A Novel Ordered Phase in the Frustrated 2D Spin System
SrCu₂(BO₃)₂ under High Pressure

A variety exotic quantum phenomena has been discovered in SrCu₂(BO₃)₂, a quasi two-dimensional frustrated spin system with a dimer-singlet ground state (Fig. 1ab), most notably, the sequential magnetization plateaux at 1/8, 1/4, and 1/3 of the saturation. These plateaux accompany superlattice of triplets that breaks the translational symmetry of the crystal, as observed by NMR experiments [1].




Fig. 1. The magnetic layer of SrCu₂(BO₃)₂ viewed along (a) the c-direction and (b) the [110]-direction. The Cu²⁺ ions with spin 1/2 form orthogonal dimer sublattices as shown by the solid and the dashed blue lines. (c) Proposed VBS order of alternating magnetic (shaded) and non-magnetic (non-shaded) dimers.


Compared with the behavior in high magnetic fields, little has been known about the properties under high pressure, although pressure would be a powerful tool to investigate quantum phase transitions expected for spin systems with such a geometry. We have performed nuclear magnetic resonance (NMR) experiments on ¹¹B nuclei in a single crystal of SrCu₂(BO₃)₂ under pressure up to 2.4 GPa, which revealed a magnetic phase transition resulting in a novel type of valence-bond-solid (VBS) order. A piston-cylinder type pressure cell was mounted on a double-axis goniometer, which enabled precise alignment of the magnetic field along arbitrary crystalline directions.
The NMR spectra at 2.4 GPa in the field of 7 T along the c-axis are shown in Fig. 2 at various temperatures (T). A sharp single line is observed at high T consistent with the crystal symmetry. The line, however, splits gradually below 30K. The angle dependence of the spectrum indicates that the splitting is due to loss of C₄ symmetry of the crystal, which makes the two orthogonal dimer sublattices inequivalent (solid and dashed blue lines in Fig. 1a). With decreasing temperature, each line further splits into one sharp and one broad lines below 3.6K. The magnetic hyperfine shift (K) of the sharp line shows an activated T-dependence indicating an excitation gap, while the broad line shows gapless behavior with nearly constant K (Fig. 3a). The clear singularity in both K(T) (Fig. 3a) and the susceptibility indicates a well defined magnetic phase transition.




Fig. 2. NMR spectra for H // c at various temperatures. A gradual line splitting below 30 K is followed by another sudden splitting of each line into one sharp and one broad lines below 3.6 K.




Temperature dependence of the magnetic hyperfine shift. The black open squares show the data for unsplit lines at high T, while the blue and red open squares represent the shifts for split lines in the intermediate T-range. The filled symbols indicate the shift in the ordered phase. For comparison, the data at ambient pressure are shown by the green dots. (b) Field-temperature phase diagram obtained from the NMR data.


The detailed investigation of the angle dependence of the spectra allowed us to conclude that each dimer sublattice develops a superstructure with alternation of magnetic and non-magnetic dimers, resulting in a doubled unit cell(Fig. 1c). The magnetic dimers appear to restore a finite gap at low magnetic fields below 2 T. Hence the ground state at zero field would be a novel type of valence-bond-solid state with staggered dimer correlation, which breaks the translational symmetry but does not show any spontaneous magnetization. The transition temperature decreases with magnetic field (Fig. 3b), suggesting a quantum phase transition near 18 T. Further experiments to clarify the nature of this totally unexpected ordered phase are in progress.


References
[1] K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama, Y. Ueda, S. Miyahara, F. Becca, and F. Mila, Science 298 (2002) 395.
[2] T. Waki, K. Arai, M. Takigawa, Y. Saiga, Y. Uwatoko, H. Kageyama, Y. Ueda, J. Phys. Soc. Jpn. 76 (2007) 073710 (Selected for JPSJ Editor's Choice).