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Shusaku Saito, [Takamasa Hirai](https://orcid.org/0000-0002-5577-8018), [Weinan Zhou](https://orcid.org/0000-0003-2946-9913), Shunsuke Mori, Kota Hasegawa, [Rajkumar Modak](https://orcid.org/0000-0001-7939-3289), [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Yuya Sakuraba](https://orcid.org/0000-0003-4618-9550), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051)

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[Kirigami-structured flexible heat flux sensor driven by the anomalous Nernst effect](https://mdr.nims.go.jp/datasets/cc720115-7a6a-4330-a464-84ac64ff02e5)

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Kirigami-structured flexible heat flux sensor driven by the anomalous Nernst effectApplied PhysicsExpress      LETTER • OPEN ACCESSKirigami-structured flexible heat flux sensor drivenby the anomalous Nernst effectTo cite this article: Shusaku Saito et al 2026 Appl. Phys. Express 19 053001 View the article online for updates and enhancements.You may also likeHeat flux sensing by anomalous Nernsteffect in Fe–Al thin films on a flexiblesubstrateWeinan Zhou and Yuya Sakuraba-Screen-printed thin-film thermocouples forcurved surface temperature monitoringand human-machine interactionNingxi Zhang, Xinyi Shi, Su Ding et al.-Design of a scalable, flexible, and durablethermoelectric cooling device for softelectronics using Kirigami cut patternsZ B Rosenberg, N C Weiner, H Shahariaret al.-This content was downloaded from IP address 144.213.253.16 on 06/07/2026 at 02:45https://doi.org/10.35848/1882-0786/ae62c7/article/10.35848/1882-0786/ab79fe/article/10.35848/1882-0786/ab79fe/article/10.35848/1882-0786/ab79fe/article/10.1088/2058-8585/ae3c31/article/10.1088/2058-8585/ae3c31/article/10.1088/2058-8585/ae3c31/article/10.1088/2058-8585/ac48a0/article/10.1088/2058-8585/ac48a0/article/10.1088/2058-8585/ac48a0aaaKirigami-structured flexible heat flux sensor driven by the anomalous NernsteffectShusaku Saito1,2, Takamasa Hirai2* , Weinan Zhou2 , Shunsuke Mori1,2 , Kota Hasegawa3 , Rajkumar Modak1,2 ,Fuyuki Ando2 , Yuya Sakuraba2 , and Ken-ichi Uchida1,21Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan2Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science, Tsukuba 305-0047, Japan3Resonac Corporation, Tsukuba 300-4247, Japan*E-mail: HIRAI.Takamasa@nims.go.jpReceived March 25, 2026; revised April 15, 2026; accepted April 20, 2026; published online May 7, 2026This letter proposes and demonstrates a flexible architecture for an anomalous-Nernst-effect-based heat flux sensor inspired by kirigami, atraditional Japanese paper-cutting art. A prototype device comprises an amorphous Sm19Co81 film and Ta/Au electrode on a flexible substratepre-patterned with a periodic-cutting kirigami structure. The estimated heat flux sensitivity of the kirigami-structured sensor was comparable tothat of a conventional sensor without a kirigami structure and remained unchanged even when it was stretched by 10%. Our approach opens apathway toward versatile and mechanically compliant heat flux sensing that is applicable to various surfaces.© 2026 The Author(s). Published on behalf of The Japan Society of Applied Physics by IOP Publishing LtdH eat flux sensing is an essential thermal managementtechnology for understanding and controllingthermal transport in a wide range of systems, fromelectronic devices to materials processing and industry.Although various principles have been proposed for heatflux sensing, Seebeck-effect-based sensors are the mostwidely utilized. In the Seebeck effect, an electric field isgenerated in a direction parallel to a temperature gradientapplied to a conductor. As a consequence, Seebeck-effect-based heat flux sensors adopt a structure consisting of athree-dimensional matrix of interconnected thermocoupleswith many junctions and electrodes, which can imposecertain constraints on device durability, as these interfacestend to be the primary points of failure. Because of theparallel relationship between the electric field and tempera-ture gradient, such sensors inherently involve a trade-off;increasing the device thickness to enhance the output voltagesimultaneously increases the thermal resistance along theheat-flow direction, where the presence of other multiplethickness components, including the substrate, electrodes,and junctions, also