# Fileset [Tachibana_2025_J._Phys.__Condens._Matter_37_405401.pdf](https://mdr.nims.go.jp/filesets/a7c5f95f-2963-4ec9-8b58-4efc5a831616/download) ## Creator [Makoto Tachibana](https://orcid.org/0000-0002-5907-5563), [Cédric Bourgès](https://orcid.org/0000-0001-9056-0420), [Takao Mori](https://orcid.org/0000-0003-2682-1846) ## Rights [Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/) ## Other metadata [High-temperature thermal conductivity of yttrium and rare-earth iron garnets](https://mdr.nims.go.jp/datasets/2bf2ff1e-2b81-4a9a-b8d7-7232b92734b7) ## Fulltext High-temperature thermal conductivity of yttrium and rare-earth iron garnetsJournal of Physics:Condensed Matter      PAPER • OPEN ACCESSHigh-temperature thermal conductivity of yttriumand rare-earth iron garnetsTo cite this article: Makoto Tachibana et al 2025 J. Phys.: Condens. Matter 37 405401 View the article online for updates and enhancements.You may also likeEffective criteria for entanglementwitnesses in small dimensionsukasz Grzelka, ukasz Marcin Skowronekand Karol yczkowski-Design of beam direction controllablemultijunction rectangular VCSELYufei Wang, Yibo Yang, Sidra Farouk etal.-Gradient-descent methods for fastquantum state tomographyAkshay Gaikwad, Manuel SebastianTorres, Shahnawaz Ahmed et al.-This content was downloaded from IP address 144.213.253.16 on 30/09/2025 at 09:21https://doi.org/10.1088/1361-648X/ae09e6/article/10.1088/1751-8121/ae0c49/article/10.1088/1751-8121/ae0c49/article/10.1088/2631-8695/ae090a/article/10.1088/2631-8695/ae090a/article/10.1088/2058-9565/ae0baa/article/10.1088/2058-9565/ae0baaJournal of Physics: Condensed MatterJ. Phys.: Condens. Matter 37 (2025) 405401 (7pp) https://doi.org/10.1088/1361-648X/ae09e6High-temperature thermal conductivityof yttrium and rare-earth iron garnetsMakoto Tachibana1,∗, Cédric Bourgès2,3 and Takao Mori1,41 Research Center for Materials Nanoarchitechtonics, National Institute for Materials Science, 1-1Namiki, Tsukuba 305-0044, Japan2 International Center for Young Scientists, National Institute for Materials Science, 1-1 Namiki, Tsukuba305-0044, Japan3 University of Limoges, CNRS, IRCER, UMR 7315, Limoges F-87000, France4 Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba305-8577, JapanE-mail: TACHIBANA.Makoto@nims.go.jpReceived 28 July 2025, revised 5 September 2025Accepted for publication 22 September 2025Published 30 September 2025AbstractYttrium and rare-earth iron garnets (R3Fe5O12) are ferrimagnetic insulators that have beenwidely studied for magnetic and spintronic applications. In this study, we report the thermalconductivity (κ) between 300 and 773 K for the single crystals of R3Fe5O12, where R = Y, Gd,Dy, and Yb. For Y3Fe5O12, the κ up to the Curie temperature (TC ≈ 555 K) can be describedwell with a pure phononic model, without considering conduction or scattering by the magnons.The iron garnets containing magnetic rare-earth ions exhibit smaller κ, with Dy3Fe5O12showing the smallest values due to the strong interactions of heat-carrying phonons with thecrystal field excitations of Dy3+ ions.Keywords: thermal conductivity, heat capacity, iron garnets, single crystal, phonon, magnon1. IntroductionThe ferrimagnetic insulator Y3Fe5O12 (yttrium iron garnet orYIG) has been a compound of great importance in spintron-ics, as its spin waves or magnons possess a long lifetime evenat room temperature [1,2]. In 1962−63, thermal conductivity(κ) from magnons was reported for the first time using YIGsingle crystals [3–5]. These experiments, conducted at liquidhelium temperatures, confirmed Sato’s earlier prediction [6]that ferro- and ferrimagnetic magnon κ follow a T2 power law∗Author to whom any correspondence should be addressed.Original content from this work may be used under theterms of the Creative CommonsAttribution 4.0 licence. Anyfurther distribution of this work must maintain attribution to the