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 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

A comparative study of ultra-low-temperature thermal

conductivity of multiferroic orthoferrites

J Y Zhao,1Z Y Zhao,1,2J C Wu,1H S Xu,1X G Liu,1X Zhao,3, a

and X F Sun1,4,5, b

1Hefei National Laboratory for Physical Sciences at Microscale, University of Science

and Technology of China, Hefei, Anhui 230026, People’s Republic of China

2Fujian Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’s Republic of China

3School of Physical Sciences, University of Science and Technology of China, Hefei,

Anhui 230026, People’s Republic of China

4Key Laboratory of Strongly-Coupled Quantum Matter Physics, Chinese Academy of Sciences, Hefei, Anhui 230026, People’s Republic of China

5Collaborative Innovation Center of Advanced Microstructures, Nanjing, Jiangsu 210093,

People’s Republic of China

(Presented 3 November 2016; received 18 September 2016; accepted 13 October 2016;

published online 23 December 2016)

Ultra-low-temperature thermal conductivity (κ) of GdFeO3and DyFeO3single crys-tals 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 GdFeO3can be strongly enhanced in several tesla field and becomes weakly field dependent in higher fields up to 14 T; whereas, the κ of DyFeO3is continuously suppressed with increasing field and does not show any signa-ture 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.5,6In 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 13The rare-earth orthoferrite has a distorted perovskite

structure with an orthorhombic unit cell (Pbnm).14It is known that Fe3+ spins form an

antiferro-magnetic (AF) order at rather high temperature (TNFe> 600 K) with a G x A y F z spin configuration in Bertaut’s notation;15that is, the main component of the magnetic moment is along the a axis, accom-panied with weak ferromagnetism along the c axis.16 , 17On the other hand, the rare-earth moments order antiferromagnetically at much lower temperatures

a Electronic mail: xiazhao@ustc.edu.cn

b Electronic mail: xfsun@ustc.edu.cn

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 G x-type spin structure of Gd3+moments is formed below the N´eel temperature

TGd

N = 2.5 K.6,15,18At the same time, the ferroelectric polarization appears and is originated from the spin-exchange striction.5 , 6 , 19With applying magnetic field along the c axis, the magnetic structure changes from phase I (G x A y F zfor Fe3+spins and G x A yfor Gd3+moments) to phase IV (Fe3+: G x A y F z;

Gd3+: F z) at ∼ 2.5 T due to the spin-polarization transition of Gd3+moments.6Whereas, 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 TM= 50 K,20

where the spin configuration changes from G x A y F z to A x G y C z.17Moreover, in the c-axis field, the

Fe3+spin structure can change back to G x A y F z.5,21With further lowering temperature, the Dy3+spins

develop a long-range AF order below TNDy = 4.2 K.5 In the AF state, the Dy3+ spin configuration

can be expressed as G x A y, for which the Dy3+spins are confined in the ab plane with the Ising axis

deviating about 33◦ from the b axis,22,23and the Fe3+sublattice was believed to have the A x G y C z

structure.5The spin-induced multiferroicity was observed only at T < TNDyand when the spin flop of

Fe3+moments is introduced by a c-axis field.5However, our recent work indicated a different ground

state from A x G y C zwhen 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.26–33Our earlier works on the low-T heat transport of GdFeO3 and DyFeO3revealed that the field-dependencies of κ are strong and show anomalies at magnetic transi-tions.24,34Moreover, the low-T κ(H) isotherms with H k c show some peculiar irreversibilities, which

have different origins for two materials.24,34Here, we report a study on the thermal conductivity of GdFeO3 and DyFeO3single 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

tech-nique 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 a3He-4He dilution refrigerator at temperature regime of 70 mK–1 K; (ii) in a3He refrigerator at 0.3–8 K, and (iii) in a pulse-tube

refrig-erator for zero-field data at T > 5 K Magnetization (M) was measured by a SQUID-VSM (Quantum

Design)

Figure1shows the representative data of M(T ) and M(H) with H k c for the GdFeO3and 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.6At 2 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 4 K, which are the transition of the Fe3+ structure from G x A y F z to A x G y C z and the N´eel transition of Dy3+moments, respectively.17It can be seen from the 2 K magnetization curve that 7 T

is still too weak to polarize the Dy3+moments, because they have strong anisotropy and are confined

in the ab plane.5 , 22 , 23Therefore, 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

