Nature of spin freezing transition of geometrically frustratedpyrochlore system R2Ru2O7 (R� rare earth elements and Y)

M. Itoa, Y. Yasuia,b, M. Kanadaa,b, H. Harashinaa,b, S. Yoshiib, K. Murataa, M. Satoa,b,*,H. Okumurac, K. Kakuraib,c

aDepartment of Physics, Division of Material Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, JapanbCREST, Japan Science and Technology Corporation (JST), Japan

cNeutron Scattering Laboratory, ISSP, The University of Tokyo, 106-1 Shirakata, Tokai 319-1195, Japan

Abstract

At the spin-glass-like transition of yttrium ruthenium pyrochlore system Y2Ru2O7, a signi®cant jump of the speci®c heat has

been found, suggesting the second order-like nature of the transition. It is commonly observed for other pyrochlore systems

R2Ru2O7 (R� various rare earth elements RE). For all REs studied here, the transition temperature TG is larger for the larger R-

ions, which may be due to the increase of the transfer energies of the 4d electrons between the neighboring Ru atoms with

increasing RE ionic radius. Neutron Rietveld analyses on Y2Ru2O7 and Nd2Ru2O7 have revealed that below TG, the Ru spins are

in an almost long-range ordered antiferromagnetic state, though it is magnetically glassy in a macroscopic sense, and that the

lattice system does not participate in the transition. It is concluded that the speci®c heat jump is created by the purely magnetic

origin. q 2000 Elsevier Science Ltd. All rights reserved.

Keywords: A. Oxides; C. Neutron scattering; D. Speci®c heat; D. Magnetic structure

1. Introduction

Pyrochlore system R2Ru2O7 (R� Y, Bi, Pb, Tl, various

rare earth elements RE etc.) has the face-centered cubic

structure (space group Fd �3m) at room temperature [1].

Some of these compounds are in the Mott insulating state

and exhibit, at the temperature T � TG; a spin-glass-like

transition, which is considered to stem from the so-called

geometrical frustration inherent in the lattice structure,

formed of two individual networks of corner-sharing tetra-

hedra of R and Ru. At the transition, a signi®cant jump of

the speci®c heat has been found for Y2Ru2O7 [2], suggesting

that the transition is the second order one, even though the

glassy nature below TG can clearly be observed in the

magnetic susceptibilities, as shown in Fig. 1, for Y2Ru2O7

and Nd2Ru2O7 (inset). We have carried out experimental

studies, to clarify if the speci®c heat behavior can

commonly be observed in the systems with various kinds

of R species. We have also carried out neutron Rietveld

analyses to see if the transition at TG is primarily driven

by lattice instability, and the glassy nature is simply induced

by the lattice distortion stabilized below TG. The results

indicate that the lattice system has been found not to parti-

cipate in the transition and the transition is solely associated

with the Ru-spin system.

2. Experiments

Sintered samples of Y2Ru2O7 and RE2Ru2O7 were synthe-

sized by the solid reaction from mixed powders of M2O3

(M� Y and various RE elements) and RuO2 (for RE� Pr

and Tb, we used Pr6O11 and Tb4O7). Details of the prepara-

tion can be found in Refs. [2±4]. No impurity phase was

detected by X-ray diffraction measurements within accuracy

of a few percent, except for Nd2Ru2O7. For Nd2Ru2O7, weak

impurity peaks, which can be assigned to Nd3RuO7, were

detected. Neutron data of Y2Ru2O7 were taken on the spec-

trometer at T1-1 of the thermal guide of JRR-3M of JAERI

in Tokai. The wavelength of the beam was 2.459 AÊ . For

Nd2Ru2O7, measurements were carried out on the triple-

axis spectrometer ISSP-PONTA at JRR-3M. The neutron

wavelength was 2.353 AÊ .

The powder samples packed in a V-can were set in an Al

Journal of Physics and Chemistry of Solids 62 (2001) 337±341

0022-3697/00/$ - see front matter q 2000 Elsevier Science Ltd. All rights reserved.

PII: S0022-3697(00)00159-1

www.elsevier.nl/locate/jpcs

* Corresponding author. Tel.: 181-52-789-3537; fax: 181-52-

789-2856.

E-mail address: e43247a@nucc.cc.nagoya-u.ac.jp (M. Sato).

M. Ito et al. / Journal of Physics and Chemistry of Solids 62 (2001) 337±341338

Fig. 1. T-dependence of the magnetic susceptibility x of Y2Ru2O7 measured after zero ®eld cooling (ZFC) and ®eld cooling (FC). The inset

shows similar data for Nd2Ru2O7.

