Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet

The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional 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 Shastry-Sutherland material, SrCu2(BO3)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.Comment: 16 pages, 4 figures. Accepted for publication in PNA

High Resolution Study of Spin Excitations in the Shastry-Sutherland Singlet Ground State of SrCu2(BO3)2

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.Comment: 4 pages, 4 figures. Submitted to PR

Crystallization of spin superlattices with pressure and field in the layered magnet SrCu_2(BO_3)_2

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 SrCu_2(BO_3)_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

Incommensurate two-dimensional checkerboard charge density wave in the low dimensional superconductor Ta4Pd3Te16

We report the observation of a two-dimensional (2D) checkerboard charge density wave (CDW) in the low-dimensional superconductor Ta4Pd3Te16. By determining its CDW properties across the temperature-pressure (T-P) phase diagram and comparing with prototypical CDW materials, we conclude that Ta4Pd3Te16 features: a) an incommensurate CDW with a mixed character of dimensions (Q1D considering its needle-like shape along the b-axis, Q2D as the CDW has checkerboard wavevectors, and 3D because of CDW projections along all three axes); and b) one of the weakest CDWs compared to its superconductivity (SC), i.e. enhanced SC with respect to CDW, suggesting an interesting interplay of the two orders.Comment: Z.S. and S.J.K. contributed equally to this work / Accepted for publication in Physical Review Research Rapid Communication

Co-existing Singlet and Ordered S=1/2 Moments in the Ground State of the Triclinic Quantum Magnet CuMoO4

CuMoO4 is a triclinic quantum magnet based on S = 1/2 moments at the Cu2+ site. It has recently attracted interest due to the remarkable changes in its chromic and volumetric properties at high temperatures, and in its magnetic properties at low temperatures. This material exhibits a first order structural phase transition at T_C ~ 190 K as well as a magnetic phase transition at T_N ~ 1.75 K. We report low temperature heat capacity measurements as well as extensive elastic and inelastic neutron scattering measurements on powder samples taken above and below T_N. We observe neutron diffraction consistent with a simple (1/2, 0, 0) antiferromagnetic structure indicating a doubling of the a-axis periodicity below T_N. In addition, inelastic neutron scattering above a spin gap of ~ 2.3 meV is consistent with triplet excitations out of paired S = 1/2 moments which form singlet dimers. Low lying spin wave excitations are also observed and these originate from ordered S = 1/2 moments below T_N. Taken together these measurements show the ground state of CuMoO4 to display both non-magnetic singlets, and ferromagnetically-coupled spins coexisting within an antiferromagnetic structure below T_N ~ 1.75 K.Comment: 7 pages, 7 figure

Emergence of long-range order in sheets of magnetic dimers

Quantum spins placed on the corners of a square lattice can dimerize and form singlets, which then can be transformed into a magnetic state as the interactions between dimers increase beyond threshold. This is a strictly 2D transition in theory, but real-world materials often need the third dimension to stabilize long-range order. We use high pressures to convert sheets of Cu^2+ spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu_2(BO_3)_2. Single-crystal neutron diffraction measurements at pressures above 5 GPa provide a direct signature of the antiferromagnetic ordered state, whereas high-resolution neutron powder and X-ray diffraction at commensurate pressures reveal a tilting of the Cu spins out of the plane with a critical exponent characteristic of 3D transitions. The addition of anisotropic, interplane, spin–orbit terms in the venerable Shastry–Sutherland Hamiltonian accounts for the influence of the third dimension

Neutron and X-ray Scattering Studies of the Lightly-Doped Spin-Peierls System Cu(1-x)Cd(x)GeO3

Single crystals of the lightly-doped spin-Peierls system Cu(1-x)Cd(x)GeO3 have been studied using bulk susceptibility, x-ray diffraction, and inelastic neutron scattering techniques. We investigate the triplet gap in the magnetic excitation spectrum of this quasi-one dimensional quantum antiferromagnet, and its relation to the spin-Peierls dimerisation order parameter. We employ two different theoretical forms to model the inelastic neutron scattering cross section and chi''(Q,omega), and show the sensitivity of the gap energy to the choice of chi''(Q,omega). We find that a finite gap exists at the spin-Peierls phase transition.Comment: 15 Pages, 7 Figures, Submitted to J. Phys. :Condensed Matte

Order parameter fluctuations at a buried quantum critical point

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-NbSe2 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 longstanding expectations of enhanced quantum fluctuations in low dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.Comment: to be published in PNA

Reply to Zayed: Interplay of magnetism and structure in the Shastry–Sutherland model

The connection between electronic and structural degrees of freedom—whether successive, coincident, or causal—suffuses the study of phase transitions. The Shastry–Sutherland model of a planar network of coupled spin dimers (1) and its physical realization in SrCu_2(BO_3)_2 (SCBO) provide a fundamental quantum mechanical test of this connection at the onset of antiferromagnetic order. We summarize in Fig. 1 the current understanding of SCBO’s phase diagram for T < 200 K and an intermediate pressure range of 3.5–6 GPa (2–4). At pressures below ∼4–5 GPa, SCBO has a tetragonal structure that hosts several low-temperature magnetic phases. Above this pressure, monoclinic distortions reduce the symmetry of the lattice. In ref. 2, we performed full structural refinements of X-ray and neutron scattering measurements to identify a change in space group at 5.5 GPa as a function of temperature (red circles in Fig. 1). This structural change coincides with the onset of antiferromagnetic ordering as a function of temperature, and we argue that this is not a coincidence but instead represents a cooperative effect between distortions of the lattice, the dimers tilting out of the plane, and the emergence of long-range magnetic order. In his comment on our work, Zayed (5) proposes an alternative scenario, in which the antiferromagnetic ordering onsets at lower pressure, within the tetragonal phase, and is then stabilized by the structural distortion associated with the monoclinic phase. He further speculates that this earlier onset may be associated with the dome in the phase boundary reported in ref. 4 (dark red region, Fig. 1)