# Fileset [s43246-024-00465-9.pdf](https://mdr.nims.go.jp/filesets/a364e429-76c1-4947-889b-495db847469d/download) ## Creator Hiroto Arima, Md. Riad Kasem, [Hossein Sepehri-Amin](https://orcid.org/0000-0002-7856-7897), [Fuyuki Ando](https://orcid.org/0009-0003-7789-8170), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), Yuto Kinoshita, Masashi Tokunaga, Yoshikazu Mizuguchi ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [Observation of nonvolatile magneto-thermal switching in superconductors](https://mdr.nims.go.jp/datasets/43130689-c104-4314-ba31-73f98736b81e) ## Fulltext Observation of nonvolatile magneto-thermal switching in superconductorscommunicationsmaterials Articlehttps://doi.org/10.1038/s43246-024-00465-9Observation of nonvolatile magneto-thermal switching in superconductorsCheck for updatesHiroto Arima1, Md. Riad Kasem1, Hossein Sepehri-Amin 2, Fuyuki Ando2, Ken-ichi Uchida 2,Yuto Kinoshita3, Masashi Tokunaga 3 & Yoshikazu Mizuguchi 1Applying amagnetic field to a solid changes its thermal-transport properties. Although suchmagneto-thermal-transport phenomena are usually small effects, giant magneto-thermal resistance hasrecently been observed in spintronic materials and superconductors, opening up new possibilities inthermal management technologies. However, the thermal conductivity conventionally changes onlywhen amagnetic field is applied due to the absence of nonvolatility, which limits potential applicationsof thermal switching devices. Here, we report the observation of nonvolatile thermal switching thatchanges the electron thermal conductivity when amagnetic field is applied and retains the value evenwhen the field is turned off. This unconventional magneto-thermal switching arises in commercial Sn-Pb solders and is realized by phase-separated superconducting states and resultant nonuniformmagnetic flux distributions. This result confirms the versatility of the observed phenomenon and aidsthe development of active solid-state thermal management devices.Thermal switching is a growing and crucial component of thermalmanagement1,2 because heat flow control is essential to achieve high effi-ciencies in electronic devices. In particular, thermal switching withoutmechanical motion is important to control the heat flow in solids; metal-insulator transition3, electrochemical interactions4, electric fields5, andmagneticfields6 (H) have beenused to switch the thermal conductivity (κ) ofmaterials. Magneto-thermal switching (MTS) is a promising technologybecause a hugeMTS has been observed in spintronic multilayer films7,8 andsuperconducting materials9,10. After investigations on various MTS mate-rials, the MTS ratio (MTSR), which is defined as [κ(H)−κ(0)]/κ(0), nowexceeds 1000%without observation of nonvolatile characteristics ofMTS inthe superconductors. If nonvolatilitywith a largeMTSwhoseκ(H) value canbe maintained at zero fields after experiencing H are obtained, they canprovide anewpathway to achieve efficient thermalmanagement in solids. Inthis study, we show that conventional (commercial) Sn–Pb solders exhibit anonvolatile MTSR of 150%, which is defined as [κ(0, demagnetized)−κ(0,initial)]/κ(0, initial).MTS of superconductors is achieved below its superconducting tran-sition temperature (Tc) by forming Cooper pairs in the superconductingstate, where the Cooper pairs do not transfer heat, which results in thereduction of carrier κ. The MTSR of superconductors can be extremelylarge; MTSR > 1000% has been confirmed in highly pure Pb10. This largeMTSR has been achieved using the difference in electron thermal con-ductivity (κel) between the superconducting andnormal states.Although theworking temperature of superconductors is quite low, they are potentiallysuitable for the thermal management of low-temperature electronicdevices11,12. However, pure superconductors do not exhibit nonvolatilecharacteristics related to κel in the H dependence of κ. It should be noticedthat there is a report on nonvolatileMTS in a type-II superconductor Nb inthe mixed states13, and the nonvolatility is caused by the changes in thelattice thermal conductivity (κlat) in its mixed states; at higher temperatures,the fluxes also affect κel13. However, the nonvolatile MTS mainly based onthe changes in κlat in the superconductingmixed states is highly sensitive topurity9,13; hence, achievement of nonvolatile MTS using the changes in κelbetween superconducting and normal conducting