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[Ping Tang](https://orcid.org/0000-0003-2533-0156), [Ken-ichi Uchida](https://orcid.org/0000-0001-7680-3051), [Gerrit E. W. Bauer](https://orcid.org/0000-0002-3615-8673)

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Giant Magnon-Driven Magnetothermal Transport in Magnetic MultilayersPing Tang1,∗ Ken-ichi Uchida2,3, and Gerrit E. W. Bauer1,4,51WPI-AIMR, Tohoku University, Sendai 980-8577, Japan2National Institute for Materials Science (NIMS), Tsukuba 305-0047, Japan3Department of Advanced Materials Science, Graduate School of Frontier Sciences,The University of Tokyo, Kashiwa 277-8561, Japan4Institute for Materials Research and CSIS, Tohoku University, Sendai 980-8577, Japan and5Kavli Institute for Theoretical Sciences, University of the Chinese Academy of Sciences, Beijing 10090, China(Dated: April 28, 2025)All-solid-state nanoscale devices capable of efficiently controlling a heat flow are crucial for ad-vanced thermal management technologies. Here we predict a magnon-driven magnetothermal resis-tance (mMTR) effect in multilayers of ferromagnets and normal metals, i.e. a thermal resistancethat varies when switching between parallel and antiparallel magnetization orientations of the fer-romagnetic layers, even in the absence of conduction electrons in the ferromagnets. The mMTRarises from an interfacial temperature drop caused by magnon spin accumulations and can be engi-neered by the layer thicknesses, spin diffusion lengths, and spin conductances. The mMTR predictedhere enables magnetothermal switching in insulator-based systems; we already predict large mMTRratios up to 40% for superlattices of the electrically insulating magnet yttrium iron garnet andelemental metals.Introduction.—The magneto-thermal resistance(MTR) effect enables the magnetic control of thermaltransport. Solid-state devices with a high MTR ratioand a broad operating temperature range around roomtemperature are essential for thermal managementtechnologies [1]. A traditional approach focuses onthe MTR of single-phase bulk materials, but it oftenrequires impractically high magnetic fields or extremelylow operation temperatures [2–8]. More promising isthe giant MTR in ferromagnetic (FM)|nonmagnetic(NM) multilayers [9–17], the thermal version of thegiant magnetoresistance (GMR) [18, 19], where thethermal conductivity varies with the magnetizationconfigurations of the ferromagnetic layers, opening apathway towards nonvolatile, nanoscale thermal switch-ing devices [20]. Similar to the essential role of electronicspin accumulation in the GMR, spin-dependent heataccumulation or temperature of electrons is proposedto explain the MTR in magnetic multilayers [15, 21].Because of the Wiedemann-Franz law and short spin-dependent heat relaxation length (compared to the spindiffusion length), the MTR has long been considereda byproduct of the GMR and has only received littleattention. Surprisingly, several experimental groupsreport an MTR exceeding the GMR [12, 13, 16, 17],implying an unconventional magneto-thermal transportmechanism.Magnons, the collective quasi-particle excitations ofmagnetic order, serve as an additional carrier of energyand spin in a magnetic metal [22]. Under the gradient ofa temperature or non-equilibrium magnon accumulation[23–25], magnon diffusion contributes to both heat andspin currents, leading to magnetic-field dependent ther-mal conduction [26–28] and the spin Seebeck effect [29],∗ tang.ping.a2@tohoku.ac.jpFIG. 