Figure2shows the temperature dependencies of the c-axis thermal conductivity of GdFeO3and 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

T2.7at subKelvin temperatures, which is close to the T3boundary scattering limit of phonons.35The DyFeO data are rather comparable to those of YFeO , including the similar T dependence at the

FIG 1 Magnetization of GdFeO 3 and DyFeO 3measured in magnetic field along the c axis These data were taken after cooling the samples to 2 K in zero field In panel (b), the M(H) curve is reversible between 0 and 7 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 7 T The arrows indicate the direction of changing field.

FIG 2 Temperature dependencies of the c-axis thermal conductivity of GdFeO3 , DyFeO 3 , and YFeO 3 The data with a 14 T

field (along the c axis) of GdFeO3are also shown The dashed line shows a T2.7 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 that at T < TNDy, the magnon excitations from the Dy3+spin system can have a significant scattering

on phonons and result in a downward deviation from the T2.7behavior With lowering temperature

further, the κ recovers to the T2.7dependence 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

GdFeO3shows a rather different behavior of κ(T ) at very low temperatures.34First of all, the zero-field curve also exhibits a concavity feature below 2 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 T3law, which indicates stronger magnetic scattering of phonons in this material.35This 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 < 2 K become larger and the concavity feature disappears, which clearly indicates the negative effect of magnons on the heat transport A T2.7

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.1

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 κph=1

3C3 p l,35where C = βT3

is the phonon specific heat at low temperatures, 3p 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 × 10−4J/K4mol and

FIG 3 (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.

1.28 × 10−4 J/K4mol for GdFeO3and DyFeO3, respectively.24,34Then, the phonon velocity can be calculated and finally the mean free path is obtained from the κ.30,34The inset to Fig.2shows the ratio

between l and the averaged sample width W= 2√A/π,30 , 34 , 35where A is the area of cross section, for

DyFeO3in zero field and GdFeO3in 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.34The 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.34It 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 4 Magnetic-field dependencies of the c-axis thermal conductivity of DyFeO3single 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 DyFeO3at 92–360 mK are shown in Fig.4 Note that the

low-field data (H ≤ 8 T) have been published elsewhere,24while Fig.4shows data in field up to 14 T

It has been known that the κ(H) of DyFeO3display rather complicated irreversibility with lowering

temperature At very low temperatures, the hysteresis of κ(H) at ∼ 4 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 GdFeO3data In present work, one finding is that the high-field data of DyFeO3also 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 GdFeO3and DyFeO3single

crys-tals 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 dif-ferent in these two materials, which is closely related to the magnetic excitations at low temperatures, determined by their different spin anisotropy of the rare-earth ions Furthermore, the magnon excita-tions seem to act only as phonon scatterers and there is no signature for their ability of transporting heat

This work was supported by the National Natural Science Foundation of China (Grant Nos

11374277, 11574286, 11404316, U1532147), the National Basic Research Program of China (Grant Nos 2015CB921201, 2016YFA0300103), and the Opening Project of Wuhan National High Magnetic Field Center (Grant No 2015KF21)

1 H Katsura, N Nagaosa, and A V Balatsky, Phys Rev Lett.95, 057205 (2005).

2 I A Sergienko and E Dagotto, Phys Rev B73, 094434 (2006).

3 M Mostovoy, Phys Rev Lett.96, 067601 (2006).

4 T Kimura, T Goto, H Shintani, K Ishizaka, T Arima, and Y Tokura, Nature426, 55 (2003).

5 Y Tokunaga, S Iguchi, T Arima, and Y Tokura, Phys Rev Lett.101, 097205 (2008).

6 Y Tokunaga, N Furukawa, H Sakai, Y Taguchi, T Arima, and Y Tokura, Nat Mater.8, 558 (2009).

7 J.-H Lee, Y K Jeong, J H Park, M.-A Oak, H M Jang, J Y Son, and J F Scott, Phys Rev Lett.107, 117201 (2011).

8 A V Kimel, A Kirilyuk, A Tsvetkov, R V Pisarev, and T Rasing, Nature429, 850 (2004).

9 A V Kimel, A Kirilyuk, P A Usachev, R V Pisarev, A M Balbashov, and T Rasing, Nature435, 655 (2005).

10 A V Kimel, B A Ivanov, R V Pisarev, P 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, Phys Rev Lett.110, 137204 (2013).