Fig. 2. Speci®c heat data of Y2Ru2O7 and RE2Ru2O7 taken around the temperatures TG. The scale of DC is shown by the vertical bar. The offsets

of the vertical axes are chosen to align the data almost linearly.

cell sealed in the He gas atmosphere. Then, the Al cell was

set in a closed cycle refrigerator, which was put on the

sample table. The packing factors of the Y2Ru2O7 and

Nd2Ru2O7 samples were about 0.4 and 0.3, respectively.

From these values the neutron absorption factors have

been estimated and used in the Rietveld analyses. The

diffraction patterns were analyzed by the Rietveld method

using a computer program RIETAN [5]. Further details on

the experimental conditions can be found in Ref. [3].

3. Experimental results and discussion

Fig. 2 shows the speci®c heat anomalies at TG for

Y2Ru2O7 and RE2Ru2O7, where the offsets of the vertical

axis are chosen for the purpose of aligning the observed

data. For all the R atoms, the speci®c heat jump is very

clear, suggesting that the transition is second order-like.

The TG values of RE2Ru2O7 monotonically increase with

increasing ionic radius ri of RE31. It can be explained by

considering that, as Lee et al. [6] pointed out, the transfer

energy t of the 4d electrons between the nearest neighboring

Ru ions increases as ri increases. Since the exchange inter-

action increases as t increases, TG is naturally expected to

increase as ri increases, if the transition is primarily driven

by a magnetic origin.

Neutron diffraction data were taken at 100

(T . TG , 76 K) and 10 K (,TG) for Y2Ru2O7; and 160

(T . TG , 145 K) and 30 K (,TG) for Nd2Ru2O7. They

were used in the present Rietveld analyses. For both

systems, the ®tting above TG is satisfactory. However,

below TG, the intensities of the 111 and 220 re¯ections are

found to be too large to be explained by the ®tting. Then, we

have used the possible maximal subgroups of Fd �3m within a

restriction that their lattice parameters are not the multiples

of those of the original cubic cell. (note that we have

observed no superlattice re¯ection in the low-temperature

phase within the present experimental sensitivity.)

However, no signi®cant improvement of the ®tting has

been obtained at these re¯ections, which probably indicates

that the discrepancy is not due to a second-order structural

phase transition to the lower symmetry phase, but due to a

magnetic transition. Then, the data in the 2u -regions of the

111 and 220 re¯ections were omitted in the structural analy-

sis with the space group Fd �3m: The obtained Rwp values are

presented in Table 1 together with those at 100 K (obtained

by ®tting to the whole data). Fig. 3 shows the results of the

®ttings around the 111 re¯ection: at 100 K, the re¯ection

intensities are well reproduced. However, at 10 K the

observed re¯ection intensities are found to be signi®cantly

larger than the values (solid line) calculated by using the

M. Ito et al. / Journal of Physics and Chemistry of Solids 62 (2001) 337±341 339

Table 1

RWP values obtained for Y2Ru2O7 and Nd2Ru2O7 by the Rietveld ®ttings below TG are shown for various space groups. Results for the data

including and without the 2u-regions of the 111 and 220 re¯ections are in the ®rst and second rows

Y2Ru2O7 Nd2Ru2O7

Fd �3m F �43m R �3m I41/amd Fd �3m F �43m R �3m I41/amd

RWP (%) 9.01 8.30 8.24 9.00 6.24 6.02 6.22 5.99

RWP (%) 7.79 7.72 7.71 7.78 5.93 5.68 5.90 5.67

Fig. 3. Results of the Rietveld ®ttings around the 111 re¯ection of

Y2Ru2O7 are shown at 100 (T . TG) and at 10 K (T , TG). The

calculated curve at 10 K is obtained by using the parameters

obtained by ®tting to the data without the 2u-regions of the 111

re¯ection.

parameters obtained in the above ®tting to the data without

the 2u -regions of the 111 and 220 re¯ections by using the

space group Fd �3m. As was stated above, no signi®cant

improvement has been obtained in the 2u -regions of the

111 and 220 re¯ections for the maximal subgroups. We

can con®rm, therefore, that the transition at TG is not due

to a structural change and the excess intensities found in the

111 and 220 re¯ections are due to a magnetic origin.

Results similar to the case of Y2Ru2O7 have been obtained

for Nd2Ru2O7. Here, we only present in Table 1 the Rwp

values obtained by the ®ttings, as was decribed for

Y2Ru2O7. The transition observed at TG in Nd2Ru2O7 can

be considered to originate from the same mechanism as

that of Y2Ru2O7.

The temperature dependence of the integrated intensities

of the 111 and 220 re¯ections of Y2Ru2O7 is shown in Fig. 4,

where it is rather clear that the intensities begin to grow at

T � TG with decreasing T, indicating the existence of the

second order-like phase transition.

