A comparative study of ultra low temperature thermal conductivity of multiferroic orthoferrites RFeO3 (R = Gd and Dy) A comparative study of ultra low temperature thermal conductivity of multiferroic[.]
A comparative study of ultra-low-temperature thermal conductivity of multiferroic orthoferrites RFeO3 (R = Gd and Dy) J Y Zhao, Z Y Zhao, J C Wu, H S Xu, X G Liu, X Zhao, and X F Sun Citation: AIP Advances 7, 055806 (2017); doi: 10.1063/1.4973293 View online: http://dx.doi.org/10.1063/1.4973293 View Table of Contents: http://aip.scitation.org/toc/adv/7/5 Published by the American Institute of Physics Articles you may be interested in Thermal conductivity of ferrimagnet GdBaMn2O5.0 single crystals AIP Advances 7, 055807 (2016); 10.1063/1.4973294 Nanopatterning spin-textures: A route to reconfigurable magnonics AIP Advances 7, 055601 (2016); 10.1063/1.4973387 Identification of the low-energy excitations in a quantum critical system AIP Advances 7, 055701 (2016); 10.1063/1.4972802 Anisotropic electronic states in the fractional quantum Hall regime AIP Advances 7, 055804 (2016); 10.1063/1.4972854 AIP ADVANCES 7, 055806 (2017) A comparative study of ultra-low-temperature thermal conductivity of multiferroic orthoferrites RFeO3 (R = Gd and Dy) J Y Zhao,1 Z Y Zhao,1,2 J C Wu,1 H S Xu,1 X G Liu,1 X Zhao,3,a and X F Sun1,4,5,b Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China School of Physical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, People’s Republic of China Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, Hefei, Anhui 230026, People’s Republic of China Collaborative Innovation Center of Advanced Microstructures, Nanjing, Jiangsu 210093, People’s Republic of China (Presented November 2016; received 18 September 2016; accepted 13 October 2016; published online 23 December 2016) Ultra-low-temperature thermal conductivity (κ) of GdFeO3 and DyFeO3 single crystals is studied down to several tens of milli-Kelvin It is found that the κ is purely phononic and has strong magnetic-field dependence, indicating a strong spin-phonon coupling Moreover, the low-T κ(H) with H k c show rather different behaviors in these two materials In particular, the κ of GdFeO3 can be strongly enhanced in several tesla field and becomes weakly field dependent in higher fields up to 14 T; whereas, the κ of DyFeO3 is continuously suppressed with increasing field and does not show any signature of recovery at 14 T The results can be well understood by the difference in the spin anisotropy of Gd3+ and Dy3+ ions © 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4973293] Multiferroicity induced by spin order has attracted much attention due to its large magnetoelectric (ME) coupling The spin-current model or the inverse Dzyaloshinsky-Moriya (DM) interaction can explain well the production of electric polarization in the non-collinear spin systems.1–4 When the spins are aligned collinearly, the electric polarization can also be formed through the exchange striction mechanism, for example, in the rare-earth-based orthoferrites RFeO3 (R = Gd and Dy).5–7 In this case, the interaction between adjacent Fe3+ and R3+ layers drives R3+ ions to displace along the c axis so as to induce the ferroelectric polarization along the c axis.5,6 In these materials, the spin structures are playing a key role in the ME coupling and the formation of the spontaneous electric polarization Due to their key role in the ME coupling, the spin structures and spin re-orientations of rare-earth orthoferrites have been intensively studied.8–13 The rare-earth orthoferrite has a distorted perovskite structure with an orthorhombic unit cell (Pbnm).14 It is known that Fe3+ spins form an antiferromagnetic (AF) order at rather high temperature (TNFe > 600 K) with a Gx Ay F z spin configuration in Bertaut’s notation;15 that is, the main component of the magnetic moment is along the a axis, accompanied with weak ferromagnetism along the c axis.16,17 On the other hand, the rare-earth moments order antiferromagnetically at much lower temperatures a Electronic mail: xiazhao@ustc.edu.cn Electronic mail: xfsun@ustc.edu.cn b 2158-3226/2017/7(5)/055806/7 7, 055806-1 © Author(s) 2016 055806-2 Zhao et al AIP Advances 7, 055806 (2017) In GdFeO3 , a Gx -type spin structure of