Physica B 281&282 (2000) 667}668

Speci"c heat study of SrCu (BO )232
H. Kageyama*, H. Suzuki, M. Nohara, K. Onizuka, H. Takagi, Y. Ueda
Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo 106-8666, Japan

Abstract
The speci"c heat measurement of a two-dimensional spin-gap material SrCu (BO ) with an exact dimer ground state232
was performed in various magnetic "elds up to 12 T. Based on an isolated dimer model, we estimated the spin-gap size atzero "eld to be 35.0 K. The value of the spin gap decreases in proportion to the applied magnetic "eld, due to the Zeeman
splitting of the excited triplet levels. ( 2000 Elsevier Science B.V. All rights reserved.
Keywords: SrCu (BO ) ; Exactly solvable model; Speci"c heat; Spin gap
232

Our experimental investigations on SrCu (BO ) with232
a spin-1/2 two-dimensional orthogonal dimer lattice[1}3] have established that this material is the very
realization of the Shastry}Sutherland model with anexact dimer ground state [4,5]. From various measurements such as magnetic susceptibility and electron spinresonance (ESR), we estimated the value of spin gap to beabout 34 K. Of equal importance is a rather strong interdimer interaction J@ (comparable with an intradimer oneJ), which brings a spin frustration into the system [1].
In fact, J@ and J were theoretically determined to be 68
and 100 K, respectively [4]. Interestingly, the ratio J@/J
"0.68 is just below the critical boundary, (J@/J) "0.70,#beyond which the system falls onto the NeH el-orderedstate [4]. Concerning magnetic excitations, quantizedplateaus such as 1 and 1 of the Cu full moment were48
observed in the magnetization curves [1], which originate from considerable constraint upon a hopping ofa single triplet [4].
In the present paper, we measured the magnetic "eldH dependence of the speci"c heat C of SrCu (BO ) to2
32
further understand both the ground and excited states,and obtained data were analyzed in terms of an isolated
dimer model. The speci"c heat was measured by a heat-* Corresponding author. Fax: #81-3-3478-8459.
E-mail address: kage@issp.u-tokyo.ac.jp (H. Kageyama)relaxation method in a temperature ¹ range between 1.3
and 25 K in magnetic "elds up to 12 T. A bulk single
crystal of SrCu (BO ) was used, which was grown by232
the travelling solvent #oating zone method [6]. The
magnetic "elds were applied perpendicular to the abplane, i.e., the orthogonal dimer lattice.
A total speci"c heat divided by ¹, C/¹ measured at
H"0, 6, 9, 12 T is plotted against ¹ in Fig. 1. For any
magnetic "eld, C/¹ rises with decreasing ¹ from 15 K,reaches a round maximum, and then falls rapidly towardnaught. The round maximum, namely, the so-called
Schottky anomaly is typical of spin-gapped system.
A gradual increase in C/¹ with rising ¹ above 15 K
comes from the phonon term, which is, in general, known
to vary as CJ¹3. A prominent characteristic is that,with increasing H, a peak of C/¹ shifts to lower temperature: the temperatures where C/¹ reaches a maximumfor H"0, 6, 9, 12 T are, respectively, 7.5, 7.3, 6.9, 6.8 K.
This behavior is related to a reduction in the spin-gap
size *(H) with H, which will be con"rmed later.
Because of a lack of an appropriate theory to describe
the present experimental data, let us analyze the data
only in lower-¹ region well below the spin gap utilizing
the isolated dimer model, where J@ is neglected and only
J is taken into consideration [7]. In this simplest model,
the magnetic contribution of the speci"c heat in a low-¹
limit is expressed as C(H)J¹~2 exp(!*(H)/¹). Thus,
C¹2 is plotted against 1/¹ in a logarithmic scale asshown in Fig. 2. One can see that all data well satisfy

0921-4526/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.
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H. Kageyama et al. / Physica B 281&282 (2000) 667}668

Fig. 1. C/¹ versus ¹ measured at H"0, 6, 9, and 12 T.

explained by the Zeeman splitting of the excited triplet
levels (S"1). The "tting of the *(H)}H data to thefollowing relation, *(H)"*(0)!gl H (g being theBg factor of the Cu2` electron spin), yielded *(0)"35.0 K.
This value is quite consistent with the results of othermeasurements such as magnetic susceptibility (34 K) [2],ESR (34.7 K) [3].
As demonstrated above, the isolated dimer modelseems to reproduce the experiment well, providing a reasonable value of spin gap. In higher temperature region,
however, the deviation between our experiment and thetheory is appreciable.1 The magnetic entropy, forexample, at 25 K is only about 74% of the expected value
for the isolated dimer model with *(0)"35.0 K, indicating that the system is e!ectively correlated over muchhigher temperatures. It is noteworthy that the value of
J is identical with that of *(0) for the isolated dimer
model. Accordingly, J"35 K ("*(0)) obtained above ismuch smaller than J"100 K (and also J@"68 K) determined by Miyahara and Ueda [4]. We are looking forward to a theory based on the Shastry}Sutherland modelwith J and J@ to reproduce our speci"c heat data over thewhole ¹ range.

References

Fig. 2. Logarithmic plot of C¹2 as a function of 1/¹. Solid lines
denote the calculations based on the isolated dimer model. Inset:
magnetic "eld variation of *(H).

a linear "eld dependency. By the least-squares "ttings inthe low-¹ region, where the phonon contribution isnegligible, we obtained *(0)"35.9 K, *(6)"27.5 K,*(9)"22.5 K and *(12)"16.8 K. As shown in the insetof Fig. 2, *(H) decreases in proportion to H. This can be[1] H. Kageyama, K. Yoshimura, R. Stern, N.V. Mushnikov,K. Onizuda, M. Kato, K. Kosuge, C.P. Slichter, T. Goto,Y. Ueda, Phys. Rev. Lett. 82 (1999) 3168.
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Soc. Japan 68 (1999) 1821.
[3] H. Nojiri, H. Kageyama, K. Onizuka, Y. Ueda, M. Motokawa, J. Phys. Soc. Japan 68 (1999) 2906.
[4] S. Miyahara, K. Ueda, Phys. Rev. Lett. 82 (1999) 3701.
[5] C.K. Majumdar, D.K. Ghosh, J. Math. Phys. 10 (1969)
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[6] H. Kageyama, K. Onizuka, T. Yamauchi, Y. Ueda, J. Cryst.
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[7] R.L. Carlin, Magnetochemistry, Springer, Berlin, 1986
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1 As space is limited, the detailed discussion in higher-¹ region will be given elsewhere.