causes a high thermal resistance unavoid-able, thereby leading to significant sensing errors.Recently, heat flux sensors based on the anomalous Nernsteffect (ANE) in conductive magnetic thin films have beenproposed to overcome such issues.1–9) ANE is one of thetransverse magneto-thermoelectric effects and can generatean electric field in the direction of the cross product of anapplied temperature gradient and magnetization. Owing tothe orthogonal relationship between the electric field andtemperature gradient in ANE, the output voltage can beproportionally enhanced by elongating the in-plane length ofmagnetic wires without increasing their thickness.Consequently, the basic module architecture of ANE-basedheat flux sensors follows the configuration illustrated inFig. 1(a). Here, magnetic and non-magnetic thin-film stripesare laterally and alternately connected on a substrate. Notethat the non-magnetic wire is not essential; it can be replacedby a second magnetic material exhibiting the opposite sign ofthe anomalous Nernst coefficient,8,10) or even by the samemagnetic material provided that adjacent wires are magne-tized in opposite directions.11,12) When a flexible organicsubstrate is employed, the mechanical flexibility and dur-ability of thin-film devices fabricated on it can beenhanced,13–18) with maintaining the low thermal resistance.However, even with flexible substrates, it is often difficult tomount the sensors on arbitrarily curved surfaces; althoughANE-based heat flux sensors on flexible substrates can beeasily attached to a cylindrical heat source, their adhesion toa heat source with non-ruled curvature deteriorates due to theinherent tension of flexible substrates.19–21)In this study, we propose an advanced flexible architectureof ANE-based heat flux sensors by introducing the idea ofkirigami. Kirigami is a traditional Japanese paper-cutting art,but has recently attracted attention in biotechnology andflexible electronics.19–30) Applying a periodic-cutting patterncan make solid sheets greatly stretchable and flexible,improving three-dimensional deformation and adhesion onnon-ruled surfaces.20,24,27) As shown in Fig. 1(b), a kirigamistructure should be applicable to the ANE-based heat fluxsensor by cutting gaps between a magnetic and non-magneticthin-film stripes [Fig. 1(c)]. Thus, here, we fabricated aprototype device of the ANE-based heat flux sensor with andwithout a periodic-cutting kirigami pattern and estimated theheat flux sensitivity, an indicator for the performance of heatflux sensors. The heat flux sensitivity remained unchangedafter patterning kirigami and was further confirmed to beunaffected even under stretching enabled by kirigami struc-turing. Kirigami structuring is expected to substantiallyenhance the functionality and versatility of the ANE-basedheat flux sensors, enabling adaptable heat flux sensing onnon-ruled surfaces [Fig. 1(d)].As the magnetic material for the ANE-based heat fluxsensors, we selected an amorphous Sm-Co alloy film.Recently, it has been shown that Sm-Co-based alloy filmsexhibit large in-plane remanent magnetization andcoercivity,5) enabling zero-field operation of transversethermoelectric generation. The film with a thickness of100 nm was prepared on a 50-μm-thick UPILEX® (UbeContent from this work may be used under the terms of the Creative Commons Attribution 4.0 license. Any further distribution ofthis work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.053001-1© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdApplied Physics Express 19, 053001 (2026) LETTERhttps://doi.org/10.35848/1882-0786/ae62c7https://crossmark.crossref.org/dialog/?doi=10.35848/1882-0786/ae62c7&domain=pdf&date_stamp=2026-05-07https://orcid.org/0000-0002-5577-8018https://orcid.org/0000-0003-2946-9913https://orcid.org/0000-0002-1193-4322https://orcid.org/0009-0008-3508-1740https://orcid.org/0000-0001-7939-3289https://orcid.org/0009-0003-7789-8170https://orcid.org/0000-0003-4618-9550https://orcid.org/0000-0001-7680-3051mailto:HIRAI.Takamasa@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://doi.org/10.35848/1882-0786/ae62c7Corp.) via a layer-by-layer-design growth by magnetronsputtering using Sm and Co targets, where the depositionof 0.39-nm-thick Sm and 0.61-nm-thick Co layers wasrepeated 100 times [Fig. 2(a)]. Note that UPILEX® is apolyimide sheet known for its high temperature