states is desired forapplication. In this study, we investigate the MTS characteristics of Sn–Pbsolders and observe that simple solders exhibit nonvolatile MTS based onκel. We conclude that the mechanism of nonvolatile MTS in the solders isbased on trapped magnetic flux, as discussed later. Flux trapping in Sn–Pbsolders was investigated through magnetization measurements severaldecades ago14,15, in which the Sn–Pb solders were simply regarded as type-IIsuperconductors. However, the Sn–Pb solders are actually composite(phase-separated) materials composed of two type-I superconductors withdifferent Tc , i.e., Sn (Tc = 3.7 K) and Pb (Tc = 7.2 K). Here, we propose thatsuch composite superconductors trapmagnetic flux nonuniformly and giverise to nonvolatile MTS.Here, we briefly introduce the magnetic flux trapping in super-conductors. Superconductors aremainly categorized into type-I and type-II,1Department of Physics, Tokyo Metropolitan University, 1-1, Minami-osawa, Hachioji 192-0397, Japan. 2National Institute for Materials Science, 1-2-1, Sengen,Tsukuba 305-0047, Japan. 3Institute for Solid State Physics, University of Tokyo, 5-1-5, Kashiwanoha, Kashiwa 277-8581, Japan. e-mail: mizugu@tmu.ac.jpCommunications Materials | (2024) 5:34 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00465-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00465-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00465-9&domain=pdfhttp://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0002-7856-7897http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0001-7680-3051http://orcid.org/0000-0002-1401-9381http://orcid.org/0000-0002-1401-9381http://orcid.org/0000-0002-1401-9381http://orcid.org/0000-0002-1401-9381http://orcid.org/0000-0002-1401-9381http://orcid.org/0000-0002-4771-7805http://orcid.org/0000-0002-4771-7805http://orcid.org/0000-0002-4771-7805http://orcid.org/0000-0002-4771-7805http://orcid.org/0000-0002-4771-7805mailto:mizugu@tmu.ac.jpbased on the difference in their reaction to applied H16. In type-I super-conductors, perfect diamagnetism is observed up to the critical field (Hc),and the superconducting states are quickly suppressed by applying furtherfields. Therefore, magnetic flux is expelled from ideal type-I super-conductors in their superconducting state. Type-II superconductors havetwo critical fields: a lower critical field (Hc1) and an upper critical field (Hc2).At H Hc (Sn). Although the mechanisms behind the fluxtrapping are known, unexpectedly strong flux trapping in a bulk compositecomposed of type-I superconductors with different Tc would provide newinsights into the functionalities and applications of superconductors.ResultsNonvolatile magneto-thermal switching in Sn–Pb solderThe most important result of this work is the observation of nonvolatileMTS based on the modification of κel in Sn–Pb solders. It is widely knownthat solders are phase-separated composites, but the utilization of uniquesuperconducting states emerging in the phase-separated solders has notattracted much attention. Here, we show the nonvolatile characteristics ofMTS at T = 2.5, 3.0, and 4.2 K as examples. The schematic images of theconcept of nonvolatileMTS in solders are shown in Fig. 1. At the initial state(Fig. 1a), the whole sample is superconductive, and the κ is low due to thesuppressionof carrier heat transfer.AtH >Hc, the superconducting states ofthe solder are totally suppressed (Fig. 1b), and κ is increased by the revival ofthermal conductionby charge carriers. Thenonvolatility ofMTS is observedby reducing H after experiencing a large H. As shown in Fig. 1c, high κ isretained even after removing external fields (atH = 0Oe), which is achievedby the magnetic fluxes trapped in the Sn regions. The nonvolatility of κimplies that several Sn grains lose the bulk nature of superconductivity andare close to normal-conducting states because of the trapped magneticfluxes. The mechanism of nonvolatile MTS in the solder is different fromthat in Nb13 where vortices modify κlat. In addition, the trapping of a largenumber ofmagneticfluxes in the Sn regions of Sn–Pb solders hadnot been acommon understanding in the field of pure and applied science ofsuperconductors.We measured the temperature and field dependences of κ for com-mercial Sn45–Pb55 solders using a four-probe method (Fig. 2a). Figure 2bshows the temperature dependences of κmeasured at H = 0Oe after zero-field cooling (ZFC) and field cooling underH = 1500Oe (FC). In addition,the FC data measured at H = 1500Oe are plotted together with data mea-sured at H = 0Oe (after ZFC and FC). The difference in the κ–T curveappears below 7 K, which is due to the emergence of superconductivity inthe solder (at Tc for Pb; see magnetization data shown in Fig. 3a). As shownin Fig. 2b, we find that the ZFC and FC data exhibit clear differences whenthese measurements are performed after removing the applied magneticfield (H = 0Oe) in the measurement system. At H = 1500Oe (FC), thedecrease in κ at low temperatures was totally suppressed because thesuperconducting states of the solder were destroyed. Because the FC(H = 0Oe) data exhibited an intermediate trend between ZFC (H = 0Oe)and FC (H = 1500Oe), it is clear that magnetic fluxes, less than 1500 Oe,were trapped in the solder sample after the FC under 1500Oe.Figures 2c–f display the κ–H curve measured at T = 2.5, 3.0, 4.2, and8.0 K. Here, error bars are not displayed for clarity, but the data with errorbars are displayed in Supplementary Fig. 1. No MTS was observed atT = 8.0 K because the temperature was higher than Tc of the solder. AtT = 2.5 K, a clearMTSwas observed in the initial increments ofH from 0 to1700 Oe. Further, by decreasing H from 1700 to −1700 Oe, κ slightlydecreases but does not reach the initial value of κ at H = 0 Oe. At around−800 to−1000 Oe, an anomaly is seen, which is related to the critical field(Supplementary Fig. 2). By increasingH from−1700 to 1700 Oe, a similaranomaly was observed between 800 and 1000 Oe, but the value of κ neverreturned to the initial value. The κ–H data clearly shows the nonvolatileMTS characteristic in the solder. The nonvolatileMTSRwas about 150%, asshown in Fig. 2c. At T = 3.0 and 4.2 K, similar nonvolatileMTS trends wereobserved, while the MTSR decreased with increasing temperature. One ofthe reasons why nonvolatile MTS was observed at T = 4.2 K (>Tc of Sn)would be explained by the partial suppression of the superconducting statesof the Pb regions by the trapped fluxes. Another reason would be weaksuperconducting states in the Sn regions achieved by the proximity effects inthe initial state atT = 4.2 K.After field experience,Meissner states cannot beachieved due to the presence of trapped fluxes. Comparable MTSFig. 1 | Schematic images of nonvolatile magneto-thermal switching observed incommercial solder (Sn45–Pb55). a Initial state with low thermal conductivity (κ)after zero-field cooling (ZFC). The schematic image of a switch (OFF) denotes thelow-κ state. b State under a magnetic field (H) higher than the critical field (Hc).Magnetic field lines can penetrate whole samples because both Pb and Sn are innormal conducting states. In this state, κ is high (ON). c State at H = 0 afterexperiencingH >Hc. Pb is in the superconducting state, and the magnetic field linesdo not penetrate the Pb regions. Fluxes trapped in the Sn regions cannot be releasedeven at H = 0, which results in the suppression of bulk superconductivity in the Snregions. In this state, nonvolatile MTS with high κ (ON) can be observed.https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 2characteristics were obtained for an Sn45–Pb55 solder wire in an as-purchased form with a φ1.6mm cross-section (Supplementary Fig. 3).Furthermore, we examined theMTS on a flux-cored solder with a differentcomposition (Sn60–Pb40) and observed similar nonvolatile MTS (Sup-plementary Fig. 4). Therefore, nonvolatile MTS is a common behavior invarious Sn–Pb solders.Characterization of superconducting properties and phaseseparation of Sn–Pb solderTo understand the causes of nonvolatile MTS in solders, the super-conducting properties were investigated by measuring the magnetization(M) and specific heat (C). Figure 3a, b shows the T dependence of Mmeasured at approximately 10 Oe after ZFC and FC (under 1500 Oe); ZFCdata exhibits diamagnetism below 7.2 K, but FC data exhibitsferromagnetic-like signals below 7.2 K. Similar significant differences in theM–T between ZFC and FC have been observed in type-II superconductors;for a recent observation example, superhydrides (hydrogen-rich super-conductors) exhibit similar ferromagnetic-like M–T behavior after FC24.This behavior is explained by the trapped flux in the type-II super-conductors. In contrast, our Sn–Pb solder sample was composed of type-ISn and Pb, which is clearly different from the former case. As shown inFig. 