author(s) andthe title of the work, journal citation and DOI.for T → 0 K, unlike the T3 dependence of the familiar phononκ. Since the magnon κ can be suppressed under magneticfield, it was also shown that magnon and phonon contributionsbecome comparable in size below∼1 K, while phonons dom-inate the heat transport at higher temperatures [3–5]. In morerecent times, YIG has been used extensively to explore the spinSeebeck effect (SSE) [7, 8], where spin currents are generatedfrom a thermal gradient. It is within this context that the κ ofYIG was revisited by various authors, both from experimental[9–13] and theoretical [14–17] perspectives.YIG is a member of R3Fe5O12 garnets [18], or RIGs, whereR can be Y or a rare earth from Sm to Lu. The cubic garnetstructure of RIGs (space group Ia 3̄ d) is rather complex, withfour formula units in the primitive unit cell. The R3+ ions,being 8-fold coordinatedwith oxygen, are located at the c sites.Of the five Fe3+ ions in the formula unit, three at the d sites are4-fold coordinated with oxygen, while two at the a sites are 6-fold coordinated. As a result of antiferromagnetic interactions1 © 2025 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/1361-648X/ae09e6https://orcid.org/0000-0002-5907-5563https://orcid.org/0000-0001-9056-0420https://orcid.org/0000-0003-2682-1846mailto:TACHIBANA.Makoto@nims.go.jphttp://crossmark.crossref.org/dialog/?doi=10.1088/1361-648X/ae09e6&domain=pdf&date_stamp=2025-9-30https://creativecommons.org/licenses/by/4.0/J. Phys.: Condens. Matter 37 (2025) 405401 M Tachibana et albetween the majority d-site and minority a-site Fe3+ (S= 5/2)spins, YIG and other RIGs undergo a second-order ferrimag-netic transition at a Curie temperature of TC ≈ 550 −560 K[18]. The similar TCs found for the entire series indicatethat the rare-earth ions, even when magnetic, do not visiblyaffect the interactions between the Fe3+ spins. Nonetheless,the exchange coupling between Fe3+ and R3+ polarizes theR3+ moments below TC. For R=Gd−Yb there is a compens-ation temperature below 300 K where the magnetization ofthe rare-earth ions exactly cancels the net Fe3+ magnetization[18]. Recent studies [19–22] have shown that magnetic R3+ions produce features in the SSE that are not found in YIGwith the nonmagnetic Y3+ ions.Despite the continuing interest in the iron garnets, espe-cially in regard to the SSE, their κ above room temperaturehave not been studied in detail. For YIG, much of previousκ studies have focused at low temperatures, where the mag-netic field needed to suppress the magnon excitations is exper-imentally attainable. Though some high-temperature data [10,23–25] exist, they do not yet provide a clear picture on howthe κ evolves below and above the ferrimagnetic transition.As for other RIGs, no κ data appears to be available in theliterature. These situations thus prompted the present invest-igation, which reports on the κ between 300 and 773 K forthe single crystals of YIG and other RIGs (R = Gd, Dy, andYb, denoted as GdIG, DyIG, and YbIG, respectively). Ourdata on YIG up to TC strictly follow the T−1 dependenceand the values predicted by the Slack equation. These res-ults demonstrate that the κ in this temperature region is fullydescribed by anharmonic phonon-phonon scattering, withoutany visible contributions from magnon–phonon scattering ormagnon heat transport. In contrast, much weaker temperat-ure dependence (∝T−0.6) is found above TC, suggesting thatphonons are scattered from fluctuating Fe3+ spins in the para-magnetic phase. Smaller κ are found in other RIGs. In partic-ular, DyIG shows the smallest values due to the strong inter-actions between phonons and the crystal field excitations ofDy3+ ions.2. Experimental detailsSince the iron garnets melt incongruently, bulk single crys-tals are usually grown by a flux method [26] or the float-ing zone (FZ) method using excess Fe2O3 as