1. Concept of the magnon-driven thermal resistancein (FM1)|nonmagnetic metal (NM)|ferromagnet (FM2). Athermal bias excites non-equilibrium magnon accumulations(orange solid curves). Its gradient generates a back-flow heatcurrent by diffusion and thereby, for a fixed heat current bias,an additional temperature drop ∆Tm as sketched by the bluelines. (a) In the parallel configuration, the spin accumulationsinjected by the two FMs into the metal spacer cancel, corre-sponding to a high thermal conductance. In the antiparallelconfiguration (b), they add up to form a high-resistance state.The arrows on the grey dots represent the magnon spin angu-lar momenta, the green solid curves in the NM layer the spinaccumulation of electrons, and the dashed orange curves in(b) the magnonic spin accumulation opposite to the magnonnumber accumulation (solid orange curves).respectively. Recently, Hirai et al. [30] reported surpris-ingly large magnon contributions to the thermal trans-port properties of a ferromagnetic metal even at roomtemperature.Motivated by these experiments [17, 30] we present inthis Letter a pronounced magnon-driven MTR (mMTR)in magnetic multilayers (see Fig. 1): a thermally drivenmagnon current within the FM layers produces non-equilibrium magnon accumulation near FM|NM inter-faces that depends on the interlayer magnetic configu-ration and causes an additional temperature drop duemailto:tang.ping.a2@tohoku.ac.jp2to a feedback diffusion heat current, giving rise to theMTR effect. This is analogous to the GMR with cur-rent perpendicular to the interfaces, in which interfacialspin accumulation of electrons plays an essential role [31].We explain the large mMTR at room temperature bytwo factors. While in the GMR only electrons near theFermi level play a role, the boson statistics of magnonsallow all of them to contribute to transport. Moreover,the magnon diffusion length can exceed that of the mo-bile electrons by orders of magnitude. Since magnonscan exist in magnetic insulators, the mMTR goes beyondthe GMR mechanism, offering the potential for insulator-based magnetothermal switching devices.Model.—We address the mMTR for a spin valve oftwo identical FM layers and a thin NM spacer, as illus-trated in Fig. 1, as well as FM|NM multilayers. In ametallic FM, both electrons and magnons contribute tothe MTR. The electron-induced MTR is caused by spin-dependent thermal conductivities in the FM and FM|NMinterfaces and thereby directly related to the GMR bythe Wiedemann-Franz law. Here we focus on electri-cally insulting FM layers to isolate a previously unrecog-nized magnonic mechanism. Since the mMTR is causedby thermally excited (incoherent) magnons, we disregardthe coherent magnon coupling between FM layers by anon-local exchange interaction through ultrathin metalspacers [32, 33], which may play a role in the mMTRonly at low temperatures, viz. thermal energies of theorder of the modified magnon gap.In linear response a temperature (chemical potential)gradient ∂Ti (∂µi) drives spin [Ji] and heat [Qi] currentsin the ithe FM layer [25](eℏJiQi)= −(σm LmT0Lm κF)(∂µi/e∂Ti), (1)where σm and Lm are the magnon spin conductivity andspin Seebeck coefficient, respectively, while κF is the to-tal thermal conductivity including phonon contributions.We employed the Onsager reciprocity of the off-diagonalmagnon Seebeck and Peltier coefficients at the averagetemperature T0. The polarization of the magnon spincurrent in Eq. (1) is collinear with the magnetization di-rection of the ith FM layer and changes sign when re-versing the magnetization. The spin [JN ] and heat [QN ]currents in the NM layer, on the other hand, obey(JNQN)= −( ℏ4e2σN 00 κN)(∂µN∂TN)(2)where σN and κN are the electric and thermal conductiv-ities of the metal, respectively, and µN the spin chemicalpotential, i.e. the chemical potential difference of spin-up and -down electrons. In contrast to the FM layers,there are no off-diagonal elements.Biasing the spin valve by a given heat