4, the elemental mapping analysis revealed that there are phase-separated Sn and Pb regions with a typical size of 5–20 μm. In the μm-scaleorder, the superconducting states of Pb can penetrate the Sn region, whichcauses the single-step superconducting transition shown in Fig. 3a. Instead,the FC data in Fig. 3b exhibits a ferromagnetic-like behavior with a tran-sition temperature of 7.2 K, which is the Tc of Pb. This suggests that mag-netic fluxes were trapped in the solder at temperatures below Tc of Pb. As aFig. 2 | Nonvolatile magneto-thermal switching characteristics of the flux-core-free solder (Sn45–Pb55). a Schematic image of the measured sample with a cross-sectional area of 0.88×1.10 mm2. TH and TL denote two thermometers. The pur-chased solder with a diameter of 1.6 mm was polished into a uniform rectangularbar. b Temperature (T) dependence of κ. The open red circles are data measured atH = 0 Oe after ZFC. The filled red circles are data measured at H = 0 Oe after fieldcooling underH = 1500 Oe: the sample was field-cooled from 10 K to 2.5 K, and thedata were taken after reducing the external field. The blue open circles are datameasured atH = 1500 Oe after FC under H = 1500 Oe. c–f, κ–H curves measured atT = 2.5, 3.0, 4.2, and 8.0 K.https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 3fact, we observed the broadening of the temperature dependence of resis-tivity undermagnetic fields (Supplementary Fig. 2). The trend is commonlyobserved in superconductors with magnetic flux trapping25. The fact sug-gests that the trapped fluxes are thermally fluctuating, which is consistentwith the result shown in Fig. 3b.To further characterize the magnetic properties, the H dependence ofmagnetization (4πM) was measured at T = 2.5, 3.0, and 4.2 K (Fig. 3c, d),where the data was corrected by a demagnetization factor. With decreasingtemperature, the size of the 4πM-H hysteresis becomes larger, which sug-gests the enhancement of a critical current density (Jc) and critical field.However, we noticed there was no large change between T = 3.0 and 4.2 K.As Tc of pure Sn is 3.7 K, the absence of a large change in the 4πM–Hhysteresis at around 3.7 K indicates that the characteristics of the emergingsuperconducting currents are governed by Pb in the solder. To furtherunderstand what is happening in the solder under magnetic fields, weplotted inner magnetic flux density (B), which is given by B =H+ 4πM, inFig. 3e. When the solder was zero-field-cooled to T = 2.5 K, the initial B–Hcurve exhibited perfect diamagnetism (Meissner states) up to about 500Oe.Then, B becomes equal to H, which indicates the suppression of thesuperconducting states at H > 700Oe. When decreasing the field fromFig. 3 | Superconducting properties of the solder Sn45–Pb55. a, bT dependence ofmagnetization (4πM) measured at about 10 Oe after zero-field cooling (ZFC) andfield cooling under 1500 Oe (FC). c, d M–H curves measured at T = 2.5, 3.0, and4.2 K. eH dependence of inner magnetic flux density (B). f T dependence of residualspecific heat estimated by C (0 Oe) – C (1500 Oe) in the form of C/T. Both FC andZFC data are taken at H = 0 Oe after FC under 1500 Oe and ZFC, respectively. Thesuperconducting transition of Sn (Tc = 3.7 K) is seen in the ZFC data only.https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 4H > 1000Oe, an anomaly appears at H ~ 700 Oe, where the super-conducting states of Pb emerge, and magnetic fluxes are trapped inside thesolder. Even at H = 0Oe, the B remains a large value of ~500 G, which isconsistent with a previous work15. Based on those facts, we concluded thatmagnetic fluxes with B ~ 500G can be trapped after FC or application ofHgreater than 700Oe in the solder, and the flux trapping in the Sn regions isthe origin of nonvolatile MTS.To prove the assumption above, we measured the temperaturedependence of zero-field specific heat (C) after ZFC and FC (under1500 Oe). The results, including the data measured under a magnetic field(H = 1500Oe), are summarized in Supplementary Fig. 5. In Fig. 3f, the Cdata in the form of C/T after removing normal states values, estimated bysubtracting the data at 1500 Oe, are plotted as a function of temperature. Asshown in Supplementary Fig. 5, from the analysis of low-temperature C atH = 1500Oe using the low-temperature approximation ofC = γT+ βT 3+ δT 5, Debye temperature (θD) and electronic specific heatcoefficient (γ) were estimated