High resolution, inelastic neutron scattering measurements on SrCu2(BO3)2 reveal the dispersion of the three single triplet excitations continuously across the (H,0) direction within its tetragonal basal plane. These measurements also show distinct Q dependencies for the single and multiple triplet excitations, and that these excitations are largely dispersionless perpendicular to this plane. The temperature dependence of the intensities of these excitations is well described as the complement of the dc-susceptibility of SrCu2(BO3)2 .PACS numbers: 75.10. Jm, 75.25.+z, 75.40.Gb Quantum magnets which display collective singlet ground states have been of much recent interest 1 . Several of these, such as CuGeO 3 2 , MEM-(TCNQ) 2 3 , and NaV 2 O 5 4 result from spin-Peierls phenomena in low dimensions where the lattice combines with s=1/2 spin degrees of freedom to break translational symmetry below some characteristic phase transition temperature, and a non-magnetic ground state with a characteristic energy gap is observed. A related state is observed in the s=1 antiferromagnetic chain compounds, such as CsNiCl 3 5 and NENP 6 , where a non-magnetic ground state with an energy gap, the Haldane gap, forms in the absence of translational symmetry breaking.SrCu 2 (BO 3 ) 2 has been proposed 7,8 as a realization of the Shastry-Sutherland model 9 of interacting dimers in two dimensions. This material crystallizes 10 into the tetragonal space group I42m with lattice parameters a=8.995Å, c=6.649Å. Magnetically, it can be thought of in terms of well isolated basal planes populated by antiferromagnetically coupled s=1/2 moments on the Cu 2+ sites. These are arranged in dimers at right angles to each other and forming a square lattice. The microscopic Hamiltonian appropriate to this system is based on:It is known that both interactions, J and J', are antiferromagnetic and similar in strength, such that the system is not far removed from the critical value of x=J'/J known to be appropriate to the quantum phase transition which separates a 4 sublattice Neel state from a collective singlet ground state.The estimated values of J and J' have evolved over time as both theory and experiment have improved. Early estimates of J and x were J=8.6 meV and x=0.687 , very close to the critical value x c =0.6911 , where the single triplet excitation goes soft. More recently Miyahara and Ueda 12 found J=7.3 meV and x=0.635 from fits to the magnetic susceptibility. Somewhat smaller values were obtained by Knetter et al 13 who compared theoretical and experimental ratios of the energy of the lowest S=1 two triplet bound state to the single triplet gap, to obtain J=6.16 meV and x=0.603. Note that within this theory 13 , the collective singlet ground state becomes unstable when the lowest energy two triplet bound state goes soft.Earlier, relatively low resolution inelastic neutron scattering measurements 14,15,16 have directly identified three bands of excitations corresponding to single (n=1) triplet excitations, as well as to two (n=2), and...

Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe 2 at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.incommensurate electronic state | transition metal dichalcogenides | diffraction line shapes | diamond anvil cell A continuous change of phase often involves critical fluctuations that destabilize one phase in favor of another. These fluctuations characterize the nature of the phase transition, but can be difficult to measure directly. This difficulty is especially acute in broad classes of materials with quantum phase transitions (1, 2), from colossal magnetoresistance manganites (3) to heavy fermion and cuprate superconductors (4, 5) to archetypal, metallic ferromagnets (6, 7), where strong interactions can cut off the critical behavior via a structural instability, or competing ground states can shroud the quantum critical point.Charge and spin density wave (CDW/SDW) systems have been shown to be good candidates for experimental studies of quantum critical behavior, where fluctuations disrupt electron pairing and restore the metallic Fermi surface (8, 9). In these systems the interaction strengths are weaker than in strongly correlated materials, reducing the likelihood of strong first-order transitions and allowing experimental access to the quantum critical point. Recent low-temperature studies of the SDW transition in bulk, elemental Cr under pressure demonstrated a continuous quantum phase transition in an antiferromagnetic metal (10, 11), but the quantum fluctuation regime deduced via transport measurements was very narrow. Stronger fluctuations over a broader range are expected in systems with lower electronic dimensionality. Moreover, quantum criticality in two-dimensional layered systems with predilections for density wave distortions has received sustained interest due to the observation of density wave pairing in the high-T C superconductors (12-14). Here we present a low-temperature and high-pressure synchrotron X-ray diffraction study of the two-dimensional CDW system 2H-NbSe 2 , where scattering from the incommensurate charge order is possible even deep within the coexisting superconducting ground state. Our results demonstrate a wide regime of spatial fluctuations of the CDW order par...

An exact mapping between quantum spins and boson gases provides fresh approaches to the creation of quantum condensates and crystals. Here we report on magnetization measurements on the dimerized quantum magnet SrCu2(BO3)2 at cryogenic temperatures and through a quantum-phase transition that demonstrate the emergence of fractionally filled bosonic crystals in mesoscopic patterns, specified by a sequence of magnetization plateaus. We apply tens of Teslas of magnetic field to tune the density of bosons and gigapascals of hydrostatic pressure to regulate the underlying interactions. Simulations help parse the balance between energy and geometry in the emergent spin superlattices. The magnetic crystallites are the end result of a progression from a direct product of singlet states in each short dimer at zero field to preferred filling fractions of spin-triplet bosons in each dimer at large magnetic field, enriching the known possibilities for collective states in both quantum spin and atomic systems.

The Shasty-Sutherland model, which consists of a set of spin 1∕2 dimers on a 2D square lattice, is simple and soluble but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model ShastrySutherland material, SrCu 2 ðBO 3 Þ 2 , in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution X-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure-dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure. O ne of the first real-world examples encountered in elementary quantum mechanics is the hydrogen atom, where two correlated spin 1∕2 particles, the electron and the proton, combine in multiple configurations to define a set of discrete energy levels. The ground state singlet superposes up and down configurations of the spins to yield a state with total spin zero; the excited state triplet provides three ways to produce a total spin of one. The fundamental quantum mechanics of spin singlets physically placed on ladders or constrained to sheets is a natural extension, with a rich set of possibilities for collective, interacting states from spin liquids to magnets to exotic superconductors (1-4). A particularly important topology involves spin 1∕2 orthogonal dimers on a square lattice, the so-called Shastry-Sutherland model (5), because it is exactly soluble. Here we exploit a remarkably strong coupling of the spin degrees of freedom to the lattice in a model Shastry-Sutherland system to probe the evolution of the collective spin configurations with temperature and pressure using X-rays and diamond anvil cell technology. Thermal excitations from singlet to triplet define a gap, which disappears as pressure P tunes the ratio between inter-and intradimer coupling energies. This continuous quantum phase transition occurs at P ¼ 2 GPa, followed by a first-order transition at P approximately 4.5 GPa, which we associate with the full-fledged onset of long-range antiferromagnetic order.Insulating SrCu 2 ðBO 3 Þ 2 (SCBO) successfully captures the physics of the Shastry-Sutherland model (6), with corner-sharing Cu 2þ S ¼ 1∕2 dimers lying on a square lattice and only weak interactions between adjacent planes. Under ambient conditions, the system has tetragonal symmetry with a ¼ 8.995 Å and c ¼ 6.649 Å. ESR (7) and neutron (8) data establish that the spin interactions in SCBO are well describ...