparallel magnetization exhibits nearlytwice the heat-flux sensitivity of a single wire. These results establish heat-assistedmagnetization reversal as an effective way to locally control magnetization for con-structing offset-free, single-material anomalous Nernst heat-flux sensors.a)Electronic mail: ZHOU.Weinan@nims.go.jp1This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671The anomalous Nernst effect (ANE) is a transverse thermoelectric phenomenon observedin magnetic materials, where an electric field is generated perpendicular to both the tem-perature gradient (∇T ) and the magnetization (M). In recent years, the ANE has attractedincreasing attention partly due to this transverse geometry: electrical contacts can be ar-ranged orthogonally to the ∇T direction, different from the parallel configuration requiredfor the Seebeck effect (SE).1–11 This geometry decouples thermal and electrical transportpaths and enables simple and planar structures for the ANE-based thermoelectric modules,unlike the three-dimensional structure composed of serially connected p-type and n-typesemiconductor pillars used in a SE-based thermoelectric module. These features make theANE particularly well suited for heat-flux sensors (HFSs), offering flexibility and scalabilitytogether with low thermal resistance.12–16To enhance HFS sensitivity, magnetic wires are often connected in series so thatthe anomalous Nernst voltage (VANE) adds constructively, forming a meander structure[Fig. 1(a)]. This can be realized by using a nonmagnetic metal as electrodes to connect themagnetic wires [Fig. 1(b)];12–14 or by using two different magnetic materials with positiveand negative anomalous Nernst coefficient (SANE) as neighboring wires, for which VANEadds constructively when their M are in parallel alignment [Fig. 1(c)].2,16–21 In both cases,however, the neighboring wires consist of different materials and generally possess differ-ent Seebeck coefficients (SSE). When the heat flux through the HFS is nonuniform andinduces an in-plane component of ∇T along the wire direction, Seebeck voltages (VSE) aregenerated, leading to a finite ∆VSE within a repeating unit of the meander structure, whichsuperimpose on VANE and introduces an undesirable offset in the HFS output. Althoughseveral approaches have been proposed to mitigate this issue, such as tuning SSE of thematerials through multilayer structure15 or selecting specific material combinations,22 theirversatility is limited and may not be applicable to other materials. An alternative approachis to fabricate the entire meander structure from a single magnetic material while arrangingneighboring wires in antiparallel M alignment [Fig. 1(d)]. In this case, even in the presenceof an in-plane component of ∇T , VSE generated in neighboring wires are identical andcancel out, resulting in a vanishing ∆VSE and eliminating the offset in the HFS output.This includes the magneto-Seebeck effect. Previous studies have shown that the Seebeckcoefficient of a magnetic material depends on the relative angle between ∇T and M. Themeasured VSE as a function of magnetic field applied perpendicular to the direction of ∇T2This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671typically exhibits an even dependence on magnetic field, with identical values once M issaturated under either positive or negative field.23,24 In antiparallel M alignment, M inthe neighboring wires is perpendicular to the in-plane component of ∇T , and thus exhibitsthe same magneto-Seebeck effect. This approach also improves structural efficiency, as allwires contribute constructively to the output, and simplify device fabrication. However,because the width of the wires in a practical HFS typically ranges from tens to hundredsof micrometers, achieving precise local control of M without disturbing neighboring wiresremains challenging.2,25,26In this study, we propose an anomalous Nernst HFS consisting of a single magnetic ma-terial, in which neighboring wires have antiparallel M alignment. This alignment is realizedusing heat-assisted magnetization reversal, which exploits the reduction of coercivity (Hc)with increasing temperature (T ) [Fig. 1(e)]. Heat-assisted magnetization reversal has beenapplied to heat-assisted magnetic recording, where local heating enables the control of Min FePt granular films with high magnetic anisotropy using a