as 128.8(4) K and 2.14(5) mJ K−2 mol−1,respectively. As θD for Pb and Sn are about 105 and 199K26, respectively, theobtained θD for the Sn45–Pb55 solder would be reasonable. For both ZFCand FC data atH = 0Oe, jumps at Tc of Pb were observed; the large value ofthe specific heat jumpΔC/γTc ~ 1.4 for thePb regions (42% inmolar ratio toSn) is clearly greater than the value expected byweak-coupling BCSmodel27(ΔC/γTc = 1.43), which is consistent with the strong-coupling nature of Pband alloyed Pb28. Noticeably, the jump atTc of Sn (T ~ 3.7 K) correspondingto the emergence of the superconducting states of Sn was observed only forthe ZFC data, suggesting that the Sn regions do not undergo a bulk super-conducting transition with a large entropy change after FC. Therefore, thetrapped fluxes should be mainly present in the Sn regions. We did notobserve a clear decrease in the amount of FC magnetization until after atleast two days, as shown in Supplementary Fig. 6, which evidences strongtrapping of fluxes and merit when using this phenomenon in applications.DiscussionTo explore the possibility of initializing (ON-to-OFF switching) κ usingmagnetic field control, we focused on the characteristic point of the B–Hloop, as shown in Fig. 3e. Coming back from positive highH, B crosses theH = 0Oe line with finite positive B. Then, B reaches zero at −470 Oe.Therefore, we investigatedwhetherB can return to the origin (H,B) = (0 Oe,0 G). Figure 5a shows the M-H loop when measuring M atH = 0→ 1500→ 0→−470→ 0Oe;orange arrows inFig. 5a, b explain thisfield experienceprocess. 4πM reaches the originpositionof the loop, and theinner magnetic flux density B also reaches its origin, as shown in Fig. 5b.These results indicate that certainmagnetic-field controls can returnnetB tothe initial value. We expected a reduction in κ due to the recovery ofsuperconductivity of the Sn regions using the same magnetic field control,but, as shown in Fig. 5c–e, κ does not reach the initial value. Those resultsimply the absence of bulk superconductivity in the Sn regions even in thestate of net B = 0G achieved after the process ofH = 0→ 1500→ 0→−470→ 0Oe. From the results on net B and κ, weconcluded that local B does not become zero, where the compensation offluxes parallel to+H and -H resulted in net B = 0G. Although we have notdirectly measured the direction of trapped fluxes (and/or vortices) of thesolder, the coexistence of fluxes with opposite directions can be assumedfrom the results. As magnetic field control cannot achieve initialization of κin the solders, other methods should be developed to achieve nonvolatileMTSwith initialization functionality.Heating up toT > Tc (T > 7.2 K for thesolder) or flowing current greater than the critical current density will workto reset theflux-trapping states and initialize the κ value, because of breakingthe superconducting states. In Fig. 5f, the temperature evolution of κmeasured atH = 0Oe after FC (1500Oe) is shown. The initialization of κ byincreasing the sample temperature to T > Tc is achieved.To further obtain experimental proofs for the flux trapping in the Snregions, we performed magneto-optical (MO) imaging for the Sn45–Pb55solder atT = 2.5 K. The obtained images are shown in Supplementary Fig. 7.Image (i) corresponds to the initial state after ZFCwhere nomagneticflux istrapped. When the magnetic field is H = 1500Oe, greater than the criticalfield of the solder, μm-order structures are observed in image (ii). Thesestructures indicate the uniform presence of magnetic fluxes in the normalconducting states. After decreasingH to 0 Oe, magnetic fluxes are expelledfrom the Pb regions and trapped in the Sn regions only. In image (iii), weobserve blurriness of the structures and the emergence of contrast differentfrom image (ii). By applying negativeH, reversed trends are seen. In imageFig. 