13 C.-Y Kuo, Y Drees, M T Fern´andez-D´ıaz, L Zhao, L Vasylechko, D Sheptyakov, A M T Bell, T W Pi, H.-J Lin, M.-K Wu, E Pellegrin, S M Valvidares, Z W Li, P Adler, A Todorova, R K¨uchler, A Steppke, L H Tjeng, Z Hu, and

A C Komarek, Phys Rev Lett.113, 217203 (2014).

14 S Geller, J Chem Phys.24, 1236 (1956).

15E F Bertaut, Magnetism, Vol 3, (Academic Press, New York, 1963).

16 A Berton and B Sharon, J Appl Phys.39, 1367 (1968).

17 G Gorodetsky, B Sharon, and S Shtrikman, J Appl Phys.39, 1371 (1968).

18 J D Cashion, A H Coole, D M Martin, and M R Wells, J Phys C3, 1612 (1970).

19 Y J Choi, H T Yi, S Lee, Q Huang, V Kiryukhin, and S.-W Cheong, Phys Rev Lett.100, 047601 (2008).

20 F J Morin, Phys Rev.78, 819 (1950).

21 L A Prelorendjo, C E Johnson, M F Thomas, and B M Wanklyn, J Phys C: Solid Stat Phys.13, 2567 (1980).

22 L M Holmes, L G Van Uitert, R R Hecker, and G W Hull, Phys Rev B5, 138 (1972).

23 L M Holmes and L G Van Uitert, Phys Rev B5, 147 (1972).

24 Z Y Zhao, X Zhao, H D Zhou, F B Zhang, Q J Li, C Fan, X F Sun, and X G Li, Phys Rev B89, 224405 (2014).

25 J C Wang, J J Liu, J M Sheng, W Luo, F Ye, Z Y Zhao, X F Sun, S A Danilkin, G C Deng, and W Bao, Phys Rev.

B93, 140403(R) (2016).

26 A V Sologubenko, K Berggold, T Lorenz, A Rosch, E Shimshoni, M D Phillips, and M M Turnbull, Phys Rev Lett.

98, 107201 (2007).

27 A V Sologubenko, T Lorenz, J A Mydosh, A Rosch, K C Shortsleeves, and M M Turnbull, Phys Rev Lett.100,

137202 (2008).

28 X F Sun, W Tao, X M Wang, and C Fan, Phys Rev Lett.102, 167202 (2009).

29 X M Wang, C Fan, Z Y Zhao, W Tao, X G Liu, W P Ke, X Zhao, and X F Sun, Phys Rev B82, 094405 (2010).

30 Z Y Zhao, X M Wang, B Ni, Q J Li, C Fan, W P Ke, W Tao, L M Chen, X Zhao, and X F Sun, Phys Rev B83,

174518 (2011).

31 Z Y Zhao, X G Liu, Z Z He, X M Wang, C Fan, W P Ke, Q J Li, L M Chen, X Zhao, and X F Sun, Phys Rev B

85, 134412 (2012).

32 Z Y Zhao, B Tong, X Zhao, L M Chen, J Shi, F B Zhang, J D Song, S J Li, J C Wu, H S Xu, X G Liu, and

X F Sun, Phys Rev B91, 134420 (2015).

33 X Zhao, J C Wu, Z Y Zhao, Z Z He, J D Song, J Y Zhao, X G Liu, X F Sun, and X G Li, Appl Phys Lett.108,

242405 (2016).

34 Z Y Zhao, X M Wang, C Fan, W Tao, X G Liu, W P Ke, F B Zhang, X Zhao, and X F Sun, Phys Rev B83, 014414 (2011).

35R Berman, Thermal Conduction in Solids (Oxford University Press, Oxford, 1976).