a solvent [27].For this study, an FZ-grown YIG crystal was purchased fromSurfaceNet GmbH. We also grew single crystals of YIG,GdIG, DyIG, and YbIG using a PbO-PbF2-B2O3 flux [28].These flux-grown crystals had large {110} faces and theirphase purities were confirmed by x-ray powder diffraction.From electron probe microanalysis, small amounts of Pb weredetected uniformly in these crystals. Assuming that Pb ionssubstitute solely the R ions [29], the concentration of Pb atthe c site is 1.7% for YIG, 1.2% for GdIG, 1.5% for DyIG,and 0.87% for YbIG. As described below, this study alsoused a flux-grown single crystal of Y3Al5O12 (YAG) [30, 31]with an impurity content of Pb/Y = 0.03% [30] and a poly-crystalline pellet of Yb3Al5O12 (YbAG). The YbAG pelletwas obtained in a manner similar to that of Dy3Al5O12 inTachibana et al [32].The κ between 300 and 773 K was determined from therelation κ = DCpρ, where D is thermal diffusivity, Cp isheat capacity, and ρ is density. D was obtained by the flashmethod in a nitrogen atmosphere using Netzsch LFA 567. Forthe measurements, crystals were cut into square plates with6 ×6 mm2 faces and ∼1.0 mm thicknesses, and a thin layerof graphite was coated on both sides. The large faces coin-cided with {110} for the flux-grown RIGs and YAG crystals,and {111} for the FZ-grown YIG crystal. The D values havean accuracy of ⩽3% and are shown in the appendix. Cp upto 390 K was measured on smaller samples using the relax-ation method of a quantum design physical property meas-urement system, which has an accuracy of 1% [33]. Cp athigher temperatures was determined as described below. ρbetween 300 and 773 K was calculated from literature x-rayvalues. For YIG, GdIG, YAG, and YbAG, x-ray data up to773 K are available [34, 35] and these were used to obtain ρ.As only room-temperature x-ray data are available for DyIGand YbIG [36], the thermal expansion of GdIG was adoptedfor these compounds; this should be justified since R3Ga5O12(R=Gd, Dy, and Yb) show nearly identical thermal expansioncoefficient at 300 K [37]. Our own ρ measurements at 295 Kusing the Archimedes method confirmed the x-ray values towithin ±1%.3. Results and discussion3.1. Heat capacityWe first examine the high-temperature Cp of YIG, which isshown in figure 1. Our present data up to 390 K agree wellwith those of Devyatkova and Tikhonov [23]. At higher tem-peratures, there are two sets of data from differential scanningcalorimetry (DSC) that provide somewhat conflicting pictures:(1) Uchida et al’s Cp [10], while agreeing with our data below390 K, shows an unusual hump around 500 K. This broad fea-ture appears to be unrelated to the ferrimagnetic ordering ofFe3+ spins, since their magnetization data show a sharp trans-ition at TC = 553 K [10]. Also, their Cp lacks the expectedpeak at TC, which leads us to suspect some error in the meas-urement. (2) Denisov et al’s Cp [38] on Y2.93Ho0.07Fe5O12exhibits a clear peak at TC, and the overall values at highertemperatures are consistent with those of other iron garnetsdiscussed below. The λ-shape of the peak is consistent witha second-order transition that is strongly affected by criticalfluctuations. Although the 2% Ho3+ dopant in this samplesomewhat broadens the Cp peak, this level of impurity shouldnot significantly affect Cp away from TC. For T < TC, themost reasonableCp is obtained by interpolating our data below390 K and Denisov et al’s data above 450 K, which is shownwith a red solid line. These values andDenisov et al’sCp aboveTC are thus used to obtain the κ for YIG.2J. Phys.: Condens. Matter 37 (2025) 405401 M Tachibana et alFigure 1. Heat capacity Cp of Y3Fe5O12. Present data are plottedalong with those of Denisov et al [38], Uchida et al [10], andDevyatkova and Tikhonov [23]. Note that Denisov et al’s samplecontains Ho3+. The Cp shown with the red solid line is used toobtain thermal conductivity. The black