Progress of Theoretical Physics Supplement No. 145, 2002

17

Crossbreeding between Experiment and Theory on
Orthogonal Dimer Spin System
Hiroshi Kageyama,1 Yutaka Ueda,1 Yasuo Narumi,2 Koichi Kindo,2Masashi Kosaka3 and Yoshiya Uwatoko3
1 Material Design and Characterization Laboratory, Institute for Solid StatePhysics,

University of Tokyo, Kashiwa 277-8581, Japan

2 Research Center for Materials Science at Extreme Conditions, Osaka University,

Toyonaka 560-8531, Japan

3 Department of Physics, Saitama University, Saitama 338-8570, Japan(Received December 27, 2001)
We have investigated two-dimensional spin systems SrCu2 (BO3 )2 and Nd2 BaZnO5 , bothof which have a unique topology that is equivalent to the Shastry-Sutherland lattice. The
magnetization curve of SrCu2 (BO3 )2 reveals that, unlike 1/8 and 1/4 plateaux, a 1/3 plateau
is very stable, surviving at least up to 69 T. The pressure dependence of susceptibility up
to 10 kbar indicates that the pressure causes the system to approach the critical point tosome other states. On the other hand, Nd2 BaZnO5 with rather classical spins exhibits anantiferromagnetic long range ordering at 2.4 K. Finally, other experimental candidates ofextended Shastry-Sutherland system will be briefly presented.

§1.

Introduction

Exactly 20 years ago, B. S. Shastry and B. Sutherland (S-S) considered the modelcomposed of a two-dimensional square lattice with some additional diagonal bonds(Fig. 1(c)), in which the direct product of the dimer singlets is an exact ground state
when the intradimer coupling J is larger than the interdimer coupling J  . 1) The next
important event occurred in 1991 when R. W. Smith and D. A. Keszler succeeded
to synthesize SrCu2 (BO3 )2 containing the arrangement of the Cu2+ ions as shownin Fig. 1(a). 2) In 1998, crossbreeding between theory and experiment eventually
started, then involving a number of theoreticians and experimentalists, to reveal someinteresting phenomena such as magnetization plateaux and almost dispersionlesstriplet excitations. 3) - 13)
This paper will deal with several orthogonal dimer systems. Although the ﬁrst

(a)

(b)

(c)

J
J'

Fig. 1. Topologically identical structures realized by (a) SrCu2 (BO3 )2 , (b) Nd2 BaZnO5 and (c)Shastry-Sutherland.

18 H. Kageyama, Y. Ueda, Y. Narumi, K. Kindo, M. Kosaka and Y. Uwatoko
compound SrCu2 (BO3 )2 now looks well understood, there still remain some open
questions. The magnetization curve for H//c up to 53 T, for example, is far fromthe saturation. 14) We will thus demonstrate new magnetization data obtained using a
recently developed magnet available up to 69 T. Another interesting and challenging
issue is tuning exchange interactions because SrCu2 (BO3 )2 is theoretically shown to
be in the vicinity of the critical point to an antiferromagnetic or a plaquette singlet
state. 9), 11) To achieve this goal, we studied pressure dependence of the magnetic
susceptibility up to 10 kbar. The next material is a new oxide Nd2 BaZnO5 , 15) themagnetic network (Fig. 1(b)) of which is again topologically equivalent to the S-S
lattice. The magnetic properties of this material will be discussed based on themagnetic susceptibility and the magnetization measurements. In the ﬁnal part ofthe paper, we would like to brieﬂy mention the future direction of the study on theorthogonal dimer system, namely, the extended S-S systems such as KIrO3 .
§2.

Experimental

Poly- and single- crystals of SrCu2 (BO3 )2 were prepared using a conventional
solid state reaction and a travelling solvent ﬂoating zone method, respectively, as
described elsewhere. 2), 16) The high ﬁeld magnetization measurement up to 69 T at
T = 1.4 K was conducted using pulsed ﬁeld magnets at the High Magnetic Field
Laboratory, KYOKUGEN in Osaka University. We used one piece of the grown
crystals of high quality with an approximate dimension of 2mm × 2mm × 2mm.
The magnetic susceptibility measurement of polycrystalline samples under pressure
was performed at H = 0.1 T in a SQUID magnetometer (MPMS, Quantum Design)at Saitama University, in which we installed a high pressure cell with the Cu-Be
clamping-type using a pressure-transmitting ﬂuid (Fluorinert FC70:FC7751:1). 17)
To synthesize Nd2 BaZnO5 , 15) the stoichiometric starting materials Nd2 O3 , ZnO
and BaCO3 were mixed intimately in an agate mortar, pressed into a pellet, preheated at 1173 K in air overnight to decompose the carbonate. The sample was thenheated at 1273 K for 1 week with several intermediate grindings. The powder X-ray
diﬀraction study by M21X (Mac Science) using CuKα allowed us to conclude thatthe sample obtained is Nd2 BaZnO5 without any trace of impurity phases. The magnetic susceptibility of Nd2 BaZnO5 was curried out using a SQUID magnetometer atUniversity of Tokyo in the temperature range between 1.8 K and 300 K. The magnetization measurement up to 7 T at 1.8 K was performed using a PPMS magnetometer(Quantum Design).
§3.

