Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some such compounds (KCuCl3 and TlCuCl3), two Cu2+ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose-Einstein condensation occurs. Here we report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.
A quantum critical point (QCP) is a singularity in the phase diagram arising due to quantum mechanical fluctuations. The exotic properties of some of the most enigmatic physical systems, including unconventional metals and superconductors, quantum magnets, and ultracold atomic condensates, have been related to the importance of the critical quantum and thermal fluctuations near such a point. However, direct and continuous control of these fluctuations has been difficult to realize, and complete thermodynamic and spectroscopic information is required to disentangle the effects of quantum and classical physics around a QCP. Here we achieve this control in a high-pressure, high-resolution neutron scattering experiment on the quantum dimer material TlCuCl 3 . By measuring the magnetic excitation spectrum across the entire quantum critical phase diagram, we illustrate the similarities between quantum and thermal melting of magnetic order. We prove the critical nature of the unconventional longitudinal ("Higgs") mode of the ordered phase by damping it thermally. We demonstrate the development of two types of criticality, quantum and classical, and use their static and dynamic scaling properties to conclude that quantum and thermal fluctuations can behave largely independently near a QCP.In "classical" isotropic antiferromagnets, the excitations of the ordered phase are gapless spin waves emerging on the spontaneous breaking of a continuous symmetry [1]. The classical phase transition, occurring at the critical temperature T N , is driven by thermal fluctuations. In quantum antiferromagnets, quantum fluctuations suppress long-range order, and can destroy it completely even at zero temperature [2]. The ordered and disordered phases are separated by a quantum critical point (QCP), where quantum fluctuations restore the broken symmetry and all excitations become gapped, giving them characteristics fundamentally different from the Goldstone modes on the other side of the QCP (Fig. 1). At finite temperatures around a QCP, the combined effects of quantum and thermal fluctuations bring about a regime where the characteristic energy scale of spin excitations is the temperature itself, and this quantum critical (QC) regime has many special properties [3].Physical systems do not often allow the free tuning of a quantum fluctuation parameter through a QCP. The QC regime has been studied in some detail in heavy-fermion [14], and the green points depict the temperature and pressure values studied. Full details of this panel are presented in Fig. 4(c). The centre (E, T ) panel shows neutron intensity data collected from T = 1.8 K to 12.7 K at p = 1.75 kbar, where TN = 5.8 K. The rightmost (E, T ) panel shows the corresponding data at p = 3.6 kbar, where TN = 9.2 K. The data in both (E, T ) panels display a clear softening of the magnetic excitations at TN (p). The bottom (p, E) panel indicates the softening of the excitations, measured at T = 1.8 K, across the QPT [19]. T1, T2 and L denote the three gapped triplet excitations of th...
We follow the evolution of the elementary excitations of the quantum antiferromagnet TlCuCl3 through the pressure-induced quantum critical point, which separates a dimer-based quantum disordered phase from a phase of long-ranged magnetic order. We demonstrate by neutron spectroscopy the continuous emergence in the weakly ordered state of a low-lying but massive excitation corresponding to longitudinal fluctuations of the magnetic moment. This mode is not present in a classical description of ordered magnets, but is a direct consequence of the quantum critical point.Although quantum fluctuations of both spin and charge degrees of freedom are the key to the essential physics of many challenging problems in condensed matter systems, the microscopic control of zero-point fluctuations has to date remained largely a theoretical abstraction. However, full control over the interaction parameters can now be effected in cold atomic condensates through the standing-wave amplitudes of the optical lattice. Similarly, in quantum magnets the exchange interactions can be controlled by the application of pressure, altering the effect of spin fluctuations. We follow this approach to investigate the physics of a quantum system whose fluctuations are "tuned" in a continuous way.The most dramatic manifestation of such control is the driving of a quantum phase transition [QPT, Fig. 1(a)] between two different ground states [1]. Structurally dimerized S = 1/2 spin systems offer a particularly clean realization both of the magnetic field-induced QPT, which has been studied extensively in a number of materials [2], and of the qualitatively different magnetic QPT driven by hydrostatic pressure [3]. The Hamiltonian