reduced magnetic field.27,28Here, we used FePt with an in-plane magnetic easy axis, and achieved antiparallel M byselectively heating one wire via Joule heat induced by flowing an electric current (I) throughthe wire. Under magnetic field (H) that is sufficient to align M at elevated T but insufficientat room T [Fig. 1(e)], only the heated wire undergoes magnetization reversal. By systemat-ically varying I and H, we mapped the conditions for heat-assisted magnetization reversalin a single FePt wire. Then, using a device with a Π-shaped FePt element, we selectivelyreversed one half of the element and realized antiparallel M alignment. The Π-shaped FePtelement with antiparallel M exhibited nearly twice the HFS sensitivity compared to that ofa single FePt wire.The thin film used in this study was prepared using an ultrahigh-vacuum magnetronsputtering system. The stacking structure was MgO (110) substrate // Cr (1 nm) / Pt (5nm) / FePt (28 nm). The MgO substrate was first heated to 600 ◦C to clean the surface,after which the Cr layer was deposited. The substrate temperature was then reduced to300 ◦C for the deposition of the Pt and FePt layers. The crystalline structure of the thinfilm was characterized by X-ray diffraction (XRD) with Cu Kα radiation, and the magneticproperties were characterized using a superconducting quantum interference device. Thesemeasurements confirmed that the L10-FePt layer was epitaxially grown with its magneticeasy axis aligned along the MgO [001] direction (see Supplementary Material for the X-ray3This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671FIG. 1. (a) Schematic illustration of an anomalous Nernst HFS with a meander structure on aflexible substrate. The black dashed square denotes one repeating unit of the meander structure.(b) A repeating unit consists of a magnetic material and a nonmagnetic metal. Only the magneticmaterial generates a voltage due to ANE (VANE) under an out-of-plane ∇T . If ∇T also has anin-plane component, voltages due to SE (VSE) emerge in both materials, and a finite ∆VSE isadded to VANE owing to the difference in SSE. (c) A repeating unit consists of two differentmagnetic materials with positive and negative SANE. When their magnetizations (M) are alignedparallel along x-axis, the generated VANE points in opposite directions under an an out-of-plane∇T , resulting in additive VANE. However, if ∇T also has an in-plane component, a finite ∆VSEemerges owing to different SSE. (d) A repeating unit consists of a single magnetic material withantiparallel M on the left and right sides. The generated VANE is additive, whereas ∆VSE = 0under in-plane ∇T owing to identical SSE. (e) Schematic illustration of achieving antiparallel Malignment by applying an electric current (I) for Joule heat and exploiting different coercivities(Hc1 and Hc2) at room T and an elevated T .diffraction pattern and M -H curves).29,30 The composition of the FePt layer was determinedto be Fe44Pt56 by X-ray flourescence analysis performed on a reference sample without the Cr/ Pt buffer layer. For device fabrication, the thin film was patterned into wires and Π-shapedelements by photolithography and Ar ion milling. The wire width was 10 µm, and the widthdirection was aligned parallel to the MgO [001] direction. The distance between wires was14 µm for the Π-shaped elements. Ta (2 nm) / Au (150 nm) electrodes were then fabricated4This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671using a lift-off process. The distance between the electrodes on each end of the wires was100 µm. To apply an out-of-plane ∇T , on-chip heaters were microfabricated on top of theFePt wires and elements to cover them entirely. The heaters were electrically insulated fromthe FePt by a 10-µm-thick epoxy photoresist (SU-8) layer. After patterning the SU-8 layerand then curing it at 200 ◦C for 30 min, the on-chip heaters were fabricated from Ta (5 nm)/ Au (100 nm) thin film using a lift-off process. The heater wire width and the gap betweenadjacent wires were both 8 µm, and the heater covered an area of approximately 160 × 160µm2 [Fig. 2(a) and Fig. 3(a)]. The measurements were primarily carried out using a proberstation equipped with an in-plane electromagnet. The T dependence of the wire resistance(R) was measured using a physical property measurement system (PPMS).To investigate the conditions for heat-assisted