and mechan-ical durability and good surface smoothness, which is oftenused for flexible electronics.31,32) A dc power source with10 W for the Sm deposition and rf power source with 100 Wfor the Co deposition were used. A base pressure was<6.0× 10−6 Pa and a process Ar gas pressure was 0.4 Pa.The structural and stoichiometric determination of the Sm-Co film deposited on the UPILEX® substrate was investi-gated using a scanning transmission electron microscope(STEM) with energy-dispersive X-ray spectroscopy (EDS)(Titan G2 80–200, FEI). In STEM experiments, the film wascoated by Pt to protect the film surface from irradiation of afocused ion beam. As shown in Fig. 2(b), the halo ringsobserved in the electron diffraction pattern confirm theamorphous nature of the Sm-Co film and the cross-sectionalhigh-angle annular dark field STEM image reveals thesmooth interface and surface of the film even on the flexibleorganic substrate. Figures 2(c) and 2(d) represent the EDSelemental maps of Sm and Co, respectively. Uniformdistribution of Sm and Co indicates that the Sm and Coatoms were mixed as a solid solution or binary alloyalthough the Sm-Co film was deposited by the layer-by-layer-design growth. The EDS analysis also shows that thecompositions of Sm and Co were 19.4 and 80.6 at%,respectively (thus, hereafter referred to as Sm19Co81), whichis quite close to the Sm20Co80 composition reported tomaximize the anomalous Nernst coefficient SANE for theamorphous Sm-Co film.5)Next, we investigated the thermoelectric and magneticproperties of the Sm19Co81 film. These measurements weredone using the film on a sapphire c-plane substrate depositedsimultaneously with that on the UPILEX® substrate. Ourprevious study has shown that, owing to the amorphousnature, the Sm-Co films maintain the same magneto-thermo-electric transport properties regardless of substrates.5) TheSm19Co81 film was processed to a bar-shaped wire with awidth of 3 mm and a length of 6 mm for measurements ofANE using photolithography and Ar ion milling, and thenTa/Au electrode pads were formed by the lift-off method.Figure 3(a) shows the result of the ANE measurement of theSm19Co81 film at room temperature. In this measurement, thetemperature gradient ∇T and external magnetic field H wereapplied in the film width and thickness directions, respec-tively. The ∇T value was quantified using an infrared cameraby coating the film surface with black ink before sweeping Hand the transverse thermoelectric voltage VT was measuredat various ∇T values.33,34) The VT signal showing the odddependence on H was observed, with the VT value saturatingfor |μ0H| > 2.5 T, with μ0 being the vacuum permeability,and increasing monotonically with increasing the ∇T value,whose behavior was totally consistent with the transversethermoelectric generation due to ANE. The electric fieldinduced by ANE, EANE, was calculated by dividing theFig. 1. (a)–(d) Schematics of a conventional ANE-based heat fluxsensor without a kirigami structure (a), kirigami-structured heat fluxsensor (b), kirigami-structured heat flux sensor under stretching (c), andkirigami-structured heat flux sensor attached on a spherical heat source(d). Here, jq, M, and EANE denote the vectors of the heat flux density,magnetization, and electric field induced by ANE, respectively.Fig. 2. (a) Schematic of the Sm-Co film prepared by the layer-by-layer-design growth. (b) Cross-sectional high-angle annular dark field STEMimage of the Sm-Co film on a UPILEX® substrate. The inset selected areaelectron diffraction pattern was captured from the Sm-Co layer enclosedby the red-dashed circle. (c), (d) STEM-EDS elemental maps of Sm (c)and Co (d).053001-2© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 053001 (2026) S. Saito et al.average VT in the range of |μ0H| = 3–5 T by the wire width.Figure 3(b) shows the ∇T dependence of EANE. The SANEvalue of our Sm19Co81 film was estimated to be0.72 μV K−1. This value is comparable but slightly smallerthan that reported in previous studies,5) which may beattributed to differences in sputtering conditions35) andnanostructure in amorphous films.36) Although thisSm19Co81 film has no perpendicular magnetic anisotropy[Fig. 3(a)], the clear hysteresis loop was observed in the in-plane magnetic field with remanent magnetization andcoercivity [Fig. 3(c)]. From these results, heat flux sensingwithout any external