Pressure-Induced Quantum Critical and Multicritical Points in a Frustrated Spin Liquid

Abstract

The quantum spin-liquid compound (C4H12N2)Cu2Cl6 is studied by µSR under hydrostatic pressures up to 23.6 kbar. At low temperatures, pressure-induced incommensurate magnetic order is detected beyond a quantum critical point at Pc ∼ 4.3 kbar. An additional phase transition to a different ordered phase is observed at P1 ∼ 13.4 kbar. The data indicate that the high-pressure phase may be a commensurate one. The established (P −T ) phase diagram reveals the corresponding pressure-induced multicritical point at P1, T1 = 2.0 K.Traditionally, magnetic insulators have been the most important prototype systems for testing concepts and theories of phase transitions, universality and scaling [1,2]. They owe this to their well-defined short-range interactions, a broad range of interaction topologies and dimensionalities, and their amenability to numerical modeling. With a more recent interest in quantum phase transitions [3,4], magnetic insulators have become the prototypes of choice to study quantum critical points (QCPs). Realizations of such important QCPs as BoseEinstein condensation (BEC) [5], deconfinement in one dimension [6,7], and the Ising model in a transverse field [8] have been found in quantum magnets in applied magnetic fields. Magnetic BEC, for example, occurs in gapped quantum antiferromagnets (AFMs) with a spin singlet ground state, when an external field drives the energy gap to zero by virtue of Zeeman effect. The result in spontaneous long-range magnetic order in the perpendicular direction, and thus a breaking of SO(2) symmetry [5]. At the QCP, the soft mode has a parabolic dispersion, so that the dynamical critical exponent is z = 2. By now, this transition has been extensively studied experimentally and theoretically [5].A qualitatively different type of soft mode transition in gapped quantum AFMs may occur if the spin gap is driven to zero by varying the ratio of exchange constants. The resulting spontaneous long-range magnetic order breaks SO(3) symmetry, and the spectrum is expected to be linear at the QCP (z = 1). In practice, the only way to continuously tweak the exchange interactions is by applying external pressure. Closing the spin gap with pressure in quantum Heisenberg AFMs has been attempted in experiments [9][10][11]. However, only one good realization of pressure-induced ordering in such systems has been found to date, namely, that in TlCuCl 3 [12][13][14]. Further studies of this QCP brought fascinating new insights [15], particularly the observation of a longitudinal mode, which is a magnetic analog of the celebrated Higgs boson [4]. In the present work, we report the observation of pressure-induced ordering in the S = 1/2 frustrated gapped quantum AFM (C 4 H 12 N 2 )Cu 2 Cl 6 (abbreviated PHCC), and use muon spin rotation (µSR) experiments to map out the P − T phase diagram. We show that the pressure-driven transition leads to an incommensurate magnetic order. At still higher pressures, we detect an additional transition and multicritical point. The indication is that these are an inc...

Spin dynamics in pressure-induced magnetically ordered phases in(C4H12N2)Cu2Cl<

“…12 Our wave vector resolution is approximately 0.07, 0.26 and 0.05 reciprocal lattice units FWHM along h, k, and l, respectively. This sets an upper bound on the magnitude of the incommensurate propagation vector in the system.…”

“…This is consistent with the observation of long-range magnetic order above a QCP at p c ≈ 4.3 kbar using µ + SR. 12 Our analysis uses an empirical dispersion relation and the isotropic single-mode approximation allowing us to determine that the quantum phase transition itself is driven primarily by the weakening of one particular exchange pathway. Unlike at ambient pressure, at high pressure PHCC is by no means a two-dimensional system, with a substantial magnon dispersion along the 'interlayer' (b * ) direction.…”

“…11 In contradiction with this result, more recent muon-spin relaxation (µ + SR) experiments have discovered that the destruction of the spin-singlet state and the onset of magnetic long-range order occur at a much lower p c ≈ 4.3 kbar. 12 A magnetically ordered phase of a Heisenberg spin system must have gapless spin waves, yet Ref. 11 reported a spectral gap persisting well beyond the transition pressure observed in muon experiments.…”

Effect of disorder on a pressure-inducedz=1magnetic quantum phase transition

“…Subsequent muon-spin relaxation (μ + SR) experiments determined the presence of two distinct high-pressure magnetically ordered phases above a critical pressure p c ∼ 4.3 kbar [7]. The presence of a linearly dispersing gapless Goldstone mode at a pressure of 9(1) kbar was then confirmed by inelastic * manniga@ethz.ch † jmoeller@phys.ethz.ch ‡ http://www.neutron.ethz.ch/ neutron scattering experiments [8], and the application of pressure was shown to induce large changes in a single exchange pathway in the material leading to the closing of the gap at the QCP.…”

“…In these transitions, the spectrum is expected to be linear at the quantum-critical point, and hence z = 1. To date, the only known experimental realizations of such a pressure-induced QCP are TlCuCl 3 [3][4][5] and (C 4 H 12 N 2 )Cu 2 Cl 6 (PHCC) [6][7][8].…”