solid line is the Cp ofY3Al5O12 [39], and the dashed line corresponds to the estimatedlattice Cp of Y3Fe5O12.The black solid line in figure 1 represents the Cp forYAG [39], which is a nonmagnetic isomorph of YIG. TheDebye temperature Θ of YAG is 741 K, whereas that ofYIG is 560 K [40]. From these data, the lattice Cp forYIG can be roughly estimated by multiplying the temperat-ure scale of Cp for YAG by 560/741 [41], as shown withthe dashed line. Bearing in mind the crude nature of thisestimate, we obtain the magnetic Cp contribution in YIG at300 K as 27.4 JK−1mol−1. This value is much larger than2.4 JK−1 mol−1 calculated from the single parabolic magnonband formula [16, 17], but rather close to 10.3 JK−1 mol−1obtained from the ‘semi-quantum’ calculation using allmagnon modes [42]. (The latter predicts TC = 680 K[42].) Perhaps even better agreement may be achievedif finite temperature effects are fully incorporated intothe calculation.The Cp for other RIGs (R = Sm −Lu) have been meas-ured by Parida et al using DSC [43]. Their data for GdIG,DyIG, and YbIG are reproduced in figure 2. Compared toYIG, these compounds have slightly larger Cp due to the heav-ier molecular mass and crystal-field contributions (for Dy3+)from the rare-earth ions. (Θ = 491 K for GdIG [40], whilethe values are not known for DyIG and YbIG.) The sharppeak at TC affirms the high quality of the samples. However,Parida et al’s Cp contains a shoulder structure near 400 K,an extrinsic feature found in all their data [43]. We thusdiscard this contribution by extrapolating our Cp to highertemperatures, as shown with the red solid lines. The Cp forYbAG is also presented in figure 2(c). Here, the black solidline refers to the Neumann–Kopp (NK) values, which areobtained by adding the weightedCp of Yb2O3 and Al2O3 [44].The agreement with our experimental data below 390 K isexcellent.Figure 2. Heat capacity Cp of (a) Gd3Fe5O12, (b) Dy3Fe5O12, and(c) Yb3Fe5O12. Present data are plotted along with those of Paridaet al [43]. The Cp shown with the red solid lines are used to obtainthermal conductivity. In (c), the Cp of Yb3Al5O12 from the presentstudy and the Neumann–Kopp (NK) values are also shown.3.2. Thermal conductivity of YIGWenow discuss heat transport data, starting with those of YIG.The inset of figure 3 shows D near TC for our FZ crystal,our flux-grown crystal, and Hofmeister’s crystal [25] (growthmethod not specified). In each case, D exhibits a sharp, inver-ted λ-type dip at TC, similar in shape to that of sound velocity[45] and signifying interaction of acoustic phonons with thecritical fluctuations of the Fe3+ spins. There is excellent agree-ment between our FZ crystal and Hofmeister’s crystal, forwhich TC ≈ 555 K can be located. On the other hand, the flux-grown crystal exhibits smaller values of D and TC (≈535 K),most likely due to the presence of Pb impurity. These resultson D are then combined with the Cp in figure 1 to yield threesets of κ data shown in the main panel of figure 3. Due to thesample dependence of Cp, the κ near TC is plotted with opensymbols for our crystals and should be disregarded. However,one may expect the dip in D and the peak in Cp to mirror andcancel each other, as occurs in the κ of ferrimagnetic NiFe2O4(TC = 860 K) [46] and ferromagnetic EuO (TC = 69 K) [47],for example. As expected for a nonmetallic crystal, the κ ofYIG decreases rapidly on heating. The κ at 300 and 773 K forour FZ crystal are 6.6 and 3.0 Wm−1K−1, respectively, andnearly identical values are seen for Hofmeister’s crystal. Thus,3J. Phys.: Condens. Matter 37 (2025) 405401 M Tachibana et alFigure 3. Thermal conductivity κ of Y3Fe5O12. Present data fromthe FZ- and flux-grown crystals are plotted along with four sets ofpublished data [10, 23–25]. The κ for Hofmeister is calculated usingthe Cp obtained in this study. Due to the sample dependence of Cp,κ near the Curie