magnetization reversal by Joule heating, wefirst performed measurements on a device with a single FePt wire. M reversal was evaluatedby measuring VANE of the wire as a function of H. Figure 2(a) shows a photograph of thedevice and the measurement configuration. The nanovoltmeter on the right measured VANE,while the sourcemeter on the right applied I through the wire to generate Joule heat andelevate its T . The sourcemeter on the left applied a heater current to the on-chip heaterto generate an out-of-plane ∇T , and the nanovoltmeter on the left was used to estimatethe electrical power dissipated in the heater and calculate the heat flux density (JQ) as thepower divided by the heater area. Figure 2(b) shows VANE as a function of H measured witha heater current of 10 mA, corresponding to JQ = 331 kW m−2. Prior to the measurement,M of the FePt wire was aligned along the −x direction. H was swept from 0 to 240 mT, to−240 mT, and back to 0, as indicated by the numbered arrows in Fig. 2(b). In this case, theM reversal was driven solely by H, which can be clearly seen as sharp change in VANE, andHc is obtained to be ∼ 167 mT. For heat-assisted magnetization reversal operation, after Mwas aligned along the −x direction, we fixed H at a certain positive value (HR) smaller thanHc, and applied I through the FePt wire for 1 s. After turning off I and returning H back tozero, the VANE-H curve was measured to investigate the direction of M, following the sameH sequence as shown in Fig. 2(b). This procedure was repeated for different combinationsof I and HR, with I ranging from 30 to 50 mA (both polarities) and HR ranging from 15to 147 mT. We define ∆VANE as the averaged VANE value in the range of 0 < µ0H < 150mT minus the averaged value at µ0H > 200 mT in the initial curve [Fig. 2(f)]. A value of∆VANE ∼ −5 µV indicates that the operation was not able to reverse M [Fig. 2(e)], whereas5This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671FIG. 2. (a) Photograph of the device containing a single FePt wire, together with a schematic ofthe measurement configuration. The positive H direction and the ∇T direction are indicated. Thescale bar corresponds to 20 µm. (b) VANE as a function of H measured with a heater current of 10mA. Numbered arrows indicate the sequence of varying H. (c) Color map of ∆VANE as a functionof HR and positive I, showing the conditions for heat-assisted magnetization reversal of FePt. (d)∆VANE as a function of HR and negative I. (e)-(g) VANE-H curves measured after the operationwith I = 48.0 mA and (e) HR = 56, (f) 96, and (g) 127 mT, corresponding to the gray dots in(c). ∆VANE is defined as the averaged VANE value in the range of 0 < µ0H < 150 mT minus theaveraged value at µ0H > 200 mT, as indicated in (f).∆VANE ∼ 0 means that M was fully reversed and the operation is successful [Fig. 2(g)].Figure 2(c) (Figure 2(d)) summarizes ∆VANE as a function of HR and positive I (negativeI). Representative VANE-H curves measured after the operations with I = 48.0 mA andHR = 56, 96, and 127 mT are shown in Figures 2(e), 2(f), and 2(g), respectively. Theconditions for successful operations, indicated by ∆VANE being close to zero, appears in theupper-right region of the color map, corresponding to large I and HR. Intermediate ∆VANE6This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671FIG. 3. (a) Photograph of the device containing a Π-shaped FePt element, together with aschematic of the measurement configuration. The positive H direction and the ∇T directionare indicated. The scale bar corresponds to 20 µm. (b) Color map of ∆VANE as a function of HRand positive I, showing the conditions for achieving antiparallel M alignment in FePt. (c) ∆VANEas a function of HR and negative I. (d)-(f) VANE-H curves measured after the operation with (d)I = 36.1 mA and HR = 107 mT, (e) I = 48.0 mA and HR = 127 mT, and (f) I = 48.0 mA andHR = 147 mT, corresponding to the gray dots in (b).values at the boundary between successful operation and no M reversal suggest partial Mreversal [Fig. 2(f)], and this boundary region expanded in HR as I increased towards 50 mA.Although spin torque arising from the spin Hall effect in the Pt layer could, in principle,influence M reversal of the FePt layer, the very similar color maps obtained for positive andnegative I [Fig. 2(c) and 2(d)] suggest that such effect does not play a significant