4 | μm-scale phase separation of Pb and Sn in the solder. a Scanning-electron microscope (SEM) image on the polished surface of the solder (Sn45–Pb55).b, c Elemental mapping by energy-dispersive X-ray spectroscopy (EDX). d Line profiles of the compositions of Sn and Pb along the white arrow in (c).https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 5(iii), the light parts would be Pb-rich regions, and the dark parts would beSn-rich regions. Because of the inhomogeneous distribution of Sn regions,we just observed the blurriness and the changes in contrast. If magneticfluxes are trapped at the grain boundaries, the MO image should show auniform image in the flux-trapping states. Therefore, the present results canexclude the scenario of trapping at the grain boundaries. To obtain furtherevidence of the magnetic fluxes in the Sn regions, investigation with othertechniques is needed to directly observe trapped fluxes in the solders.For the future application of this phenomenon, the tunability ofnonvolatile MTS is preferred. Here, we investigated the Sn-contentdependence of nonvolatile MTS (Supplementary Fig. 8). For Sn90-Pb10,clear nonvolatility is not observed, but for Sn10-Pb90, nonvolatileMTS of ~300% is observed. In addition, the κ values change with changing Snamount. Furthermore, we evaluated minor-loop characteristics of κ-H forthe Sn45–Pb55 solder (Supplementary Fig. 9). As shown in SupplementaryFig. 10i, nonvolatile MTS is determined by the maximum field. The tun-ability of nonvolatileMTS by composition andmagnetic field provides newthermal management functionalities.Here, we demonstrated that Sn–Pb solders exhibit nonvolatileMTS byutilizing the superconducting states of Pb and flux trapping in the Snregions. In the solders, the coexistence of two superconducting phases withdifferentTc ,Tc = 7.2 K for Pb andTc = 3.7 K for Sn, gives rise to nonvolatileMTS based on the changes in κel. In addition, the trapped fluxes largeenough to suppress bulk superconductivity of the Sn regions are essential forthis phenomenon; hence, B >Hc for Sn was the preferred condition in thepresent case. The concept that superconductor composites can work asnonvolatile MTSmaterials is quite simple and applicable to various pairs ofsuperconductors. For example, using high-Tc superconductors in thenonvolatileMTS composite would increase the working temperature of thenonvolatileMTS phenomena bymaking a composite withmetals, alloys, orintermetallic compounds. Optimizing phase-separation conditions shouldenhance the switching ratio and flexibility of nonvolatile MTS.Furthermore, since the Sn–Pb solder is widely used in electrical wiring,the large nonvolatile thermal switching and magnetic flux trapping in thesolders should significantly affect low-temperature transport measurementtechniques that were believed to have already established. Therefore,understanding themagneto-transport phenomena in solders is essential forreliable transportmeasurements at low temperatures undermagnetic fields.MethodsSamplesWe used commercial solders: flux-core-less Sn45–Pb55 solder wires(φ1.6 mm, TAIYO ELECTRIC IND. CO., LTD.) and flux-cored Sn60-Pb40 solder wires (φ0.8mm, HOZAN). The data shown in the main textwas taken on a polished sample of Sn45–Pb55 solder wire. The purity of theSn45-Pb55 solder wire was investigated by X-ray Fluorescence (XRF), andthe actual Sn ratio was confirmed as 43.84(2)% in the weight ratio andSn0.58Pb0.42 in the molar ratio. The Cu impurity with a weight ratio of 0.2%was detected by XRF. The Sn10-Pb90 and Sn90-Pb10 solders with 99.9%purity were purchased from SASAKI SOLDER INDUSTRY CO., LTD.CharacterizationScanning-electron microscope (SEM) and energy-dispersive X-ray spec-troscopy (EDX) were used to analyze chemical compositions on the surfaceof the solders. The images for Sn45–Pb55 shown in themain textwere takenusing Carl Zeiss Cross-Beam 1540ESB and those for Sn60-Pb40 were takenFig. 5 | Minor loop measurements and initialization of κ. a, b H dependence of4πM and B at T = 2.5 K for the solder (Sn45–Pb55), measured when H was sweptbetween 1500 Oe and−470Oe. See the arrows for the guide formeasurement order.c, H dependence of κ, measured when H was swept from 0 to 1500 Oe (red), from1500 to−470 Oe (green), and from−470 to 0 Oe (blue). It is clearly shown that theinitial κ cannot be recovered by any magnetic-field control. d, e Measurementnumber dependence of H and κ at T = 2.5 K, extracted from the data in (c).f Initialization of κ by heating the sample above Tc. Measurement number depen-dence of κ, T andH. First, the ON state was produced by applyingH = 1500 Oe andreducing the field to zero at T = 2.5 K (measurement number: 1–9). For numbers10–24, temperature was gradually increased to T = 8.0 K. Then, temperaturedecreased to T = 2.5 K for numbers 25–40, and the initial κ is recovered as indicatedby the dashed line.https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 6using TM3030 (Hitachi Hightech). XRF was performed using JSX-1000S (JEOL).Physical