temperature are plotted with open symbols for ourcrystals. The inset shows thermal diffusivity D near the Curietemperature for the FZ- and flux-grown crystals and Hofmeister’scrystal [25].these data likely represent the κ of high-quality YIG crystals.In contrast, our flux-grown crystal shows ∼10% lower κ val-ues for the entire temperature range, signifying strong phononscattering from the Pb impurity.Also shown in figure 3 are the literature κ data from threesources [10, 23, 24]. Two of these [23, 24] were obtained onpolycrystalline YIG. Their overall agreement with our singlecrystal data indicates that the κ is not severely affected bygrain-boundary scattering. On the other hand, Uchida et al.’ssingle crystal data [10] exhibit much larger κ, exceeding othervalues by ∼30% at 600 K. Although the origin of this dis-crepancy is not clear, it is worth pointing out that both theirκ and Cp data (see figure 1) do not show any anomaly at TC.This indicates that their D (not reported in [10].) also lacksany anomaly at TC, which is surprising in view of the resultsshown in the inset of figure 3.3.2.1 Thermal conductivity below TC. An important issueto address on YIG is whether magnons play any visible rolein the κ at room temperature, either as (1) carriers of heat or(2) scatterers of heat-carrying phonons. In regard to (1), manystudies have assumed the magnon κ to be very small, of theorder of <0.1 Wm−1 K−1 at 300 K [16, 17], while two theor-etical studies [14, 15] predicted much larger values of 5 and12 Wm−1 K−1, respectively. For (2), various studies reportedthe evidence of magnon–phonon interactions [8, 48–50], buttheir impact on κ has not been explored. These questions canbe examined from two approaches. First, we evaluate the abso-lute magnitude of κ using the Slack equation [51, 52]κ=AM̄δΘ3γ2N 2/3T, (1)where A = (2.43 × 10−8)/[1 − (0.514/γ) + (0.228/γ2)],M̄ = 36.9 u is the mean atomic mass, δ = 2.28 Å is thecubic root of the average volume of each atom, Θ = 560 Kis the Debye temperature [40], γ = 1.15 is the Grüneisenparameter [53], and N = 80 is the number of atoms in theprimitive unit cell. This equation assumes that only acous-tic phonons contribute to the heat transport, and that phon-ons interact only among themselves via anharmonic three-phonon Umklapp processes [51, 52]. Using the above values,we obtain κ = 6.75 Wm−1 K−1 at 300 K, which is nearlyidentical to the experimental value of 6.6 Wm−1K−1. Sincethere is some uncertainty in the value of γ [53], the near per-fect agreement is most likely fortuitous. Nevertheless, this res-ult clearly shows that a pure phononicmodel can reproduce theheat transport in YIG at room temperature.We next evaluate the temperature dependence of κ. Infigure 4, the κ of the FZ- and flux-grown YIG are comparedwith that of nonmagnetic YAG on a log-log scale. For YAG,the best fit to κ = AT−α over the entire temperature rangeyields α = 1.02. This is the T−1 dependence due to three-phonon scattering processes [54], a feature widely seen inweakly anharmonic insulators and which is captured in theSlack equation. The figure also shows that essentially the sameT−1 dependence (α= 1.01 and 0.97) is found for the two YIGcrystals up to TC. (The slightly smaller α in the flux-growncrystal may arise from the Pb impurity scattering.) Thus, thepresence of ferrimagnetically ordered Fe3+ spins in YIG hasno apparent effect on the temperature dependence of κ, and itis reasonable to conclude that magnons in YIG do not play anysignificant role as carriers or scatterers of heat from 300 K toTC. It should be noted that this conclusion does not contradictthe observation of the SSE: previous studies have shown thatthe SSE in YIG is driven mostly by low-energy (<1.5 meV)magnons [9, 17], which constitute only a tiny fraction of themagnons excited at room temperature. Since the majority ofthermal magnons have very short mean free paths (