Gd3+ moments is formed below the N´eel temperature = 2.5 K.6,15,18 At the same time, the ferroelectric polarization appears and is originated from the spin-exchange striction.5,6,19 With applying magnetic field along the c axis, the magnetic structure changes from phase I (Gx Ay F z for Fe3+ spins and Gx Ay for Gd3+ moments) to phase IV (Fe3+ : Gx Ay F z ; Gd3+ : F z ) at ∼ 2.5 T due to the spin-polarization transition of Gd3+ moments.6 Whereas, the electric polarization decreases to zero as long as the Gd3+ moments are polarized at high field.6 In DyFeO3 , with lowering temperature, the Fe3+ spins undergo a Morin transition at T M = 50 K,20 where the spin configuration changes from Gx Ay F z to Ax Gy C z 17 Moreover, in the c-axis field, the Fe3+ spin structure can change back to Gx Ay F z 5,21 With further lowering temperature, the Dy3+ spins Dy develop a long-range AF order below TN = 4.2 K.5 In the AF state, the Dy3+ spin configuration can be expressed as Gx Ay , for which the Dy3+ spins are confined in the ab plane with the Ising axis deviating about 33◦ from the b axis,22,23 and the Fe3+ sublattice was believed to have the Ax Gy C z Dy structure.5 The spin-induced multiferroicity was observed only at T < TN and when the spin flop of Fe3+ moments is introduced by a c-axis field.5 However, our recent work indicated a different ground state from Ax Gy C z when cooling the sample in zero field.24,25 Low-temperature heat transport is an important physical property of solids and is useful for probing elementary excitations, such as phonons and magnons In magnetic insulators, the thermal conductivity (κ) can show drastic changes at the magnetic transitions, due to either magnon transport or magnon-phonon scattering.26–33 Our earlier works on the low-T heat transport of GdFeO3 and DyFeO3 revealed that the field-dependencies of κ are strong and show anomalies at magnetic transitions.24,34 Moreover, the low-T κ(H) isotherms with H k c show some peculiar irreversibilities, which have different origins for two materials.24,34 Here, we report a study on the thermal conductivity of GdFeO3 and DyFeO3 single crystals at very low temperatures down to several tens of milli-Kelvin and in magnetic fields up to 14 T The main finding in this work is that the heat transport has rather different field-dependence in two materials, which is originated from the significant difference in the spin anisotropy of the rare-earth ions High-quality RFeO3 (R = Gd, Dy, and Y) single crystals were grown by the floating-zone technique in flowing oxygen-argon mixture with the ratio of 1:4 or pure oxygen The samples for the κ measurements were cut along the crystallographic axes into long parallelepiped after orientation by using the x-ray Laue photographs Thermal conductivity was measured by using a “one heater, two thermometers” technique and three different cryostats:24,28–34 (i) in a He-4 He dilution refrigerator at temperature regime of 70 mK–1 K; (ii) in a He refrigerator at 0.3–8 K, and (iii) in a pulse-tube refrigerator for zero-field data at T > K Magnetization (M) was measured by a SQUID-VSM (Quantum Design) Figure shows the representative data of M(T ) and M(H) with H k c for the GdFeO3 and DyFeO3 single crystals These results are in good consistency with the earlier works.5,6,17 For GdFeO3 , the M(T ) curve has a weak transition at ∼ 2.5 K, which is known to be due to the N´eel transition of Gd3+ moments.6 At K, the c-axis field can easily polarize the Gd3+ moments, as the M(H) curve indicates For DyFeO3 , the M(T ) curve measured in H = 5000 Oe, shown in Fig 1(c), has two transitions at 5.2 and K, which are the transition of the Fe3+ structure from Gx Ay F z to Ax Gy C z and the N´eel transition of Dy3+ moments, respectively.17 It can be seen from the K magnetization curve that T is still too weak to polarize the Dy3+ moments, because they have strong anisotropy and are confined in the ab plane.5,22,23 Therefore, the c-axis field can hardly to change either the N´eel transition or the Dy3+ spin orientation, whereas the two transitions at ∼ 2.5 and 3.5 T in the M(H) curve are due to the magnetic transitions of Fe3+ spins.24 Figure shows the temperature dependencies of the c-axis thermal conductivity of GdFeO3 and DyFeO3 down to 70 mK For