property measurementsThermal conductivity (κ) was measured by means of a Physical PropertyMeasurement System (PPMS, Quantum Design) with a thermal transportoption (TTO) using a four-probe steady-state method with heater, twothermometers, and base-temperature terminal. The lengths between twothermometers attached to the measured samples were 55.5mm for theSn45–Pb55 rectangular bar with a cross-section area of 0.88 × 1.10mm2(reported in the main text), 65.0 mm for the Sn45–Pb55 wire with aφ1.6 mm in diameter (reported in Supplementary Fig. 3), and 44.5mm forSn60-Pb40 (reported in Supplementary Fig. 4). Due to the limitation of thesample-roomspace of theTTOstage, the samplewas screwed to store insidewith four probes, a heater, two thermometers, and thermal base. The typicalmeasurement duration for a single measurement was 30 s. The main result(κ–H at 2.5 K) was measured manually (not in a sequence mode) to checkthe temperature stability and the reliability of the relaxation curves.Magnetization was measured by a superconducting quantum inter-ference device (SQUID) magnetometry on Magnetic Property Measure-ment System (MPMS3, QuantumDesign) with a VSMmode. Specific heatwasmeasured onPPMSby a relaxationmode.The samplewas attached to astage using APIEZON N grease. Electrical resistivity was measured onPPMS by a four-probe method under magnetic fields.Magneto-optical imaging. For magneto-optical imaging, we usedPPMS and an infinity-corrected objective lens inserted into the samplespace by the microscope which is set above the PPMS at approximately1 m from the sample position29. The images shown here were prepared bysubtracting the images taken atT = 8.0 K (normal state) from those takenat T = 2.5 K and normalized by data taken at T = 8.0 K.Data availabilityAll relevant data are available from the corresponding author upon rea-sonable request.Received: 7 December 2023; Accepted: 26 February 2024;References1. Li, N. et al. Phononics: Manipulating heat flowwith electronic analogsand beyond. Rev. Mod. Phys. 84, 1045 (2012).2. Wehmeyer, G., Yabuki, T.,Monachon,C.,Wu, J. &Dames,C. Thermaldiodes, regulators, and switches: physical mechanisms and potentialapplications. Appl. Phys. Rev. 4, 041304 (2017).3. Nishimura, Y. et al. Electronic and lattice thermal conductivityswitching by 3D−2D crystal structure transition in nonequilibrium(Pb1−xSnx)Se. Adv. Electron. Mater. 8, 2200024 (2022).4. Cho, J. et al. Electrochemically tunable thermal conductivity of lithiumcobalt oxide. Nat. Commun. 5, 4035 (2014).5. Ihlefeld, J. F. et al. Room-temperature voltage tunablephonon thermalconductivity via reconfigurable interfaces in ferroelectric thin films.Nano Lett. 15, 1791 (2015).6. Kimling, J., Gooth, J. & Nielsch, K. Anisotropic magnetothermalresistance in Ni nanowires. Phys. Rev. B 87, 094409 (2013).7. Nakayama, H. et al. Above-room-temperature giant thermalconductivity switching in spintronic multilayer. Appl. Phys. Lett. 118,042409 (2021).8. Kimling, J. et al. Spin-dependent thermal transport perpendicular tothe planes of Co/Cu multilayers. Phys. Rev. B 91, 144405 (2015).9. Yoshida, M., Kasem, Md. R., Yamashita, A., Uchida, K. & Mizuguchi,Y. Magneto-thermal-switching properties of superconducting Nb.Appl. Phys. Express 16, 033002 (2023).10. Yoshida, M., Arima, H., Yamashita, A., Uchida, K. & Mizuguchi, Y.Largemagneto-thermal-switching ratio in superconducting Pb wires.J. Appl. Phys. 134, 065102 (2023).11. Huang, H. L., Wu, D., Fan, D. & Zhu, X. Superconducting quantumcomputing: a review. Sci. China Info. Sci. 63, 180501 (2020).12. Kjaergaard, M. et al. Superconducting qubits: current state of play.Annu. Rev. Condens. Matter Phys. 11, 369–395 (2020).13. Kes,P.H., vander Veeken, J. P.M.&deKierk,D. Thermal conductivityof niobium in the mixed state. J. Low Temp. Phys. 18, 355 (1975).14. Livingston, J. D. Magnetic properties of superconducting lead-basealloys. Phys. Rev. 129, 1943–1949 (1963).15. Furuya, S., Tominaga, A. & Narahara, Y. The wall-thicknessdependence of magnetic shielding or trapping in a low-fieldsuperconductor, Pb40Sn60. J. Low Temp. Phys. 53, 477–485 (1983).16. Abrikosov, A. A. Nobel Lecture: Type-II superconductors and thevortex lattice. Rev. Mod. Phys. 76, 975–979 (2004).17. Harada, K. et al. Real-time observation of vortex lattices in asuperconductor by electron microscopy. Nature 360, 51–53(1992).18. Hess, H. F., Robinson, R. B. & Waszczak, J. V. STM spectroscopy ofvortex