P-63

Proc. Int. Symposium on Advances in Neutron Scattering Research, Tokai, 2000
J. Phys. Soc. Jpn, 70 (2001) Suppl. pp. 000-000

Magnetic Excitations in the Two-Dimensional Spin Gap System
SrCu2 (BO3 )2Naofumi Aso , Katsuyuki Nukui , Masakazu Nishi , Hiroshi Kageyama , Kenzo Onizuka ,Tomoyuki Yosihama , Kazuhisa Kakurai and Yutaka Ueda
111

21;

21;321 Neutron Scattering Laboratory, Institute for Solid State Physics, University of Tokyo, Tokai, Ibaraki 319-1106,

Japan

2 Material Design and Characterization Laboratory, Institute for Solid State Physics, University of Tokyo,

Kashiwa 277-8581, Japan

3 CREST, Japan Science and Technology Corporation (JST), Tsukuba 305-0047, Japan

Neutron inelastic scattering has been performed on single crystals of 2D spin-gap system
SrCu2 (BO3 )2 , which has an exact dimer ground state of the Shastry-Sutherland model. We
observed three magnetic excitations around 3, 5 and 9 meV at 1.7 K. The lowest singlet-triplet
excitation at 3 meV shows little wavevector dependence in all directions, indicating a localized
character of the triplet state. The two triplet excitation at 5 meV exhibits more dispersive naturein the 2D a-b plane, but is dispersionless in the out-of-plane. This observation suggest that thecorrelated hopping of the two-triple excitations is con ned to the 2D a-b plane.
KEYWORDS: SrCu2 (BO3 )2 , neutron scattering, 2D quantum spins, spin gap, Shastry-Sutherland modelx1.

Introduction

23 21)

2Counts/9600kmon (~5min)

Study on spin gap systems with the singlet groundstate in low-dimensional quantum spin systems, which
are realized by the strong quantum e ect, is one of thehot topics in strongly correlated electron physics in recent years. SrCu (BO ) is a recently discovered twodimensional (2D) spin-gap system which is actively studied by both theorists and experimentalists.
SrCu (BO ) has a tetragonal structure of the spacegroup of 42 and lattice parameters = 8.995 A and= 6.649 A at room temperature. All Cu ions withspin are located crystallographically equivalent sites.
The 2D layers containing the Cu ions are separated byplanes of Sr ions. The magnetic susceptibility showsa broad maximum around 15 K and drops rapidly to zerowith reducing the temperature, indicating a transition toa non-magnetic singlet ground state. A neighboring pairof the Cu ions forms a spin dimer and the neighboring dimers are connected orthogonally. Miyahara andUeda found that its unique 2D spin structure is equivalent to the Shastry-Sutherland model, which has anexact dimer ground state. Another interesting aspect isquantized plateaux in the magnetization, for example, atone-quarter and one-eighth of the full Cu moment
owing to the extremely localized nature of the excitedtriplet state. From previous experimental results andtheoretical calculations, it has been recognized thatSrCu (BO ) is an = 1/2 highly frustrated spin gap
system with an energy gap of  = 34 K and with a ratioof intradimer ( ) and interdimer ( 0 ) exchange of 0= 0.68 ( = 100 K, 0 = 68 K) very close to the criticalvalue of ( 0 )  0 7, where Miyahara and Ueda also2)

3 2Ima1
2: 24K

300
200
100
I

II0III

51015E (meV)Fig.1. Energy scans at Q = (2,0,0) obtained at T = 1.7 K (circles)and 24 K (triangles). The excitations are labeled at the bottomsof the gure. The solid curve is the t to the pro le at 1.7 K.
The abrupt upturn around energy zero is due to the incoherent
elastic scattering.

2+2+: 1.7 K

400

02+c

Q =(2,0,0)

5002)

2+

indicated that a phase transition from0 a singlet dimer toa Neel state occurs with increasing .
In the present work, we have investigated magnetic
excitation spectrum of single crystals of SrCu (BO )by means of inelastic neutron scattering techniques. We
discuss the features of the excited triplet states in connection with the orthogonality of the dimers.

1)

J =J3)

2+22)2)1)

2x2.

JJJ =J cJ23J =J

11J:Experimental

Single crystals of SrCu ( BO ) with a total mass of 1.5 cm were prepared by the traveling solvent oatingzone method using Li BO ux.
Inelastic neutron scattering experiments were performed on the ISSP-PONTA triple-axis spectrometer installed at JRR-3M reactor at Tokai establishment of theJapan Atomic Energy Research Institute. The spectrom-S

3 23 21)

 Present address: Advanced Science Research Center, Japan
Atomic Energy Research Institute, Tokai, Ibaraki 319-1195, Japan11123 24)

Naofumi Aso et al.

