ARTICLE IN PRESS

Journal of Magnetism and Magnetic Materials 272–276 (2004) 25–26

Spin superstructure in the 18-magnetization plateau phase of the2D orthogonal dimer spin system SrCu2ðBO3 Þ2
K. Kodamaa, M. Takigawaa,*, M. Horvatic! b, C. Berthierb,c, H. Kageyamaa,
Y. Uedaa, S. Miyaharaa,d, F. Beccad, F. MiladaInstitute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, 277-8581 Chiba, Japanb
Grenoble High Magnetic Field Laboratory, CNRS and MPI-FKF, Grenoble 38042, Francec
Laboratorie de Spectrom!etrie Physique, Universit!e Joseph Fourier Grenoble I, St.-Martin d’H"eres 38402, FrancedInstitut de Physique Th!eorique, Universite! de Lausanne, Lausanne CH-1015, Switzerland

Abstract
Nuclear magnetic resonance (NMR) experiments have been performed on the quasi-two-dimensional quantum spin
system SrCu2 ðBO3 Þ2 : The Cu NMR spectrum in the 18-magnetization plateau state at 27:6 T and 35 mK shows ﬁne
structure, providing clear evidence for a magnetic superlattice in the plateau state. We conclude that the superlattice hasa rhomboid unit cell with oscillating spin polarization, which is in good agreement with the numerical calculation on theShastry–Sutherland spin model.
r 2003 Elsevier B.V. All rights reserved.
PACS: 75.25.+z; 75.30.Kz; 76.60.Jx; 75.10.Jm
Keywords: Quantum phase transition; Magnetization plateau; Spin superstructure

SrCu2 ðBO3 Þ2 has a two-dimensional network oforthogonal dimers of spin-12; which is equivalent to theShastry–Sutherland spin model [1]. The ground state is
the dimer singlet state [2] with an excitation gap [3] andthe dispersion of the triplet excitations has an extremely
small width [4], in accord with the prediction for theShastry–Sutherland model [5]. The most striking property of this compound are the plateaus in the magnetization curve at 18; 14 and 13 of the fully saturated moment[3,6]. Theoretical studies have suggested that the excitedtriplets with small kinetic energy localize due torepulsive interactions to form a superlattice [7], when
the density of the triplets is commensurate with thecrystal lattice. This is analogous to the Wigner crystallization or charge ordering in electron systems. The
inequivalent Cu-sites in the superlattice should havedifferent hyperﬁne ﬁelds, which can be observed byNMR. We have performed NMR measurements on a*Corresponding author. Tel.: +81-4-7136-3225; fax.: +81-47136-3225.
E-mail address: masashi@issp.u-tokyo.ac.jp (M. Takigawa).

single crystal of SrCu2 ðBO3 Þ2 in the magnetic ﬁeld up to28 T applied along the c-axis at 35 mK [8]. This ﬁeld
range covers the 18 plateau state, which is observed for
27–28:5 T:
Fig. 1 shows the Cu NMR spectra at 26 T (inset) andat 27:6 T (main panel). One type of Cu-sites with a
speciﬁc value of the hyperﬁne ﬁeld generally gives six
NMR lines, three lines split by electric quadrupolarinteraction for each of two isotopes 63 Cu and 65 Cu: Thespectrum at 26 T can indeed be represented as a
combination of such six lines, indicating that themagnetization is largely uniform at this ﬁeld except forsome degree of random distribution causing the ﬁnite
line width.
At 27:6 T; the ﬁeld near the middle of the 18magnetization plateau, we observed a completelydifferent spectrum with a large number of sharp peaks
distributed over a wide frequency range. This provides
clear evidence for a magnetic superlattice with broken
translational symmetry in the 18 plateau phase. The six
sharp peaks in the frequency range 105–165 MHz are
ascribed to one type of Cu sites with the negative

0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmmm.2003.11.029

ARTICLE IN PRESS
K. Kodama et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 25–26

26

Intensity

IntensityH=27.6 T

H=26 T0260 280 300 320

Frequency (MHz)124356100

150200250300

350

400

4508

Frequency (MHz)Fig. 1. Cu NMR spectra obtained at T ¼ 35 mK is shown byblack dots. The inset is the spectrum at H0 ¼ 26 T; and themain panel is the one at H0 ¼ 27:6 T:

hyperﬁne ﬁeld Hn ¼ 16:2 T; corresponding to thelargest local magnetization /Sz S ¼ 0:30: Similarly, thebroad peaks for 165–235 MHz represent another type ofsites with /Sz S ¼ 0:20: The rest of the spectrum comesfrom the sites with much smaller values of /Sz S: It
should be noted, however, that some of these sites havepositive hyperﬁne ﬁelds, i.e., spins polarized opposite to
the ﬁeld. Thus the magnetization oscillates within theunit cell of the superlattice.
We found that any satisfactory ﬁtting of the spectrum
requires at least 11 distinct Cu sites. This fact leads tothe conclusion that the superlattice has the rhomboid
unit cell as shown in Fig. 2, since any other types of unit
cell cannot produce such a large number of inequivalentsites. The number of inequivalent Cu sites for therhomboid cell is eight for a single layer. However, it may
increase up to 16 depending on the pattern of stacking
the layers along the c-axis. The magnetization proﬁlecalculated by the exact diagonalization of the Shastry–
Sutherland model on a 16-spin cluster of a rhomboid cell
[8,9] is shown in Fig. 2. One can clearly recognize abuilding unit consisting of one strongly polarized dimer
surrounded by decaying oscillation of magnetization. Itresembles the Friedel oscillation near impurities inmetals. The distribution of hyperﬁne ﬁeld at Cu site
derived from the calculated magnetization proﬁlecaptures the essential feature of the experimental results,indicating that such a magnetic superstructure is indeed
realized in the 18 plateau phase.

787
563241Fig. 2. Magnetization proﬁle in the 18 plateau state. Closed(open) cirle shows the positive (negative) /Sz S: The circle size
represents the magnitude of /Sz S:This work was supported by the Grant-in Aid for
Scientiﬁc Research on Priority Area (B) on ‘‘FieldInduced New Quantum Phenomena in Magnetic Systems’’ from the ministry of Education, Culture, Sports,
Science and Technology, Japan and the Swiss National
Fund.

References[1] B.S. Shastry, B. Sutherland, Physica B 108 (1981) 1069.
[2] K. Kodama, et al., J. Phys. Condens. Matter 14 (2002)
L319.
[3] H. Kageyama, et al., Phys. Rev. Lett. 82 (1999) 3168.
[4] H. Kageyama, et al., Phys. Rev. Lett. 84 (2000) 5876.
[5] S. Miyahara, K. Ueda, Phys. Rev. Lett. 82 (1999) 3701.
[6] K. Onizuka, et al., J. Phys. Soc. Japan. 69 (2000) 1016.
[7] S. Miyahara, K. Ueda, Phys. Rev. B 61 (2000) 3417.
[8] K. Kodama, et al., Science 298 (2002) 395.
[9] S. Miyahara, F. Becca, F. Mila, cond-mat/0302332.