Physica B 281&282 (2000) 656}658

Multiple singlet and triplet states in the 2D orthogonal-dimer
compound SrCu (BO )232
P. Lemmens!,*, M. Grove!, M. Fischer!, G. GuK ntherodt!, H. Kageyama",
K. Onizuka", Y. Ueda"!2. Physikalisches Institut, RWTH-Aachen, 52056 Aachen, Germany"Institute for Solid State Physics, University of Tokyo, Roppongi 7-22-1, Tokyo 106-8666, Japan

Abstract
The compound SrCu (BO ) is a quantum spin system with a 2D arrangement of orthogonal spin dimers, an exact
232
singlet ground state and a singlet}triplet gap D "34 K. Triplet excitations in this compound are extremely localized01
and strongly interacting due to the strong inherent frustration. Experimentally, two triplet modes were observed both inneutron scattering and ESR investigations. In Raman scattering experiments further well-de"ned modes with energies
close to D exist for low temperatures (¹;D ). The properties of these modes resemble the magnetic bound states
01
01
found in dimerized spin chain and spin ladder systems. ( 2000 Elsevier Science B.V. All rights reserved.
Keywords: SrCu (BO ) ; Spin gap; Bound states; Raman scattering
232

1. Introduction
Low-dimensional quantum spin systems with a "nitespin gap have been a subject of intense research in the lastyears. The singlet ground state is realized in one dimension in the dimerized phase of spin-Peierls systems(¹(¹ ), alternating spin chains or spin ladders. ComSPpounds that have been investigated within this context
are, e.g., CuGeO , a@-NaV O , (VO) P O or Sr
32 5
2 2 714~x
Ca Cu O . Of even greater interest is the existence ofx 24 41a gap in a two-dimensional (2D) spin system. Unfortunately only very few 2D spin systems, such as CaV O ,4 9
are discussed in which the gap is relatively large, i.e. notcaused by spin anisotropies. Recently, SrCu (BO ) with232
a layered structure has been identi"ed as a 2D system[1,2]. Furthermore, due to its exceptional exchange
topology this compound can be regarded as a model
system with an exactly known ground state given by thedirect product of singlet pairs [3,4].

* Corresponding author. Tel.: #49-241-807-113; fax: #49241-888-8306.
E-mail address: peter.lemmens@physik.rwth-aachen.de (P.
Lemmens)

SrCu (BO ) has a tetragonal unit cell (D ) with
2322dCu2` ions that carry spin s"1 and have distances to2nearest and next-nearest Cu neighbors of approximately
2.9 and 5.1 As , respectively. A spin dimer consists ofa neighboring pair of planar rectangular CuO . Dimers
4
are connected orthogonally by a triangular BO . This
3
2D lattice in the ab plane of the compound is topologically equivalent to the Shastry}Sutherland lattice studied
earlier [3] and is given by a 2D square lattice with anadditional alternating diagonal interaction. This interaction serves as a spin frustration. The Shastry}Sutherland
lattice thus can be considered as a 2D analog of theMajumdar}Ghosh model for a one-dimensional zigzag
spin chain [5]. The strength of the next-nearest-neighboror interdimer interaction J "68 K, which brings a frus2
tration into the system, and an intradimer coupling ofJ "100 K have been estimated [4]. It has been high1
lighted that the ratio J /J "0.68 is just below the2 1
critical value of J /J "0.70 separating the exact dimer
2 1state and a NeH el-ordered state. Thus this compound isvery close to a quantum critical point between a gapfull
exact dimer and a gapless phase [4,6].
Recent ESR [7] and neutron scattering investigations[8] observed triplet excitations from the singlet groundstate "xing the spin gap at D "34 K. This triplet
01

0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 9 3 4 - 5

P. Lemmens et al. / Physica B 281&282 (2000) 656}658

branch observed at 3 meV has a very small dispersion of
only 0.2 meV. This value is much smaller than expected
theoretically [6] and points to extremely localized triplet
excitations. In addition, a second triplet branch
D@ "55 K,4.7 meV with a larger dispersion is ob01
served. A further interesting aspect of this compound is
its magnetic phase diagram. Quantized plateaus at 1 and4
1 of the saturated Cu moment are observed in the mag8
netization for "elds up to 50 T [9]. Although similar
e!ects are well known for 1D spin systems this is the "rstobservation of ordered triplet phases in a 2D compound[4].