current Q in-duces temperature and chemical potential gradients. In-verting the above relations∂Ti(x) =− QκF− T0LmeκF∂µi(x) (3)∂TN (x) =− QκN, (4)where magnon Peltier effect generates a non-equilibriummagnon accumulation and the second term in Eq. (3).The thermal resistivity ρ of the spin valve with spacerthickness dN and equal thickness dF of the two magnetsreadsρ ≡ ∆TLQ=1L(2dFκF+dNκN)+ ρm, (5)where L = 2dF + dN , ∆T is the total temperature drop.Here we introduced a magnon-driven magnetothermal re-sistivity ρm = ∆Tm/(LQ), where∆Tm =T0LmeκF∫dx′[∂µ1(x′) + ∂µ2(x′)] (6)is the temperature drop in the presence of a magnon ac-cumulation. In the following, we calculate Eq. (6) and ρmby spin diffusion theory when the two magnetizations areparallel and antiparallel.Results.—The solutions to the magnon diffusion equa-tion (∂2 − λ−2m )µi = 0 are [23–25],µi(x) = Aiex/λm +Bie−x/λm , (7)where Ai and Bi are coefficients determined by boundaryconditions and λm the magnon diffusion length. Theelectronic spin chemical potential in the NM layer obeysµN (x) = Cex/λN +De−x/λN (8)where λN is the spin diffusion length of electrons. Ina collinear configuration without interfacial spin torques,the spin currents at two NM-FM interfaces are conserved,i.e.J1(0) = JN (0), JN (dN ) = sJ2(dN ) (9)where s = ± accounts for the polarization of themagnonic spin current in the second FM layer, i.e., (+)when the magnetization of the second FM layer is alignedparallel (−) when antiparallel to that of the first FMlayer. Assuming transparent NM|FM interfaces [34], themagnon and electron spin chemical potentials are alsocontinuous at the interfaces withµ1(0) = µN (0), µN (dN ) = sµ2(dN ) (10)where s = −1 reflects the annihilation of magnons in thesecond FM by a spin-flip in the normal metal when itsmagnetization is antiparallel, i.e., “magnon holes” withopposite spins are created in the second FM layer. Whenthe FM thickness is smaller than or comparable to themagnon diffusion length we must specify the boundary3conditions at the outer interfaces. In the following, weconsider several experimentally relevant cases.(i) Spin-sinking contact. We first consider a spin valvesandwiched between good spin sinks such as Pt, whichimplies that µ1(−dF ) = µ2(dN+dF ) = 0. The solution ofEq. (7) with these boundary conditions leads to thermalresistivitiesρPm =2ℏe2LT0L2mκ2FGm +GN tanh dFλmtanh dN2λNcoth dFλmG2m + tanh dFλmG2N + 2GmGN coth dNλN(11)ρAPm =2ℏe2LT0L2mκ2FGm +GN tanh dFλmcoth dN2λNcoth dFλmG2m + tanh dFλmG2N + 2GmGN coth dNλN(12)TABLE I. The parameters for several normal metal spacerswith long spin diffusion lengths at room temperature.NM σN (S/µm) κN (W/(K·m)) λN (nm) GN (1016 m−2)Al 31 237 600 [35] 5Cu 35 401 350 [36] 10Au 19 318 60 [37] 32for the parallel and antiparallel configurations, re-spectively. Here Gm ≡ (ℏ/e2)σ̄m/λm and GN ≡(ℏ/4e2)σN/λN are the spin conductances (per unit area)in the FM and NM, respectively, andσ̄m ≡ σm(1− T0L2mκFσm)= σm(1− zTmκmκF)(13)is the magnon spin conductivity corrected for the spinSeebeck/Peltier effects, where zTm ≡ T0L2m/(κmσm) isa thermomagnonic figure of merit and κm the magnonthermal conductivity. Here ρPm and ρAPm scale as κ−2F , im-plying that they can be enhanced by choosing FM layerswith low thermal conductivities.We measure the heat-valve performance by the mMTRratio (ρAP − ρP)/ρPmMTR =η2dFλm+ κFκNdNλm+ 2η1+ξ tanhdFλmtanhdN2λNcothdFλm+2ξ cothdNλN+ξ2 tanhdFλm×4ξ tanh2 dFλmcsch dNλN1 + 2ξ tanh dFλmcoth dNλN+ ξ2 tanh2 dFλm, (14)where ξ = GN/Gm is the ratio of the spin conductancesof electrons to magnons andη = zTmκmκF(1− zTmκmκF)−1(15)is another dimensionless figure of merit that measuresthe impact of a magnon accumulation on the thermalconductivity. According to Eq. (14), η, ξ and the nor-malized thicknesses of the NM and FM layers govern theFIG. 