comparison, the data for YFeO3 single crystal are also taken in the same temperature regime Note that the Y3+ ions are nonmagnetic and there is only AF order of Fe3+ ions YFeO3 shows a simple and pure phonon heat transport behavior at low temperatures First, the κ(T ) curve exhibits a very large phonon peak at about 20 K, with the magnitude of 520 W/Km, indicating high quality of the single crystal Second, the temperature dependence of κ is roughly T 2.7 at subKelvin temperatures, which is close to the T boundary scattering limit of phonons.35 The DyFeO3 data are rather comparable to those of YFeO3 , including the similar T dependence at the TNGd 055806-3 Zhao et al AIP Advances 7, 055806 (2017) FIG Magnetization of GdFeO3 and DyFeO3 measured in magnetic field along the c axis These data were taken after cooling the samples to K in zero field In panel (b), the M(H) curve is reversible between and T for GdFeO3 In panel (d), the M(H) curve shows a low-field hysteresis for DyFeO3 The first transition at 2.5 T disappears when sweeping down field from T The arrows indicate the direction of changing field FIG Temperature dependencies of the c-axis thermal conductivity of GdFeO3 , DyFeO3 , and YFeO3 The data with a 14 T field (along the c axis) of GdFeO3 are also shown The dashed line shows a T 2.7 dependence Inset: temperature dependence of the phonon mean free path l divided by the averaged sample width W 055806-4 Zhao et al AIP Advances 7, 055806 (2017) lowest temperatures However, the κ(T ) curve has a clear concavity structure at 0.3–3 K It is clear Dy that at T < TN , the magnon excitations from the Dy3+ spin system can have a significant scattering on phonons and result in a downward deviation from the T 2.7 behavior With lowering temperature further, the κ recovers to the T 2.7 dependence at T < 300 mK It is likely that the magnon spectra has a finite energy gap, which prevents the low-energy magnons from being thermally excited at very low temperatures It is compatible with the strong anisotropy of Dy3+ spins GdFeO3 shows a rather different behavior of κ(T ) at very low temperatures.34 First of all, the zerofield curve also exhibits a concavity feature below K, which should be due to the magnon-phonon scattering when the Gd3+ moments order antiferromagnetically at 2.5 K.6 However, the κ(T ) data show a distinct deviation from the T law, which indicates stronger magnetic scattering of phonons in this material.35 This result can be understood from the fact that the Gd3+ spins have weak anisotropy6 and the magnon gap is negligibly small, in contrast to the strong anisotropy of Dy3+ spins The effect of magnetic field on κ(T ) is also tested for GdFeO3 As shown in Fig 2, when 14 T magnetic field is applied along the c axis, the κ at T < K become larger and the concavity feature disappears, which clearly indicates the negative effect of magnons on the heat transport A T 2.7 dependence of the 14 T data indicates that magnetic scattering on phonons is almost smeared out in 14 T field Apparently, 14 T is strong enough to polarize the Gd3+ spins and the low-energy magnons are hardly thermally excited It is consistent with the M(H) data shown in Fig It is useful to make an estimation of the mean free path of phonons at low temperatures The phononic thermal conductivity can be expressed by the kinetic formula κ ph = 13 C3p l,35 where C = βT is the phonon specific heat at low temperatures, p is the average velocity and l is the mean free path of phonons The β value can be obtained from the specific-heat data, which is 1.67 × 10−4 J/K4 mol and FIG (a) Magnetic-field dependencies of the c-axis thermal conductivity of GdFeO3 single crystal at very low temperatures The magnetic field is applied along the c axis All the data are measured after zero-field cooling (b–d) The low-field data show a hysteresis behavior As indicated by the arrows, the data shown with solid symbols are measured in the field-up process, while the open symbols show the data in the field-down process 055806-5 Zhao et al AIP Advances 7, 055806 (2017) 1.28 × 10−4 J/K4 mol for GdFeO3 and DyFeO3 , respectively.24,34 Then, the phonon velocity can be calculated and finally the mean free path is obtained the κ.30,34 The inset to Fig shows the ratio √ from 30,34,35 