2. Results and discussion
Raman scattering experiments on SrCu (BO ) at
232
room temperature show numerous phonon lines in thefrequency range 30}1200 cm~1. In the low-energy region
drastic changes happen for ¹(5 K leading to the appearance of several new modes. In Fig. 1 Raman spectra
are shown at ¹"1.7 K and in several scattering con"gurations within the ab plane of the crystal. Spectrain the upper panel show data in (b@b@) : A #B and12(aa) : A #B con"guration, while the lower panel gives
11(a@b@) : B and (ab) : B . Symmetry components are de1
2
noted with respect to the Dpoint group using
2db@"a#b.
We "rst concentrate on the (ab) component in thelower panel. Modes with weak intensity are observed at24.5, 31 and 40 cm~1. All other signals in this polarization are extremely weak and probably have their originin spurious contributions from other polarizations. The"rst and the third mode are identical in frequency withthe triplet modes observed in ESR and neutron scattering
discussed above. In the (a@b@) polarization additionalmodes are observed at 29.3 and 56 cm~1. These modes
show up with an intensity three times larger than that of
the modes in (ab) polarization. They are also observed inthe (aa) and (b@b@) polarizations given in the upper panel.
Further broadened modes with no distinct selection rules
appear at 45}47 and 65}75 cm~1. In contrast, the mode
at 61 cm~1 observed both in (aa) and (b@b@) polarization
has a well-de"ned A symmetry, a smaller line shape and1exists also at higher temperatures. All these properties
are in favor of its interpretation as a phonon mode.
The low-excitation spectrum of SrCu (BO ) is very
2
32
detailed and complex. However, comparing these observations with earlier experiments on 1D spin-gap systems[10,11] several conclusions are drawn. The temperaturedependence of the intensity and the energy of the abovemodes, except the 61 cm~1 mode, both point to their
origin in the singlet}triplet gap. Selection rules allow to
divide the observed modes into three groups as triplet
excitations (B symmetry, three modes), predominant2
singlet excitations (A #B symmetry, two modes) and1
1657

Fig. 1. Low-energy Raman spectra of SrCu (BO ) in di!erent
232
scattering geometries in the ab plane (see text) at ¹"1.7 K. The
vertical dotted lines indicate the frequencies of the observed
modes. With the exception of the phonon mode at 61 cm~1 allother modes are of magnetic origin.

mixed modes (two modes). Indeed, in systems withstrongly localized triplets a number of singlet and triplet
bound states are possible. We propose to identify
D "24.5 cm~1 as the original triplet branch and01
D@ "40 cm~1 as the "rst triplet bound state. The01
modes at 29.3, and 56 cm~1 may be assigned to singlet
bound states. All other modes have to be attributed tohigher-order bound states as they are either very weak inintensity or triplet states are not observed in neutron andESR experiments [12].
The binding energy of the "rst triplet ("rst singlet)bound state with respect to 2D
is E "9 cm~1015(E "19.7 cm~1). These binding energies are large if
4compared to 1D frustrated spin systems. However, due tothe strong localization [4] of the triplet excitations on theorthogonal dimer sites strong binding e!ects are expected. Evidence for a multitude of magnetic excitations
is also given in recent ESR experiments [7]. In conclusion, Raman scattering experiments at low temperatures on SrCu (BO ) showed a multitude of magnetic
232excitations with energies close to the singlet}triplet gap.
The number, selection rules and other properties of thesemodes are more complicated compared with 1D alternating chain systems.

Acknowledgements
Financial support by DFG/SFB 341 and INTAS 96410 is gratefully acknowledged.

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