magnetic field is expected by usingSm19Co81 as a magnetic material of thermopiles.Then, we prepared two types of ANE-based heat fluxsensors: the sensors without and with a periodic-cuttingpattern, referred to as an uncut sensor and kirigami-cutsensor, respectively. The procedure for making the uncutsensor is as follows. After depositing the 100-nm-thickSm19Co81 film on the UPILEX® substrate, the film wasprocessed to multiple wires with the width w = 300 μm andlength l using photolithography and Ar ion milling.Subsequently, 5-nm-thick Ta and 150-nm-thick Au filmswere deposited and processed to electrode wires withw = 300 μm by the lift-off method [Fig. 4(a)]. The intervalbetween the Sm19Co81 and Ta/Au wires d was 100 μm. Formaking the kirigami-cut sensor, prior to the Sm19Co81 filmdeposition, the kirigami cutting pattern was introduced intothe UPILEX® substrate using a CO2 laser. Then, theSm19Co81 and Ta/Au electrode wires with w = 500 μmand d = 750 μm were formed in the same manner as thefabrication of the uncut sensor [Fig. 4(b)]. The values of l inthe uncut and kirigami-cut sensors were 12.50 and14.25 mm, respectively. In ANE-based heat flux sensors,the output voltage signal VANE depends on the total length ofthe magnetic wire.37) Thus, to quantitatively compare theperformance as the heat flux sensor, the normalized heat fluxsensitivity VANE/jqnl was estimated, where jq is the heat fluxdensity and n is the number of the Sm19Co81 wire con-tributing VANE generation (note that we adopted the asym-metric kirigami structure to increase total length of magneticwire). For this estimation, the ANE-based heat flux sensorand a 15-mm-square commercially available Seebeck-effect-based heat flux sensor (HF15, Captec Entreprise) weresandwiched by a heater and heat bath, both made of Cu[Fig. 4(c)].1,5) To improve the thermal contact, thermalFig. 3. (a) H dependence of VT for the Sm19Co81 film on a sapphiresubstrate at various ∇T, measured under an out-of-plane magnetic field.The loop was measured through one measurement for each ∇T. (b) ∇Tdependence of EANE. Each data point was calculated by dividing theaverage VT in the range of |μ0H| = 3–5 T by the wire width and the errorbar represents the standard deviation. The solid line shows the result oflinear fitting. (c) H dependence of M, measured under an in-planemagnetic field using a vibrating sample magnetometer. All the measure-ments were performed at room temperature.Fig. 4. (a),(b) Blueprints of the thermopile structure consisting of theSm19Co81 and Ta/Au electrode wires on the UPILEX® substrates for theuncut sensor (a) and kirigami-cut sensor (b). In the kirigami-cut sensor,slits with a length of 5.0 and 7.5 mm were arrayed on the gaps betweenthe Sm19Co81 and Ta/Au wires. (c) Schematic of the experimental setupto evaluate the heat flux sensitivity of the ANE-based heat flux sensor.Here, the thickness of ANE-based heat flux sensor, Seebeck-effect-basedheat flux sensor, and thermal conductive sheet is about 50 μm, 400 μm,and 100 μm, respectively.053001-3© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 053001 (2026) S. Saito et al.conductive sheets (15-mm-square, matching the size of theSeebeck-effect-based heat flux sensor) were inserted at thetop and bottom surface of the ANE-based heat flux sensor.The heat flux was applied in the out-of-plane directionthrough two Cu blocks in an ambient temperature andpressure and in-plane H was swept under thermal equili-brium conditions, allowing the heat flux density jq, calculatedusing the calibration function provided by the manufacturerof the Seebeck-effect-based heat flux sensor, and VANE fromthe ANE-based heat flux sensor and to be measuredsimultaneously. The n value associated with the size of theheater was determined using a charge-coupled devicecamera, yielding 19 (6) for the uncut (kirigami-cut) sensor.We estimated the VANE/jqnl values for three configurations:the uncut sensor (Uncut), kirigami-cut sensor without exten-sion (Kirigami without extension), and kirigami-cut sensorwith 10% extension of its full length (Kirigami with 10%extension). In the sensitivity evaluation of Kirigami with10% extension, the kirigami-cut sensor was extended to 10%strain and then clamped between the heater and heat bath tofix the stretched state.Figures 5(a)–5(c) show the H dependence of VANE/nl forthe samples of Uncut, Kirigami without extension, andKirigami with 10% extension, respectively. In all measure-ments, the hysteresis of VANE/nl was observed although thecoercivity was slightly different between the uncut andkirigami-cut sensors. Importantly, both the remanent andsaturation VANE/nl values showed similar values inthree configurations. Figures 5(d)–5(f) reveal the propo-rtional relationship between jq and VANE/nl both at theremanent (|μ0H| = 0 T) and magnetically saturated states(|μ0H| = 0.3 T) for three configurations. The solid lines inFigs. 