between l and the averaged sample width W = A/π, where A is the area of cross section, for DyFeO3 in zero field and GdFeO3 in 14 T It can be seen that l/W increases with lowering temperature and becomes larger than one at lowest temperatures, which indicates that all the microscopic phonon scatterings (including magnon scattering) are negligible and the boundary scattering limit is actually established.35 For GdFeO3 , our previous work have studied the magnetic-field dependencies of κ with H k c and at low temperatures down to 360 mK.34 The main results include: (i) the κ(H) isotherms show a reduction at low fields followed by a strong enhancement at high fields; (ii) there is a shallow and broad “dip” of κ(H) at low field; (iii) the κ(H) exhibit hysteresis at subkelvin temperatures In present work, the magnetic-field dependencies of κ are studied at even lower temperatures, down to 92 mK As shown in Fig 3, the present data show good consistency with the earlier data However, there are several notable features First, with lowering temperature, the high-field enhancement of κ is apparently becoming smaller, which indicates that the magnon scattering of phonons is weakened This is understandable because the magnon excitations should become more difficult unless the magnon gap (caused by anisotropy) is exactly zero Second, with lowering temperature, the low-field broad dip becomes more shallow and finally evolves into a weakly field-dependent feature Third, the low-field hysteresis becomes a bit larger with lowering temperature This hysteresis has been proposed to be related to the ferroelectric domain scattering in this multiferroic material.34 It should be noted that in temperature regime of 100 mK, the low-field κ is about only two times smaller than the 14 T value, which means that the mean free path of phonons in the low field has the same order of magnitude as the sample size Therefore, the ferroelectric domain scattering seems to be ineffective and it is not very clear whether the hysteresis of κ(H) has some other origin at such low temperatures It calls for further investigations by using electric polarization measurements at ultra-low temperatures FIG Magnetic-field dependencies of the c-axis thermal conductivity of DyFeO3 single crystal in H k c after zero-field cooling The arrows indicate the direction of changing field 055806-6 Zhao et al AIP Advances 7, 055806 (2017) For comparison, the κ(H) isotherms of DyFeO3 at 92–360 mK are shown in Fig Note that the low-field data (H ≤ T) have been published elsewhere,24 while Fig shows data in field up to 14 T It has been known that the κ(H) of DyFeO3 display rather complicated irreversibility with lowering temperature At very low temperatures, the hysteresis of κ(H) at ∼ T was discussed to be related to a first-order transition of magnetic structure, with the “dip” field corresponding to the transition field.24 This is essentially different from the irreversibility of GdFeO3 data In present work, one finding is that the high-field data of DyFeO3 also behave very differently from those of GdFeO3 Actually, the κ is continuously suppressed in high field and does not show any signature of recovering even at 14 T This phenomenon is consistent with the strong spin anisotropy of Dy3+ It is known that the Dy3+ moments can hardly be polarized by the c-axis field, as Fig 1(d) shows In summary, ultra-low-T thermal conductivity are studied for GdFeO3 and DyFeO3 single crystals The magnetic field along the c axis has strong effect on the κ, which can be understood by the magnon-phonon scattering However, both the temperature and field dependencies of κ are rather different in these two materials, which is closely related to the magnetic excitations at low temperatures, determined by their different spin anisotropy of the 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Y Zhao,1,2 J C Wu,1... A Usachev, A Kirilyuk, and T Rasing, Nat Phys 5, 727 (2009) 11 Y Tokunaga, Y Taguchi, T Arima, and Y Tokura, Nat Phys 8, 838 (2012) 12 K Yamaguchi, T Kurihara, Y Minami, M Nakajima, and T Suemoto,... Kimura, T Goto, H Shintani, K Ishizaka, T Arima, and Y Tokura, Nature 426, 55 (2003) Y Tokunaga, S Iguchi, T Arima, and Y Tokura, Phys Rev Lett 101, 097205 (2008) Y Tokunaga, N Furukawa, H Sakai,