Journal of the Physical Society of Japan
Vol. 69, No. 4, April, 2000, pp. 1016-1018

Letters

1/3 Magnetization Plateau in SrCu2 (BO3 )2- Stripe Order of Excited Triplets Kenzo Onizuka, Hiroshi Kageyama∗ , Yasuo Narumi1,2 ,Koichi Kindo2,1 , Yutaka Ueda and Tsuneaki Goto
Institute for Solid State Physics, University of Tokyo,
Roppongi 7-22-1 Minato-ku, Tokyo 106-8666
1 CREST, Japan Science and Technology Corporation (JST)2 Research Center for Materials Science at Extreme Conditions, Osaka University,
1-3 Machikaneyama, Toyonaka, Osaka 560-8531(Received January 11, 2000)

High-field magnetization measurements up to 57 T have been performed at 0.08 K in a single crystal of a two-dimensional spin-gap material SrCu2 (BO3 )2 . We successfully observed thepredicted plateau at 1/3 of the total magnetization around 50 T, in which the magnetic superstructure is characterized by a novel stripe order of triplets. The 1/3 plateau is much wider thanthe previously observed 1/4 and 1/8 plateaux.
KEYWORDS: SrCu2 (BO3 )2 , Shastry-Sutherland model, quantized magnetization plateaux, stripe, spin gap

There has been a resurgent interest in the phenomena of quantized magnetization plateaux because theplateaux of recent interest are caused principally byquantum many-body effects,1) in contrast to classicalsystems previously investigated such as CoCl2 2H2 O.2)
Experimentally, several quantum-spin systems were reported to have magnetization plateaux. A 1/2 plateau of
the total magnetization was observed in [Ni2 (Medpt)2 (µox)(µ-N3 )]ClO4 0.5H2 O,3) 1/4 and 3/4 in NH4 CuCl3 ,4)and 1/8 and 1/4 in SrCu2 (BO3 )2 .5)
SrCu2 (BO3 )2 is a layered material with a tetragonal
symmetry, composed of alternating stacks of 2CuBO3
and Sr planes along the c axis. In the CuBO3 plane,nearest-neighbor Cu2+ ions constitute an S = 1/2
dimeric unit, and each dimer connects orthogonally withfour nearest-neighbor dimers. The intradimer and interdimer interactions, symbolized by J and J 0 , respectively,
lead to an exact ground state with spin gap ∆, thus realizing the 2D Shastry-Sutherland model.6, 7) The valuesof J, J 0 and ∆ were estimated to be 100 K, 68 K and34 K, respectively.8-10)The 1/4 and 1/8 plateaux in SrCu2 (BO3 )2 were firstdetected by magnetization measurements on a polycrystalline sample performed in a magnetic field H up to
H = 43 T and down to 1.5 K with a pulse magnet atISSP, the University of Tokyo,5) followed by those using field-oriented samples for H//c and H ⊥ c10) and asingle crystal for H ⊥ c.11) Theoretically, Miyahara andUeda explained that the origin of the plateaux lies in
the almost localized nature of the triplet excitations.7)
Moreover, in light of the tetragonal symmetry of thecrystal structure, they initially argued the following necessary condition for the triplets to ensure ordered rather
than disordered structures: corresponding magnetic superstructures should also be tetragonal symmetry. In∗ Corresponding author, E-mail: kage@issp.u-tokyo.ac.jp

fact, this condition satisfies the superstructures shownin Figs. 1(a) and 1(b) for the 1/8 and 1/4 plateaux, respectively. Following this simple geometrical argument,
one expects other plateaux at 1/2, 1/10, 1/16, 1/32...,
which also have square unit cells.
However, recent detailed analyses carried out independently by Momoi and Totsuka11) and by Miyahara andUeda12) have revealed the possibility that the superstructure for the 1/4 plateau is of stripe type with a rectangular unit cell, as shown in Fig. 1(c). Novel anisotropicinteractions cause the stripe order. Namely, the interaction of the next-nearest-neighbor pair of triplets ismuch weaker than that of the third-nearest-neighbor one.
By the same logic, a prediction has been made that a1/3 plateau with a superstructure of stripe order (seeFig. 1(d)) will be observable if a magnetic field higher
than that ever studied is applied.
It is unfortunate that, in spite of intensive experimental activities,5, 8-10, 13-15) the existence of the stripe
order even for the 1/4 plateau has yet not been confirmed. This is partly because the required magnetic
field is beyond the capability of facilities currently used
for microscopic techniques such as neutron diffraction.
In this letter, we measured the magnetization at 0.08 K
for single-crystalline SrCu2 (BO3 )2 up to 57 T to successfully observe the 1/3 plateau. It should be emphasized
that, unlike the 1/4 plateau, the stripe superstructure(Fig. 1(d)) is the unique candidate for the 1/3 plateau.
The high-field magnetization measurements were conducted using pulse magnets at the High Magnetic Field
Laboratory, KYOKUGEN in Osaka University. Highquality single crystals of SrCu2 (BO3 )2 were obtainedby a travelling solvent floating-zone technique, as described in ref. 16. We used one of the grown single crystals of high quality with the approximate dimensions of2 mm×2 mm×2 mm. Magnetization data for H ⊥ c werecollected at 0.08 K in magnetic fields up to 57 T, and1016

Letters1017

Fig. 3. Normalized parallel and perpendicular magnetizations forH ⊥ c (solid) and for H//c (broken), where g// = 2.28 and g⊥ =2.05 are used.