The study of interacting spin systems is of fundamental importance for modern condensed matter physics. On frustrated lattices, magnetic exchange interactions cannot be simultaneously satisfied, and often give rise to competing exotic ground states 1 . The frustrated 2D ShastrySutherland lattice 2 realized by SrCu 2 (BO 3 ) 2 3 is an important test to our understanding of quantum magnetism. It was constructed to have an exactly solvable 2-spin dimer singlet ground state within a certain range of exchange parameters and frustration. While the exact dimer state and the antiferromagnetic order at both ends of the phase diagram are well known, the ground state and spin correlations in the intermediate frustration range have been widely debated 2-12 . We report here the first experimental identification of the conjectured plaquette singlet intermediate phase in SrCu 2 (BO 3 ) 2 . It is observed by inelastic neutron scattering after pressure tuning at 21.5 kbar. This gapped plaquette singlet state with strong 4-spin correlations leads to a transition to an ordered Néel state above 40 kbar, which can realize a deconfined quantum critical point.In the field of quantum magnetism, geometrically frustrated lattices generally imply major difficulties in analytical and numerical studies. For very few particular topologies however, it has been shown that the ground state, at least, can be calculated exactly as for the Majumdar-Gosh model 13 that solves the J 1 -J 2 zigzag chain when J 1 = 2J 2 . In 2D, the Shastry-Sutherland model 2 consisting of an orthogonal dimer network of spin S=1/2 was developed in order to be exactly solvable. For an inter-dimer J to intra-dimer J exchange ratio α ≡ J /J ≤ 0.5 the ground state is a product of singlets on the strong bond J. Numerical calculations have further shown that this remains valid up to α ≤∼ 0.7 and for small values of 3D couplings J between dimer layers. At the other end, for ∼ 0.9 ≤ α ≤ ∞ the system approaches the well known 2D square lattice, which is antiferromagnetically (AFM) ordered, albeit with significant quantum fluctuations that are believed to include resonating singlet correlations resulting in fractional excitations 14 . The phase diagram of the Shastry-Sutherland model, both with and without applied magnetic field, has been intensively studied by numerous theoretical and numerical approaches 3 . In the presence of magnetic field, magnetization plateaus at fractional values of the saturation magnetization corresponding to Mott insulator phases of dimer states, as well as possible superfluid and supersolid phases have been extensively studied 6,15,16 . At zero field, the main unsolved issue is the existence and nature arXiv:1603.02039v1 [cond-mat.str-el]
The magnetic structure and electronic ground state of the layered perovskite Ba(2)IrO(4) have been investigated using x-ray resonant magnetic scattering. Our results are compared with those for Sr(2)IrO(4), for which we provide supplementary data on its magnetic structure. We find that the dominant, long-range antiferromagnetic order is remarkably similar in the two compounds and that the electronic ground state in Ba(2)IrO(4), deduced from an investigation of the x-ray resonant magnetic scattering L(3)/L(2) intensity ratio, is consistent with a J(eff)=1/2 description. The robustness of these two key electronic properties to the considerable structural differences between the Ba and Sr analogues is discussed in terms of the enhanced role of the spin-orbit interaction in 5d transition metal oxides.
We measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a spinon continuum at intermediate fields characteristic of the Luttinger-liquid phase. By tuning the magnetic field, we drive the fractionalization of magnons into spinons and, in this deconfined regime, observe both commensurate and incommensurate continua.
*When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided 1 . Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids 2 . However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum [3][4][5] . Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu 2 PO 6 , we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.A fundamental concept in condensed matter physics is the idea that strongly interacting atomic systems can be treated as a collection of weakly interacting and long-lived quasiparticles. Within a quasiparticle picture, complex collective excited states in a many-body system are described in terms of effective elementary excitations. The quanta of these excitations carry a definite momentum and energy, and are termed quasiparticles. Magnetic insulators containing localized S = 1/2 magnetic moments and having valence-bond solid ground states are ideal systems in which to study bosonic quasiparticles in an interacting quantum many-body system 6 . The elementary magnetic excitations in these materials are triply degenerate S = 1 quasiparticles called triplons, and their momentum-and energy-resolved dynamics can be probed directly though inelastic neutron scattering (INS) measurements.In particular, when the system's Hamiltonian has an interaction term coupling single-particle and multi-particle states, the single quasiparticles may decay into the continuum of multi-particle states 3,4 . In such a system, the Hamiltonian for the single quasiparticles is non-Hermitian and the energy eigenvalues are in general complex. The single-particle decay typically occurs in two ways. Often the single-particle mode stays as a resonance inside the continuum, but the lifetime becomes short and the mode is highly damped 3 . Sometimes the single quasiparticle simply ceases to exist, and the dispersion abruptly terminates when it crosses the continuum boundary 5 . However, there is a third possibility, in which the single-quasiparticle dispersion is significantly renormalized to avoid the multi-particle continuum. This is analogous to the wellknown avoided level crossing behaviour of coupled modes, but in the complex plane of energy eigenvalues 7 . Despite broad interest in strongly interacting quantum systems, experimentally realizing an ideal condition to study the interaction between a quasiparticle and a multi-particle continuum turns out to be extremely difficult. One realization occurs in semiconducting quantum do...
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