28(b) (H 0 L)-plane(a) ( H K 0)-planeEnergy (meV)76IIIIII

54
32(0,0)

(π,0)

(π,π)

(0,0) 0.0

0.5

1.0

1.5

2.0

(2 0 L) (r.l.u.)
Fig.2. Q-dependence of the excitation energies in the (H K 0) plane (left) and (H 0 L) plane ( ght) obtained at 1.7 K. The solid curves
are guides to the eye. The arrows represent the energy resolutions of the instrument (FWHM). The unit cell in the (H K 0) plane(left) by the notation of Weihong et al.5, 6) is used. Q = (2, 0, L) in the right panel corresponds to the (0, 0) point in the left one.

eter was operated with xed nal energy = 14.7 meV( = 2.67 A ) and collimations of open(40')-40'-80'80'. A PG lter was placed after the sample to reduce
the higher order contaminations. The crystals
are oriented so as the scattering plane contains - and -axesor - and -axes.
Ef1kfaabcx3.

Results and Discussion

Figure 1 shows typical energy scans obtained at 1.7 K
and 24 K for a wave vector of = (2,0,0). Three magnetic excitations at 1.7 K (  ) are observed around3, 5 and 9 meV (excitations I, II and III, respectively),while no distinct peaks are observed at 24 K. The excitation I centered at  = 3.0 meV corresponds to the transition of a single triplet from the singlet ground state, asindicated by other experiments. The solid curve is at to the 1.7 K pro le convoluted with instrumental resolution. It should be noted that the excitation I showedalmost energy resolution limited behavior, while the excitations II and III tend to have intrinsic energy widths.
Precise temperature dependence of these excitations I, IIand III (not presented here) shows that all of these three
excitations apparently vanish at about 13 K, implyingthat the excitations II and III consist of multi-triplet excitations. The temperature of 13 K is only one-third ofspin gap energy ( = 3.0 meV). A similar behavior has
also been seen in Raman scattering study. We supposethat this anomalous temperature dependence of intensity possibly comes from a strong spin frustration due tothe orthogonality of the dimers.
The dispersion relation of the excitation I and II forthe ( 0) and ( 0 ) planes are shown in Fig. 2 (a)and (b), respectively. It is noted that the energies of theexcitation I in both the planes are almost dispersionlessand change within  0.2 meV at most, indicating the single triplet hardly moves both in the 2D plane and along
the -axis. Miyahara and Ueda theoretically showedthat the dispersionless behavior in SrCu (BO ) is notdue to the spatial isolation but due to the orthogonality
QT2, 7, 8)

6)

8)

H KcHL1)

2

3 2of the neighboring dimers. According to their perturbation calculations, a hopping of the single triplet fromone site to another within the 2D - plane is possible
only from the sixth order, leading to an extremely weak
dispersion of the excitation I in the (0) plane, inexcellent agreement with the present result shown in Fig.
2 (a).
They also argured the e ects of the interlayer coupling
00 and proved that the single triplet excitation cannot
move along the -axis, indicating the complete atdispersion along the direction. As shown in Fig. 2.
(b), the obtained dispersion relation of the excitation I
is almost at with scatter of 0.2 meV, which is similar
to the dispersion energy in the 2D plane. To clarity theabove argument, we need to perform experiments with abetter energy resolution.
Then let us look at the second triplet excitation II at 5meV. This excitation II can be interpreted as correlated
two-triplet excitation, discussed in the reference, andhas been already observed by ESR and Raman Scattering. In Fig. 2 (a), the dispersive excitation II has
been observed between 5 meV and 6.5 meV. This meansthat the correlated two triplets can propagate more easily than the single triplet in accord with the thoereticalprediction. Considering the instrumental energy resolution, the intrinsic energy width of the excitation II for
any points is obtained to be about 0.7 meV. The nitewidth possibly indicates a short life time of correlated
two triplets and/or the existance of several excited statewith closely degenerate discrete energies. The striking
di erence between the two-triplet excitation in the 2D
plane and that along the  direction is that the energyof the excitation II is almost at as illustrated in Fig. 2(b). This observation indicates that the correlated two
triplets can only move within the 2D plane.
The higher-energy excitation in the energy range of 812 meV would possibly arise from the correlated threetriplet or multi-triplet excitations, due to the highly frustrated spin dimers.
9)

a bH KJ10)

cc6)

7)

8)

11)

Qc

Magnetic Excitations in SrCu2 (BO3 )2x4.

Summary

We performed inelastic neutron scattering experimenton SrCu ( BO ) to nd three magnetic excitations.
The lowest single triplet excitation from the ground state
was observed at 3.0 meV, in excellent agreement with theprevious measurements.
The almost dispersionlessbehavior arises from the orthogonality of the neighboring dimers. The second triplet excitation around 5 meV
can be interpreted as correlated two-triplet excitation. Itmoves more easily in the - plane than the single triplet
does, but hardly does along the -axis.
2113Culture, Japan.

3 22, 7, 8)

a bc

Acknowledgements

This work has been partly supported by a Grant-inAir from the Ministry of Education, Science, Sports and1) S. Miyahara and K. Ueda : Phys. Rev. Lett. 82 (1999) 3701.
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Suppl. B p72.
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