Fig. 1. Possible ordered structures between the excited triplets(open) and the remaining singlets (solid) for the 1/8 plateau(a) the 1/4 plateau (b) and (c), and the 1/3 plateau (d). The
magnetic unit cells are represented by broken lines.

Fig. 2. The magnetization curves measured at 0.08 K for H ⊥ cand at 1.4 K for H//c. The broken lines correspond to 1/3, 1/4
and 1/8 of the total magnetization.

those for H//c were collected at 1.4 K up to 53 T.
Figure 2 shows the magnetization curves for H//c andfor H ⊥ c, where within the experimental accuracy, nohysteresis was observed upon increasing or decreasing
the external field. It appears that the difference between
the two curves arises only from the g-factor. As seen in
Fig. 3, the parallel and perpendicular magnetizations canbe normalized using g// = 2.28 and g⊥ = 2.05 determinedby electron spin resonance (ESR).10) Strictly speaking,there is a slight difference around 30 T, which will bediscussed later. Note that this is the first measurementof parallel magnetization using the single crystal. The
obtained magnetization curve for H//c has more distinct

1/4 and 1/8 plateaux compared with that obtained using
the field-oriented polycrystal10) with poor orientation, asevaluated by nuclear magnetic resonance. On the otherhand, the result for H ⊥ c below 42 T is almost identicalto that previously reported using the single crystal.9) As
shown in Fig. 2, the critical fields are determined to be
H1 = 29.6 T, H2 = 31.2 T, H3 = 36.7 T and H4 = 43.6 Tfor H ⊥ c, and H1 = 26.9 T, H2 = 28.2 T, H3 = 34.1 T
and H4 = 39.1 T for H//c, which is almost consistent
with the previous results.9, 10)
A glance at Fig. 2 reveals a wide plateau at 1/3 of thefull magnetization. As mentioned earlier, the 1/3 plateau
cannot accommodate any magnetic superstructure witha square unit cell. Therefore, this observation confirms,
for the first time, the existence of the novel stripe order,
where the magnetic unit cell is composed of four singlets
and two triplets. The onset field H5 of the 1/3 plateau
is estimated to be 43.6 T for H ⊥ c and 40.2 T for H//c.
As evident in Fig. 2, the 1/3-plateau phase is stable overa much wider field range than the 1/8 and 1/4 plateaux.
Another interesting point is the sudden jump of the magnetization between the 1/4 and 1/3 plateaux, possibly
indicating a first-order phase transition, although there
is no hysteresis between the field increase and decrease
processes.
There are several theoretical papers concerning calculations of the magnetizations with varying J 0 /J.11, 12, 17)
In Fig. 4, we compare the experimental curve with thecalculations in terms of a hard-core boson model by Momoi and Totsuka11) (theory I) and Miyahara and Ueda12)(theory II), where J = 100 K and J 0 = 68 K are used.
It is noteworthy that both models quantitatively reproduce the experimental data, particularly around the 1/3
plateau. The main difference between theories I and II,in short, is that the former considers correlated hopping
terms and neglects long-range interactions, whereas thecase is reversed in the latter. In connection with this difference, the 1/3 plateau ends at 80 T according to theory
I, while theory II predicts that it ends at 110 T. Moreover, theory II concluded that a 1/2 plateau appears,
whereas theory I did not. Thus, the future direction of1018

Letters

In conclusion, our high-field magnetization measurement for SrCu2 (BO3 )2 allowed the first experimental verification of the stripe order in the orthogonal dimer lattice through the observation of the 1/3 plateau that appears around 50 T. The transition between the 1/3 and1/4 plateaux seems to be of the first order. The calculated magnetizations satisfactorily reproduce the experimental magnetization result around the 1/3 plateau
region.
We wish to thank S. Miyahara, K. Ueda, T. Momoiand K. Totsuka for kindly providing us with their theoretical results and also for motivating us to carry out
this experiment. This work was partially supported bya Grant-in-Aid for Scientific Research from the Ministryof Education, Science, Sports and Culture.

Fig. 4. Comparison with the theories by Momoi and Totsuka11)(a) and Miyahara and Ueda12) (b), where J = 100 K and J 0 =68 K are assumed. The dotted curve is the experimental resultfor H//c normalized by g = 2.28.

this area of study will be one that requires even higher
magnetic fields.
Finally, let us discuss the anomalous behavior around
30 T, as shown in Fig. 3. In ref. 9, we suggested the1/10 plateau, judging from the perpendicular magnetization that displays a bump at about 1/10 of the totalmagnetization, as observed in this experiment as well.
The behavior of the parallel magnetization, however, is
not indicative of the 1/10 plateau, as seen in Fig. 3. It
is possible that the appearance of the 1/10 plateau depends on the field direction, i.e., the orientation of theexcited triplets. Alternatively, this phenomenon could
be a quantum effect of some kind.

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