role here,since the polarity of I will determine the direction of spin torque.Using the conditions obtained for heat-assisted magnetization reversal, we next performedoperations on a device with a Π-shaped FePt element to achieve antiparallel M alignment.Figure 3(a) shows a photograph of the device and the measurement configuration, whichis largely the same as that shown in Fig. 2(a), except that the nanovoltmeter on the right7This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671measured the voltage of the entire Π-shaped element, while the sourcemeter on the rightwas connected only to the right half of the element to generate Joule heat. It is worthnoting that no specific thermal isolation measures were implemented, and the Joule heatgenerated in the wire can propagate to the neighboring wire through the MgO substrate andthe SU-8 layer. The same procedure as used for a single FePt wire was repeated here, with Iranging from 30 to 50 mA (both polarities) and HR ranging from 96 to 147 mT. Figure 3(b)(Figure 3(c)) summarizes ∆VANE as a function of HR and positive I (negative I). Thedefinition of ∆VANE remains the same. However, a value of ∆VANE ∼ 0 here indicates thatthe operation was unsuccessful and M of the left and right halves were parallel [Fig. 3(d)].The small peaks observed at |µ0H| ∼ 165 mT in the VANE-H curves are attributable tothe unsynchronized M reversal of the element driven by H. By contrast, ∆VANE ∼ 5 µVindicates that M of the right half was fully reversed, resulting in antiparallel M alignment[Fig. 3(e)]. The color maps obtained for positive and negative I [Figs. 3(b) and 3(c)] arevery similar, and the conditions for achieving antiparallel M largely overlap with thoseobserved in Figs. 2(c) and 2(d). Notably, within the area corresponding to antiparallel Malignment in Figs. 3(b) and 3(c), combinations of |I| ≥ 45.8 mA and HR = 147 mT resultin ∆VANE ∼ 0, indicating parallel M alignment. Figure 3(f) shows a representative VANE-Hcurve obtained after such an operation, where the disappearance of the small peak at µ0H ∼165 mT indicates that M of both the left and right halve were reversed. This behavior islikely caused by a combination of increased T in the left half due to heat dissipation fromthe right half under Joule heating, as well as the reversed magnetic domain propagationunder large H. Nevertheless, these results demonstrate that antiparallel M alignment in asingle-material Π-shaped element can be achieved by selective heat-assisted magnetizationreversal via Joule heating.Since the single wire and Π-shaped element of FePt are analogous to the repeating units ofHFS shown in Figs. 1(b) and 1(d), respectively, we evaluated and compared their sensitivitiesby measuring VANE as a function of JQ [Fig. 4(a)]. The data points represent VANE measuredunder zero H, and the dashed lines denote linear fits through the origin, with the slopescorresponding to the sensitivities. The Π-shaped element with antiparallel M exhibits asensitivity of 13.0×10−3 µV (kW m−2)−1, nearly twice that of the single wire (7.4×10−3 µV(kW m−2)−1). In contrast, the sensitivity of the Π-shaped element with parallel M is only−0.2×10−3 µV (kW m−2)−1. This behavior is expected because each half of the Π-shaped8This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671FIG. 4. (a) VANE under zero field as a function of JQ for devices with a single wire or with aΠ-shaped element. The dashed lines denote linear fits through the origin. (b) Measured R of asingle FePt wire as a function of T . The green dashed line denotes a linear fit. The red horizontaldashed lines mark the R values measured after operation with various I, while the red verticaldashed lines indicate the estimated wire temperature due to Joule heating.element has the same length as the single wire and generates a comparable VANE underthe same JQ; the voltages add constructively for antiparallel M, while they cancel out forparallel M. We also estimated T of the FePt wire after applying I through it for 1 s. Forthis purpose, we used R of the single FePt wire (shown in Fig. 2(a)) to estimate its T bymeasuring the T dependence of R. The green data points in Fig. 4(b) were obtained usingfour-terminal method in a PPMS, which controlled the environment T . The data exhibita linear relationship, as indicated by the green dashed line. The R values of the singleFePt wire