SrCu2 (BO3 )2 : Dimer phase

The magnetization curve up to 69 T at 1.4 K is presented in Fig. 2(a), where
the magnetic ﬁeld was applied perpendicular to the S-S lattice, i.e., the ab plane.
There is little diﬀerence between ﬁeld increasing and decreasing processes, and theobtained curve below 53 T is almost identical to that reported in Ref. 14). The point
we would like to emphasize here is the fact that the 1/3 plateau is considerably
stabler than the 1/4 and 1/8 plateaux; It survives from about 40 T to at least 69 T

Orthogonal Dimer Spin Compounds

19

0.30
0.25
0.20
0.15
0.10

SrCu2 (BO3)2

0.05
0.00
0

20

30

40

H (T)

50

60

25

20
15
10

: 2.62 kbar
: 8.48 kbar
: 10.00 kbar

5
0

20
15
10
5

1.3 K
10

χ (x10 -3emu/Cu mol)

Magnetization (µB /Cu)(a) 0.35

25

χ normalied(b) 30

0
70

0

10

20

30

40

T (K)

Fig. 2. (a) The magnetization curve of SrCu2 (BO3 )2 measured at 1.3 K with the single crystal beingaligned as H // c. (b) (upper) The temperature dependence of the magnetic susceptibility of
SrCu2 (BO3 )2 at 2.62 kbar (circles), 8.48 kbar (squares) and 10.00 kbar (triangles). (lower) thesusceptibilities normalized at 40 K.

(the maximum ﬁeld studied here), and is at least 6 times as wide as the 1/4 plateau.
To date, there are several theoretical calculations to ﬁt our experimental magnetization. Among them, the Chern-Simons theory by Misguich et al. 12) assuming
J = 74 K and J  = 29.5 K reproduces most nicely our previous data (below 53 T),
especially with respect to the critical ﬁelds of the 1/3 and 1/4 plateaux as wellas the rounding feature of these plateaux. Their theory, however, claims that the
1/3 plateau ends at about 53 T, in disagreement with the present experiment. On
the contrary, Miyahara and Ueda, 18) Totsuka and Momoi 19) predict that the 1/3magnetization phase will persist until 110 T, 80 T, respectively, although the agreement with the experiment in the low ﬁeld region looks poorer. Apparently, higher
ﬁeld experiments to cover whole magnetization as well as more elaborated theoretical treatment are needed to advance our understanding of triplet excitations in thepresence of H.
Before moving onto the pressure eﬀect, let us discuss the phase diagram as a function of J  /J and J  /J proposed by Koga and Kawakami, 20) where J  denotes theout-of-plane interdimer interaction. It is shown that with increasing J  /J the dimer
phase undergoes a phase transition to the RVB plaquette-singlet phase, whereas
raising J  /J results in the antiferromagnetic transition. Since the present material is a layered material with the Sr+2 ions being intercalated between the Cu-B-O
layers, the pressure should mainly aﬀect the interlayer distance, thus changing J 
substantially but leaving J and J  almost unchanged. The upper panel of Fig. 2(b)demonstrates raw data of the magnetic susceptibility vs T at various pressures. As
pressure is elevated as 2.62 kbar, 8.48 kbar and 10.00 kbar, the temperature at which
the susceptibility takes maximum tends to be lowered slightly: 16.1 K, 14.0 K and
12.0 K. The contrast becomes clearer when we normalize the raw data at 40 K as seen

20 H. Kageyama, Y. Ueda, Y. Narumi, K. Kindo, M. Kosaka and Y. Uwatoko
in the lower panel of Fig. 2(b). (If the diﬀerence of the susceptibility upon pressurein the high-T region originates only from the pressure cell used, then the normalized
susceptibility should represent the intrinsic one.) Although it is diﬃcult from thisresult to estimate a set of exchange constants precisely, the decrease of temperature
at maximum susceptibility possibly indicates that J  is eﬀectively varied by pressure, making the system closer to the critical point between the dimer phase andsome other phases. In order to obtain the other phase whatever, it is necessary to
execute experiments in higher pressure.
§4.

