8 7 6 5 www. sciencemag. org SCIENCE VOL 298 25 OCTOBER 2002 761 citations (7), and magnetization plateaus are to be expected as a result. The first of these appears at a value of 1/8 of the saturation magnetization. The required magnetic field of 27 T is quite large but within range of the NMR facility of the Grenoble High Magnetic Field Laboratory. The unique combination of high fields and low temperatures at this facility enabled Kodama et al.(5) to observe the magnetic superlattice as a dense series of lines in the Cu NMR spectrum at 35 mK. Analysis of the magnetization in the large supercell implied by the high order of the commensurability (1/8) required a numerical solution of the Shastry-Sutherland model. The spectra could be well fit by the magnetization pattern shown in the figure. One in eight of the dimers is strongly polarized parallel to the external field. But the magnetization pattern is much richer than a simple polarization of 1/8 of the dimers. This more complex pattern can be attributed to the high magnetic polarizability of the singlet ground state of the dimer lattice. As a result, the dilute superlattice of spin triplet dimers is accompanied by a background magnetic polarization. The transition into the superlattice state as the field is increased appears to be first order, which favors an interpretation of it as a crystallization of a dilute bosonic fluid. Turning our attention back to the quantum ground state, which appears when the kinetic terms dominate, new results on another set of copper salts, KCuCl3 and TlCuCl3, have recently been obtained. Initially, their crystal structure seemed to imply that the dimers formed the rungs of ladders with only weak interladder interactions. However, a detailed mapping of the energy dispersion of the triplet excitations showed a fully three-dimensional network of exchange interactions (8). These salts do not show magnetization plateaus but instead show a continuous rise starting at a threshold magnetization value and ending at the saturation magnetization. The Bose-Einstein condensed state in the intermediate range is characterized by a coherent superposition of the singlet and Sz=+ 1 triplet component on each dimer (9). This generates a staggered magnetization transverse to the external field. The phase in the complex superposition determines the orientation of staggered moments in the xy-plane. Elastic neutron-scattering measurements observe a staggered magnetization with long-range ordering with a finite ordering temperature (10). Recently, Ruegg et al.(11) examined the dynamics of the condensate by inelastic neutron scattering and observed a mode with linear dispersion above the threshold magnetization. As shown by Matsumoto et al.(12), this mode can be nicely interpreted as the well-known collective oscillation (or Goldstone mode) of the Bose-Einstein condensate. As these recent experiments illustrate, quantum magnetism in a magnetic field offers exemplary systems for exploring the competition between the classical and quantum ground states for interacting bosons—a subject of current research also for the dilute atomic bosonic clouds.