measured after applying various values of I for 1 s are shown as horizontal reddashed lines, and their intersections with the green dashed line provide estimates of T due toJoule heating. The maximum T reached after applying 50 mA was estimated to be ∼ 483 K,which is lower than the substrate temperature during FePt deposition (573 K). During Jouleheating, a temperature gradient may develop within a wire due to the multilayer structure(materials with different electrical resistivities) and asymmetric top and bottom boundaryconditions. However, based on our results, such a gradient does not generate a clear effecton the heat-assisted magnetization reversal of the FePt wires, which may be due to the highthermal conductivities of the metallic layers and the small total thickness of the thin film.These results show that the direction of M in the FePt wires can be reversed by theapplication of I and H via heat-assisted magnetization reversal. However, such a processis not expected to occur during normal HFS operation, which is around room temperatureand in the absence of a strong external magnetic field. We measured the M -H curves of9This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671the FePt thin film over a temperature range from 300 K to 400 K with H applied alongthe MgO [001] direction (see Fig. S3 in Supplementary material). Both Hc and saturationmagnetization Ms decrease with increasing T . At 300 K, µ0Hc = 163 mT, consistent withthat of a single FePt wire shown in Fig. 2(b). At 400 K, µ0Hc decreases to 123 mT, whichremains significantly higher than magnetic fields typically encountered in daily environments.This value is comparable to the behavior of heat-assisted magnetization reversal with I =41.2 mA, based on the estimated wire temperature due to Joule heating shown in Fig. 4(b).Although the HFS would lose functionality if the direction of M were altered by externalconditions (e.g., strong H and/or high T ), realignment of M would restore device operation.In conclusion, we propose an anomalous Nernst HFS based on a meander structure fabri-cated from a single magnetic material, which could mitigate the undesirable SE offset in theHFS output arising from an in-plane component of ∇T . Such an anomalous Nernst HFSrelies on antiparallel M alignment in neighboring wires of the meander structure, which isrealized through selective heat-assisted magnetization reversal induced by electric-current-driven Joule heating. Systematic measurements on a device with a single FePt wire showedthe conditions of I and HR required for M reversal. Applying these conditions to a devicewith a Π-shaped FePt element, we demonstrated antiparallel M alignment by selectivelyheating one half of the element. The Π-shaped element with antiparallel M exhibited nearlytwice the HFS sensitivity of a single wire. The local M control demonstrated here is appli-cable to other magnetic materials with finite coercivity. These results establish heat-assistedmagnetization reversal via Joule heating as a practical and versatile approach for construct-ing single-material anomalous Nernst HFS, paving the way for wider adoption of HFS andcontributing to the development of thermal-management technologies.SUPPLEMENTARY MATERIALSee the Supplementary Material for details of the X-ray diffraction pattern, the M -Hcurves, and the magnetic-field dependence of the Seebeck voltages of the FePt thin film.10This is the author’s peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0331671ACKNOWLEDGMENTSThis work was partially supported by ERATO “Magnetic Thermal Management Ma-terials” (Grant No. JPMJER2201) and A-STEP (Stage II, Full-scale type) (Grant No.JPMJTR253A) from JST, Japan; Grants-in-Aid for Scientific Research (C) (KAKENHI;Grant No. 25K08463) from JSPS, Japan; ARIM of MEXT (JPMXP1225NM5220); andSEMITEC corporation.DATA AVAILABILITYThe data that supports the findings of this study are available from the correspondingauthor upon reasonable request.REFERENCES1G. E. W. Bauer, E. Saitoh, and B. J. van Wees, Nat. Mater. 11, 391 (2012).2Y. Sakuraba, K. Hasegawa, M. Mizuguchi, T. Kubota, S. Mizukami, T. Miyazaki, andK. Takanashi, Appl. Phys. Express 6, 033003 (2013).3S. R. Boona, R. C. Myers, and J. P. Heremans, Energy Environ. Sci. 7, 885 (2014).4Y. Sakuraba, Scr. Mater. 111, 29 (2016).5M. Ikhlas, T. 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