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arXiv:1407.2794 · Physical Review B

Quasiparticle breakdown in the quasi-one-dimensional Ising ferromagnet CoNb2O6

Neil J. Robinson, Fabian H. L. Eßler, I. Cabrera, R. Coldea

Published Nov 6, 2014• 33 citations
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Abstract

We present experimental and theoretical evidence that an interesting quantum many-body effect---quasiparticle breakdown---occurs in the quasi-one-dimensional spin-$\frac{1}{2}$ Ising-like ferromagnet ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ in its paramagnetic phase at high transverse field as a result of explicit breaking of spin inversion symmetry. We propose a quantum spin Hamiltonian capturing the essential one-dimensional physics of ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ and determine the exchange parameters of this model by fitting the calculated single-particle dispersion to the one observed experimentally in applied transverse magnetic fields [1]. We present high-resolution inelastic neutron scattering measurements of the single-particle dispersion which observe ``anomalous broadening'' effects over a narrow energy range at intermediate energies. We propose that this effect originates from the decay of the one particle mode into two-particle states. This decay arises from (i) a finite overlap between the one-particle dispersion and the two-particle continuum in a narrow energy-momentum range and (ii) a small misalignment of the applied field away from the direction perpendicular to the Ising axis in the experiments, which allows for nonzero matrix elements for decay by breaking the ${\mathbb{Z}}_{2}$ spin inversion symmetry of the Hamiltonian.

DOI
10.1103/physrevb.90.174406

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We construct a microscopic spin-exchange Hamiltonian for the quasi-one-dimensional (1D) Ising magnet [Formula: see text] that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field-tuned quantum critical point in [Formula: see text] corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.
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Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the E8{E}_{8}E8​ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E8{E}_{8}E8​ particles, m1{\mathrm{m}}_{1}m1​ to m6{\mathrm{m}}_{6}m6​, and the two-particle (m1+m2)({\mathrm{m}}_{1}+{\mathrm{m}}_{2})(m1​+m2​) continuum in an applied transverse magnetic field of Bc1D=4.75T{B}_{c}^{\text{1D}}=4.75 \mathrm{T}Bc1D​=4.75T, before the three-dimensional magnetic order is suppressed above ${B}_{c}^{\text{3D}}\ensuremath{\approx}5.3 \mathrm{T}$. The observation of the higher-energy particles (m3tom6)({\mathrm{m}}_{3} \mathrm{to} {\mathrm{m}}_{6})(m3​tom6​) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.
CoNb2O6\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ is one of the few materials that is known to approximate the one-dimensional transverse-field Ising model (1D-TFIM) near its quantum critical point. It has been inferred that Co2+{\mathrm{Co}}^{2+}Co2+ acts as a pseudospin 1/21/21/2 with anisotropic exchange interactions that are largely Ising-like, enabling the realization of the TFIM. However, the behavior of CoNb2O6\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ is known to diverge from the ideal TFIM under transverse magnetic fields that are far from the quantum critical point, requiring the consideration of additional anisotropic, bond-dependent (Kitaev-like) terms in the microscopic pseudospin-1/21/21/2 Hamiltonian. These terms are expected to be controlled in part by single-ion physics, namely the wave function for the pseudospin-1/21/21/2 angular momentum doublet. Here, we present the results of both inelastic neutron scattering measurements and electron paramagnetic resonance spectroscopy on CoNb2O6\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​, which elucidate the single-ion physics of Co2+{\mathrm{Co}}^{2+}Co2+ in CoNb2O6\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ for the first time. We find that the system is well-described by an intermediate spin-orbit coupled Hamiltonian, and the ground state is a well-isolated Kramers doublet with an anisotropic ggg tensor. We provide the approximate wave functions for this doublet, which we expect will be useful in theoretical investigations of the anisotropic exchange interactions.
Experimental Observation of High-Energy E8E_8E8​ Particles in the Ising Chain Ferromagnet CoNb2_22​O6_66​
Close to the quantum critical point of the transverse-field Ising spin-chain model, an exotic dynamic spectrum was predicted to emerge upon a perturbative longitudinal field. The dynamic spectrum consists of eight particles and is governed by the symmetry of the E8E_8E8​ Lie algebra. Here we report on high-resolution terahertz spectroscopy of quantum spin dynamics in the ferromagnetic Ising-chain material CoNb2_22​O6_66​. At 0.25 K in the magnetically ordered phase we identify characteristics of the first six E8E_8E8​ particles, m1\mathbf{m}_1m1​ to m6\mathbf{m}_6m6​, and the two-particle (m1+m2\mathbf{m}_1+\mathbf{m}_2m1​+m2​) continuum in an applied transverse magnetic field of Bc1D=4.75B_c^{1D}=4.75Bc1D​=4.75 T, before the three-dimensional magnetic order is suppressed above Bc3D≈5.3B_c^{3D}\approx 5.3Bc3D​≈5.3 T. The observation of the higher-energy particles (m3\mathbf{m}_3m3​ to m6\mathbf{m}_6m6​) above the low-energy two-particle continua features quantum many-body effects in the exotic dynamic spectrum.
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 ${\mathrm{CoCl}}_{2}\ifmmode\cdot\else\textperiodcentered\fi{}2{\mathrm{D}}_{2}\mathrm{O}$ 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>HcH>{H}_{c}H>Hc​. 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 1/21/21/2, 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=1/2S=1/2S=1/2 Ising chain in a transverse field. We attribute the difference to weak but finite three-dimensionality of the magnetic interactions.