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Physical review. B./Physical review. B

Spin excitations and quantum criticality in the quasi-one-dimensional Ising-like ferromagnet CoCl2·2D2O in a transverse field

Jacob Larsen, T. K. Schäffer, Ursula Hansen, S. L. Holm, S. R. Ahl, Rasmus Toft-Petersen, J. Taylor, Georg Ehlers, Jens Jensen, Henrik Moodysson Rønnow, Kim Lefmann, Niels Bech Christensen

Published Nov 20, 2017• 10 citations
Publisher

Abstract

We present experimental evidence for a quantum phase transition in the easy-axis $S=3/2$ anisotropic quasi-one-dimensional ferromagnet ${\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}$ in a transverse field. Elastic neutron scattering shows that the magnetic order parameter vanishes at a transverse critical field ${\ensuremath{\mu}}_{0}{H}_{c}=16.05$(4) T, while inelastic neutron scattering shows that the gap in the magnetic excitation spectrum vanishes at the same field value, and reopens for $H>{H}_{c}$. The field dependence of the order parameter and the gap are well described by critical exponents $\ensuremath{\beta}=0.45\ifmmode\pm\else\textpm\fi{}0.09$ and $z\ensuremath{\nu}$ close to $1/2$, implying that the quantum phase transition in ${\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}$ differs significantly from the textbook version of a $S=1/2$ Ising chain in a transverse field. We attribute the difference to weak but finite three-dimensionality of the magnetic interactions.

DOI
10.1103/physrevb.96.174424

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We present experimental evidence for a quantum phase transition in the easy-axis S=3/2S=3/2S=3/2 anisotropic quasi-one-dimensional ferromagnet CoCl2\ifmmode⋅\else\textperiodcentered\fi2D2O{\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}CoCl2​\ifmmode⋅\else\textperiodcentered\fi2D2​O in a transverse field. Elastic neutron scattering shows that the magnetic order parameter vanishes at a transverse critical field \ensuremathμ0Hc=16.05{\ensuremath{\mu}}_{0}{H}_{c}=16.05\ensuremathμ0​Hc​=16.05(4) T, while inelastic neutron scattering shows that the gap in the magnetic excitation spectrum vanishes at the same field value, and reopens for H>HcH>{H}_{c}H>Hc​. The field dependence of the order parameter and the gap are well described by critical exponents \ensuremathβ=0.45\ifmmode±\else\textpm\fi0.09\ensuremath{\beta}=0.45\ifmmode\pm\else\textpm\fi{}0.09\ensuremathβ=0.45\ifmmode±\else\textpm\fi0.09 and z\ensuremathνz\ensuremath{\nu}z\ensuremathν close to 1/21/21/2, implying that the quantum phase transition in CoCl2\ifmmode⋅\else\textperiodcentered\fi2D2O{\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}CoCl2​\ifmmode⋅\else\textperiodcentered\fi2D2​O differs significantly from the textbook version of a S=1/2S=1/2S=1/2 Ising chain in a transverse field. We attribute the difference to weak but finite three-dimensionality of the magnetic interactions.
Quantum phase transitions occur at zero temperature upon variation of some nonthermal control parameters. The Ising chain in a transverse field is probably the most-studied model undergoing such a transition, from ferromagnetic to paramagnetic state1,2. This model can be exactly solved by using a Jordan-Wigner transformation, which transforms the spins into noninteracting spinless fermions1. At the quantum critical point, the magnetic excitations can carry arbitrarily low energy and dominate the low temperature properties. Here we report the unveiling of such quantum critical point in quasi-one-dimensional Ising ferromagnet CoNb2O6 by ultra-low-temperature thermal conductivity measurements. We find that in the paramagnetic state, phonons are scattered by the magnetic excitations above certain temperature Ts, which corresponds to a gap. As predicted by the theoretical model1, this gap linearly goes to zero with decreasing the transverse field, thus determining the quantum critical point of the Ising chain.
We study effects of a transverse magnetic field on the properties of the one-dimensional spin-1/2 Ising-like antiferromagnet. In order to emphasize the relevant role of domain walls between opposite antiferromagnetic domains, the spin Hamiltonian is exactly mapped to the interacting fermion Hamiltonian, via the dual transformation as well as the Jordan-Wigner transformation. Within the generalized Hartree-Fock approximation, we find that the excitation spectrum exhibits characteristic features, which are explained as a result of the different roles of the transverse field and of the transverse components of the exchange interactions in the propagation of the domain wall. At a critical field where the excitation gap vanishes, a ground-state phase transition is found to take place in the same manner as that in the transverse Ising model. In addition, we discuss the relevance of our magnetization curve with regard to experimental data in CsCoCl 3 .
The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.
By combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising-like quantum antiferromagnet BaCo2V2O8{\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCo2​V2​O8​ in a longitudinal magnetic field applied along the Ising anisotropy, which is also the chain direction. The external field closes the excitation gap due to the magnetic anisotropy, inducing a transition from the N\'eel ordered state to an incommensurate longitudinal spin density wave phase. If the field is increased further, another transition into a transverse antiferromagnetic phase takes place at 9 T due to the competition between longitudinal and transverse correlations. We numerically and experimentally show that the model of XXZ chains connected by a weak interchain interaction well reproduces this transition. We also calculate the dynamical susceptibility and demonstrate that it agrees quantitatively with inelastic neutron scattering measurements. In contrast to the abrupt change of magnetic ordering, the spectra do not change much at the transition at 9 T, and the spin dynamics can be described as a Tomonaga-Luttinger liquid. We also refine the modeling of BaCo2V2O8{\mathrm{BaCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}BaCo2​V2​O8​ by including a four-site periodic term arising from the crystal structure which enables one to account for an anomaly of the magnetic susceptibility appearing at 19.5 T, as well as for the anticrossing observed in the inelastic neutron scattering spectra.
Abstract We report on high-resolution terahertz spectroscopic studies of quantum spin dynamics in the quasi-one-dimensional Ising-like ferromagnet CoNb2O6 and antiferromagnet BaCo2V2O8 as a function of an applied transverse magnetic field. In the ordered phases stabilized by inter-chain couplings, we reveal characteristics for confined spinon excitations, E 8 dynamical spectrum, and field-induced quantum phase transitions. The connections between these characteristic dynamical features are found in the field-dependent evolution of the excitation spectra.
Combining inelastic neutron scattering and numerical simulations, we study the quasi-one-dimensional Ising anisotropic quantum antiferromagnet BaCo_{2}V_{2}O_{8} in a longitudinal magnetic field. This material shows a quantum phase transition from a Néel ordered phase at zero field to a longitudinal incommensurate spin density wave at a critical magnetic field of 3.8 T. Concomitantly, the excitation gap almost closes and a fundamental reconfiguration of the spin dynamics occurs. These experimental results are well described by the universal Tomonaga-Luttinger liquid theory developed for interacting spinless fermions in one dimension. We especially observe the rise of mainly longitudinal excitations, a hallmark of the unconventional low-field regime in Ising-like quantum antiferromagnetic chains.