2. (a) and (b): The mMTR ratio as a function of ξand dF /λm of a YIG|NM|YIG spin valve calculated for outerboundary conditions corresponding to an (i) ideal spin sink,(ii) zero spin current, and (iii) a superlattice stack. HeredF /λm = 1 and dN/λN = 0.1 in (a), and dN/λN = 0.1 andκFλN/(κNλm) = 0.01 in (b). (c) and (d): mMTR depen-dence on FM and NM thicknesses in a [FM|NM] superlatticewith different NMs with dF /λF = 0.1 in (c) and dN/λN = 0.1in (d).magnitude of the mMTR that increases monotonicallywith increasing η or decreasing dN/λN , but decreases forlarge dF /λm and ξ. In Fig. 2(a) and (b) we tune theparameters to maximize the effect. When dN ≪ λN ,the mMTR ratio approaches a ξ-independent maximumvaluemMTRdN≪λN→ η1 + RNRFλmdFtanhdFλm(16)where RN = dN/κN and RF = 2dF /κF are the thermalresistances in the absence of the magnon accumulation(ii) Zero spin current. When the spin valve issandwiched by nonmagnetic insulators (e.g., MgO), themagnon spin currents at the outer interfaces of two FM4layers vanish, leading tomMTR =η2dFλm+ κFκNdNλm+ 2η2 tanhdF2λm+ξ cothdN2λN1+ξ cothdFλmcothdN2λN×2ξcsch2 dN2λNtanh2 dF2λm(ξ coth dFλm+ coth dN2λN)(1 + ξ coth dFλmcoth dN2λN)dN≪λN→η λmdFtanh2 dF2λmtanh dFλm1 + RNRF+ η λmdFtanh dFλm, (17)which agrees with Eq. (14) in the limit of dF /λm ≫ 1,as expected. However, an FM thickness comparable toλm suppressed the effect [Fig. 2(b)] because the magnonaccumulation near the outer interfaces compensates forthe ones near the FM|NM interfaces.(iii) Superlattice condition. In a spin valve embed-ded in a magnetic superlattice with [FM|NM] unit cell,the same surroundings for two interfaces of each FMlayer correspond to outer boundary conditions whenthe magnon chemical potentials at the outer boundaryare opposite to the ones at the FM|NM interfaces, i.e.,µ1(−dF ) = −µ1(0) and µ2(dN ) = −µ2(dN + dF ).mMTR =η2dFλm+ κFκNdNλm+ 4ηtanhdF2λm1+ξ cothdN2λNtanhdF2λm8ξ tanh2 dF2λmcsch dNλN(1 + ξ tanh dF2λmtanh dN2λN)(1 + ξ tanh dF2λmcoth dN2λN)dN≪λN→ 2η1 + RNRFλmdFtanhdF2λm. (18)Since the magnon accumulation near both two inter-faces of each FM layer contributes to the magnetothermaltransport, the mMTR is enhanced compared to the pre-vious cases [Fig. 2(a) and (b)], in the limit of dN ≪ λNand dF ≫ λm the mMTR becomes two times larger thanEq. (16). A similar enhancement of the spin Seebeck ef-fect has been reported in metallic magnetic multilayers[38].Let us consider a specific spin valve composed ofNM (= Al, Cu, Au) and the magnetic insulator yt-trium iron garnet (YIG) with well-known parameters atroom temperature (T0 = 300K): σm = 5 × 105 S/m[25], Lm/σm = 110µV/K [39] and λm = 70nm [40],κYIG = 6.6W/(K·m) [41], which gives η = 0.38 andGm = 2.12× 1016 m−2. Table I summarizes the relevantparameters for Al, Cu, and Au. Fig. 2(a) and (b) plotsthe mMTR ratio as a function of ξ and dF /λm for theaforementioned outer boundary conditions, respectively.Fig. 2(c) and (d) shows the mMTR with the superlat-tice boundary condition for Al, Cu, and Au spacers asa function of the FM and NM thicknesses, respectively.The mMTR decreases monotonically with the NM thick-ness; it is largest (∼ η) at an optimal thickness of the FMthat is much smaller than its magnon diffusion length,approaching zero when κF dN/(κNλm) → 0.Conclusion.—We predict a substantial room-temperature mMTR in spin valves with electricallyinsulating FM layers. We trace its origin to an inter-facial temperature drop caused by a non-equilibriummagnon spin accumulation that depends on the relativeorientation between two FM layers. The mMTR ratiocan be engineered by the spin conductances, boundaryconditions, and layer thicknesses. 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