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2009 MAGNETIC SYSTEMSNuclear magnetic resonance determination of spin-superlattice structureof magnetization plateaus in SrCu 2 (BO 3 ) 2Quantum spin systems are nowadays in the focus of considerableexperimental and theoretical efforts, in particularfor the magnetic field induced exotic quantum states. Ofspecial interest are interacting systems of Heisenberg, antiferromagnetic,S=1/2 spin dimers in a magnetic field whichcloses the gap between the singlet and one of three Zeemansplittriplet levels of each dimer. At low temperature, whenonly these two states per dimer are relevant, the systemcan be described by the corresponding S=1/2 pseudospins,or the equivalent hard-core bosons. Interacting dimers arethen equivalent to a system of interacting bosons where boson(triplet) density can be tuned by the magnetic field. Thissystem generally undergoes a Bose-Einstein condensation(BEC) and therefore provides an exceptional access for experimentalstudies of this phenomenon. In the hard-coreboson representation the balance of the kinetic and the interaction(repulsion) energy is determined by the degree offrustration of interdimer spin coupling, where frustrationstrongly reduces kinetic energy. In this latter case, insteadof being itinerant and undergo BEC, bosons can be localizeddue to mutual repulsion into a charge ordered state,that is a Wigner crystal. Since this state is gapped, the bosondensity will be magnetic field independent and the systemwill present a plateau of magnetization.Perfect frustration occurs in the geometry of orthogonaldimers in 2D, given by the Shastry-Sutherland Hamiltonian,and the SrCu 2 (BO 3 ) 2 compound is its first recognizedrealization. The discovery of the magnetization plateaus at1/8, 1/4 and 1/3 of the saturation magnetization in this compoundwas followed by extensive experimental and theoreticalinvestigation. In particular, NMR study performed atLNCMI proved that the 1/8 plateau, as predicted, indeedcorresponds to a commensurate spin superstructure. Subsequentstudies showed that a superstructure persists at highermagnetic field [Takigawa et al., Phys. Rev. Lett. 101,037202 (2008)], and that there are other, yet undiscoveredplateaus. One of these, adjacent to the 1/8 plateau on thehigh field side, was indeed confirmed by the torque measurements[Levy et al., EPL 81, 67004 (2008)]. At the sametime appeared several contradictory predictions for the existenceof many other magnetization plateaus in this system,calling for experimental verification. However, theoreticaldescription of SrCu 2 (BO 3 ) 2 is very difficult, because the interdimerinteraction is too strong to be properly describedby a perturbation theory, while exact numerical methods arelimited to only very small 2D systems.We have therefore continued our NMR investigation to observeevolution of the spin superstructure through magneticfield dependence of 11 B NMR spectra in the 27-34 T range,at 0.43 K. From the observed spectra we clearly identifyplateau phases where the NMR spectra, and thus the spinsuperstructure, is magnetic field independent. In additionto the long known 1/8 and 1/4 plateau and the recently discoveredplateau adjacent to the 1/8 plateau, a new plateauwas discovered half way up towards the 1/4 plateau (seefigure 111). Between these plateaus NMR spectra evolvecontinuously with magnetic field, and no other plateau wasdetected. The same sequence of plateaus was confirmedby the new, “differential” torque measurements, performedat ∼0.1 K. This method determines the magnetization withconsiderably enhanced precision, allowing us to find thatthe magnetization of the first three plateaus scales as 1/8: 2/15 : 1/6, which confirms some of the theoreticallyproposed values and excludes others. Detailed analysis ofthe 11 B NMR spectra allows us to make complete determinationof the spin-polarization superstructures. We findthat previously identified “extended triplets” are always arrangedin stripe structures, specific to each plateau, oftendifferent from what is proposed theoretically [Takigawa etal., unpublished].Figure 111: The distribution of the internal field at the 11 B sites,obtained by deconvoluting the NMR spectra from the quadrupolesplitting. Presented spectra are representative of 4 magnetizationplateaus, attributed to fractions 1/8, 2/15, 1/6 and 1/4 of saturationmagnetization.M. Horvatić, C. Berthier, S. Krämer, I. SheikinM. Takigawa, T. Waki, Y. Ueda (ISSP, University of Tokyo, Japan), H. Kageyama (Kyoto University, Japan), F. Mila(EPFL, Lausanne, Switzerland)83