cores and the flux lattice. Physica B 169, 422–431 (1991).19. Wells, F. S., Pan, A. V., Wang, X. R., Fedoseev, S. A. & Hilgenkamp, H.Analysis of low-field isotropic vortex glass containing vortex groups inYBa2Cu3O7-x thin films visualized by scanning SQUID microscopy.Sci. Rep. 5, 8677 (2015).20. Iguchi, Y. et al. Superconducting vortices carrying a temperature-dependent fraction of the flux quantum. Science 380,1244–1247 (2023).21. Dolan, G. J. & Silcox, J. Critical thicknesses in superconducting thinfilms. Phys. Rev. Lett. 30, 603–606 (1973).22. Ge, J., Gutierrez, J., Cuppens, J. &Moshchalkov, V. V. Observation ofsingle flux quantum vortices in the intermediate state of a type-Isuperconducting film. Phys. Rev. B 88, 174503 (2013).23. Doll, R. & Näbauer, M. Experimental proof of magnetic fluxquantization in a superconducting ring. Phys. Rev. Lett. 7,51–52 (1961).24. Minkov, V. S., Ksenofontov, V., Bud’ko, S. L., Talantsev, E. F. &Eremets, M. I. Magnetic flux trapping in hydrogen-rich high-temperature superconductors. Nat. Phys. https://doi.org/10.1038/s41567-023-02089-1 (2023).25. Xing, X. et al. Anisotropic Ginzburg–Landau scaling of Hc2 andtransport properties of 112-type Ca0.8La0.2Fe0.98Co0.02As2 singlecrystal. Supercond. Sci. Technol. 29, 055005 (2016).26. Stewart, G. R. Measurement of low‐temperature specific heat. Rev.Sci. Instrum. 54, 1–11 (1983).27. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory ofsuperconductivity. Phys. Rev. 108, 1175–1204 (1957).28. Padamsee, H., Neighbor, J. E. & Shiffman, C. A. Quasiparticlephenomenology for thermodynamics of strong-couplingsuperconductors. J. Low Temp. Phys. 12, 387–411 (1973).29. Kinoshita, Y., Miyakawa, T., Xu, X. & Tokunaga, M. Long-distancepolarizing microscope system combined with solenoid-type magnetfor microscopy and simultaneous measurement of physicalparameters. Rev. Sci. Instrum. 93, 073702 (2022).AcknowledgementsThe authors thank O. Miura, A. Yamashita, M. Yoshida, T. D. Matsuda, K.Hattori, R. Kurita, Y. Oikawa, H. Fujihisa, A. Kikkawa, and T. Machida forsupport in experiments and fruitful discussion on the results. This work waspartly supported by JST-ERATO (JPMJER2201), TMU Research Project forEmergent Future Society, the joint research in the Institute for Solid StatePhysics, the University of Tokyo (202306-HMBXX-0090), and Tokyo Gov-ernment Advanced Research (H31-1).https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 7https://doi.org/10.1038/s41567-023-02089-1https://doi.org/10.1038/s41567-023-02089-1https://doi.org/10.1038/s41567-023-02089-1Author contributionsK.U. and Y.M. planned and supervised the study. H.A., H.S.A., K.U., Y.K.,M.T., and Y.M. designed the experiments. H.A., M.R.K., H.S.A., Y.K., M.T.,and Y.M. collected and analyzed the data. H.A., F.A., K.U., and Y.M.prepared the manuscript. All the authors discussed the results, developedan explanation of the experiments, and commented on the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-024-00465-9.Correspondence and requests for materials should be addressed toYoshikazu Mizuguchi.Peer review information Communications Materials thanks theanonymous reviewers for their contribution to the peer review of this work.Primary Handling Editor: Aldo Isidori.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in anymedium or format, as longas you give appropriate credit to the original author(s) and the source,provide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this article areincluded in the article’s Creative Commons licence, unless indicatedotherwise in a credit line to the material. If material is not included in thearticle’sCreativeCommons licence and your intended use is not permittedby statutory regulation or exceeds the permitted use, you will need toobtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024https://doi.org/10.1038/s43246-024-00465-9 ArticleCommunications Materials | (2024) 5:34 8https://doi.org/10.1038/s43246-024-00465-9http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/ Observation of nonvolatile magneto-thermal switching in superconductors Results Nonvolatile magneto-thermal switching in Sn–Pb�solder Characterization of superconducting properties and phase separation of Sn–Pb�solder Discussion Methods Samples Characterization Physical property measurements Magneto-optical imaging Data availability References Acknowledgements Author contributions Competing interests Additional information