Nd2 BaZnO5 : Antiferromangnetic phase

Nd2 BaZnO5 with a space group I4/mcm (tetragonal) can be also regarded asa layered compound. 15) As shown in Fig. 3(a), the Nd-O and the Ba-Zn-O layers
alternatively stack along the c direction. The magnetic ions, i.e., the Nd3+ ions occupying a crystallographically equivalent site (8h), form the two-dimensional network
as shown in Fig. 1(b), where the nearest neighbor and the next nearest neighborNd3+ -Nd3+ distances are very close: dNN = 3.324 Å and dNNN = 3.525 Å, respectively. The Nd3+ ion is 8-fold oxygen coordinated with three kinds of Nd-O distance(2.299 Å ×2, 2.493 Å ×2, 2.636 Å ×4) to provide superexchange interactions, J andJ  . The temperature dependence of the magnetic susceptibility as well as the inverse susceptibility for the polycrystal of Nd2 BaZnO5 is shown in Fig. 4(a). The
susceptibility at high-T regime obeys the Curie-Weiss law, and the ﬁtting yields the
Weiss constant θW = −44.5 K, where J = 9/2 and g = 8/11 are used, which are
expected for the ground state of the tripositive neodymium ion with the 4f 3 conﬁguration. The negative sign of θW is an indication of antiferromagnetic interaction.
On cooling, the deviation from Curie-Weiss behavior is observed from 70 K maybe
due to development of short range ordering, and further decreasing T ﬁnally resultsin the antiferromagnetic transition at 2.4 K as seen in the inset of Fig. 4(a). We
can conﬁrm the antiferromagnetic state by plotting the magnetizations against H,
where spin-ﬂop like behavior is observed for the 1.8 K curve (Fig. 4(b)). The gradualincrease with H after the spin-ﬂop transition should come from the strong exchange

(a)

(b)

O

Zn

c

Nd

Ba

2.493 ÅO

2.299 Å2.493 Å2.636 ÅNdbaFig. 3. Crystal structure of Nd2 BaZnO5 .

Orthogonal Dimer Spin Compounds

0.15

0.1 T

TN=2.4 K

250

0.10

200

1

0.10

2

3
T (K)

4

5

150
100

0.05

Nd 2BaZnO5
0

50

100

150

200

250

300

0

-1

0.00

50

(b)

3

300

Magnetization (x10 emu/mol Nd)

Susceptibility (emu/mol Nd)

0.15

Reciprocal Susceptibility (emu/mol Nd)

350(a) 0.20

21

8
7
6
5
4
3

: 1.8 K
: 5.0 K2
1
0

Nd 2BaZnO5
0

1

T (K)

2

3

4

H (T)

5

6

7

Fig. 4. (a) Magnetic susceptibility and reciprocal susceptibility for Nd2 BaZnO5 . The inset represents the enlarged plot for the low temperature region. (b) Magnetization curves for thepolycrystalline sample of Nd2 BaZnO5 measured at 1.8 K (closed) and 5.0 K (open).

SrCu2(BO3)2

anisotropy of the Nd3+ ion which istypical for f electron systems. Con3
Exact Dimer
sidering the closer values between dNN
J/J'
and dNNN as mentioned above, we can2
intuitively expect that J  and J are
helical L.R.O.
close to each other as well. If so,
1
Nd2BaZnO5
there should be strong spin frustra0.5
Neél L.R.O.
tion, and this can explain why the ob2
01
tained θW is much smaller than T N
1/S(θW /TN = −19). In Fig. 5, we redraw
the phase diagram as a function of 1/S
Fig. 5. The phase diagram proposed by
Shastry and Sutherland, 1) on which
and J/J  in the isotropic limit, which
SrCu2 (BO3 )2 and Nd2 BaZnO5 are mapped.
was established by Shastry and Suther1)land. SrCu2 (BO3 )2 (J /J = 0.64) andNd2 BaZnO5 (J  /J = 1) are successfully mapped onto this phase diagram, though
the neodymium oxide is magnetically anisotropic.
§5.

Extended S-S models

As described in Ref. 21), one cantheoretically invent various analoguesof the S-S lattice. Chemists must accomplish a mission to explore model
materials. KIrO3 is a possible candidate of the three-dimensional version of
the S-S model. Its structure, shownin Fig. 6, has a cubic symmetry witha space group of P n-3Z (No. 203). 22)
Each IrO6 octahedron is coupled toedge-share with the neighboring IrO6

Fig. 6. Crystal structure of KIrO3 , where the
IrO6 octahedra and the K ions are represented.

22 H. Kageyama, Y. Ueda, Y. Narumi, K. Kindo, M. Kosaka and Y. Uwatoko
octahedron, and the dimers are connected in a three dimensional way by cornersharing. Since 5d electron systems tend to take low spin state due to relatively large
crystal ﬁeld stabilization energy, it is natural to assume that the Ir5+ ions (5d4 ),located at a crystallographically equivalent site (12g), carry S = 1. Interestingly,
there exist several 4d and 5d transition metal oxides such as La4 Os6 O19 , La4 Ru6 O19
containing the identical magnetic network with KIrO3 . 23), 24) KIrO3 diﬀers from theothers in that the former has one kind of valence (5+), while the latter has a mixed
valence (4.333+). Investigation of the magnetic and electric properties of this seriesof compounds is currently underway.
Acknowledgements
This work is supported by Grant-in-Aid for Scientiﬁc Research (C) (No. 40302640)
from Ministry of Education, Science, Technology, Sports and Culture, Japan.
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