5(d)–5(f) show the results of linear fitting and theirslopes indicate VANE/jqnl. Table Ⅰ summarizes the VANE/jqnlvalues at |μ0H| = 0 and 0.3 T for three configurations.Notably, the VANE/jqnl value of the kirigami-cut sensorexhibited no change either without or with extension.It is known that uniform stretching of a kirigami sheetintroduces locally non-uniform strain within the patternedregion.23,26,27,30) The invariance of VANE against such straindistribution indicates that the thermoelectric transport prop-erties of the amorphous Sm19Co81 film are insensitive tostrain and further suggests robust sensor operation even inthe presence of the non-uniform strain inevitably induced bythree-dimensional deformation (note that, in the presentconfiguration, out-of-plane deformation of kirigami wassuppressed by clamping the sensor between Cu blocks,which resulted in a slight difference in the internal straindistribution from that arising from simple uniaxialstretching). In addition, the invariant VANE, despite thechange in heat transfer area upon the 10% extension–evenwith the formation of void regions induced by stretching thekirigami–ensures the assumption of one-dimensional heatflow in the kirigami-cut sensor owing to its low thermalresistance [this assumption is reasonable given that thesensors and sheets are very thin (total thickness is about0.6 mm) relative to the clamping region (about 15 mmsquare)], thereby enabling the quantitative estimation of jqunder the various deformation conditions.In summary, we proposed a flexible architecture of ANE-based heat flux sensors by designing a kirigami structureonto the flexible substrate and demonstrated its sensoroperation at zero magnetic field. Kirigami structuring didnot deteriorate the performance as a heat flux sensor, and thesensor characteristics remained unchanged even under 10%stretching, which is the most basic deformation of kirigamistructure, yet far exceeds the elastic limit of uncut flexiblesubstrates (typically a few %31,38,39)). Since numerouskirigami patterns exist beyond the one employed in thisstudy and provide a wide variety of deformability, optimiza-tion of the kirigami structure will further boost the mechan-ical adaptability of the heat flux sensor comprising magneticthin films. Specifically, to realize thermoelectric heat fluxsensing on arbitrary curved surfaces, it is necessary tooptimize both the kirigami design and selection of substratematerials to prevent thermal contact from deteriorating dueto out-of-plane deformation of kirigami. Finally, it should beFig. 5. (a)–(c) H dependence of VANE/nl for Uncut (a), Kirigamiwithout extension (b), and Kirigami with 10% extension (c) at variousvalues of jq. The insets show the photograph of the fabricated sensors.The loop at each jq represents the average of three measurements. (d)–(f)jq dependence of VANE/nl extracted at |μ0H| = 0 and 0.3 T for Uncut (d),Kirigami without extension (e), and Kirigami with 10% extension (f).Table I. VANE/jqnl value at remanent and magnetically saturated states forthe configurations of Uncut, Kirigami without extension, and Kirigami with10% extension.VANE/jqnl (×10−7 VW−1m)|μ0H| (T) UncutKirigami withoutextensionKirigami with 10%extension0 0.62 ± 0.01 0.51 ± 0.05 0.54 ± 0.050.3 0.93 ± 0.01 1.05 ± 0.01 1.06 ± 0.01053001-4© 2026 The Author(s). Published on behalf ofThe Japan Society of Applied Physics by IOP Publishing LtdAppl. Phys. Express 19, 053001 (2026) S. Saito et al.noted that the device architecture based on kirigami structureproposed in this study can be applied not only to ANE butalso to other transverse thermoelectric conversionphenomena,37) highlighting the versatility of this concept.Acknowledgments The authors thank D. Chiba for technical support andK. Hirata and Y. Nakanishi for valuable discussions. 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