Although the susceptibility data indicate that the transi-

tion of the magnetic system is to the glassy state, we assume

M. Ito et al. / Journal of Physics and Chemistry of Solids 62 (2001) 337±341340

Fig. 4. Temperature dependence of the integrated intensities of the 111 and 220 re¯ections of Y2Ru2O7. The TG value is indicated by the arrow.

The inset shows the pro®les of the 111 re¯ections taken at 10 and 100 K.

Table 2

Intrinsic integrated intensities of the magnetic re¯ections after the

absorption correction are compared with those of the model calcu-

lations (see text for details)

Y2Ru2O7 Nd2Ru2O7

Exp. Calc.a Exp. Calc.b

111 165 ^ 13 165 737 ^ 58 737

220 60 ^ 13 76 407 ^ 69 344

113 39 ^ 20 32 155 ^ 19 147

331 , 26 13 38 ^ 52 58

a For m � 1:36 mB:b For m � 1:18 mB:

Fig. 5. The spin structure that can explain the observed magnetic

re¯ection intensities of Y2Ru2O7 and Nd2Ru2O7 are shown. The

magnetic moments of all tetrahedra are aligned in-phase.

that the transition can be regarded as an almost long-range

ordered state. The problem is if there exists a magnetic

ordering pattern that can reproduce the magnetic re¯ection

intensities. In Table 2, the intrinsic (absorption corrected)

integrated intensities of the magnetic re¯ections experimen-

tally deduced by using the differences between observed

intensities at temperatures below and above TG are shown

for both Y2Ru2O7 and Nd2Ru2O7, and in Fig. 5 and Table 3 a

possible ordering pattern, which roughly reproduces these

intensity distributions, is shown. The magnetic intensity

distribution calculated for this pattern is also shown in

Table 2. The moment values m per Ru of Y2Ru2O7 and

Nd2Ru2O7 are estimated by comparing the magnetic re¯ec-

tion intensities with the 440 nuclear Bragg intensities, to be

about 1.36 and 1.18 mB, respectively. These reasonable

values of m suggest that the assumption made above is

quite likely, that is, the speci®c heat anomaly observed at

TG is due to a magnetic transition to the almost long-range

ordered state, even though the glassy nature is observed in

the macroscopic measurements.

In the above analyses, we have assumed that the magnetic

moments of Nd31 in Nd2Ru2O7 remain paramagnetic down

to the lowest temperature studied here and do not contribute

to the neutron diffraction intensities, which is naturally

expected by the fact that the exchange interactions in

RE2B2O7 between RE atoms (B� Ti and other nonmagnetic

elements) are much smaller than that of Y2Ru2O7 [7].

The magnetic correlation length is considered to be quite

large, because the pro®le widths of the magnetic re¯ections

at 111 and 220 points are found to be almost resolution

limited. It also con®rms that the above assumption is reason-

able.

The present study has revealed that the lattice system does

not participate in the transition at TG. The magnetic

moments at the corners of the tetrahedra tend to undergo

the transition to the static ordered state. But they cannot go,

due to the geometrical frustration, to the ideal antiferromag-

netic state and macroscopically exhibit the spin-glass-like

behavior at low temperatures.

References

[1] M.A. Subramanian, G. Aravamudan, G.V. Subba Rao, Prog.

Solid State Chem. 15 (1983) 55.

[2] S. Yoshii, M. Sato, J. Phys. Soc. Jpn 68 (1999) 3034.

[3] M. Ito, Y. Yasui, M. Kanada, H. Harashina, S. Yoshii, K.

Murata, M. Sato, H. Okumura, K. Kakurai, J. Phys. Soc. Jpn

69 (2000) No3.

[4] S. Yoshii, K. Murata, M. Sato, J. Phys. Soc. Jpn 69 (2000) 17.

[5] F. Izumi, in: R.A. Young (Ed.), The Rietveld Method, Oxford

University Press, Oxford, 1993 (chap. 13).

[6] K.-S. Lee, D.-K. Seo, M.-H. Whangbo, J. Solid State Chem.

131 (1997) 405.

[7] H.W.J. BloÈte, R.F. Wielinga, W.J. Huiskamp, Physica 43

(1969) 549 (for example).

M. Ito et al. / Journal of Physics and Chemistry of Solids 62 (2001) 337±341 341

Table 3

The direction n of the ordered Ru-spins at four corners of a tetra-

hedron are shown, where i and j are a set of real numbers that satisfy

a condition 2�i2 1 ij 1 j2� � 1

x y z nx ny nz

1 0 0 0 i j 2 i 2 j

2 14

14

0 2 i 2 j 2 i 2 j

3 14

0 14

2 i j i 1 j

4 0 14

14

i 2 j i 1 j