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arXiv:1811.07178 · Physical Review Letters

Thermal Control of Spin Excitations in the Coupled Ising-Chain Material RbCoCl3

Mattia Mena, Nora Hänni, Simon Ward, E. Hirtenlechner, Robert Bewley, Claudius Hubig, Ulrich Schollwöck, Bruce Normand, Karl W. Krämer, MCMORROW Desmond Francis, Christian Rüegg

Published Jun 22, 2020• 17 citations
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Abstract

We have used neutron spectroscopy to investigate the spin dynamics of the quantum (S=1/2) antiferromagnetic Ising chains in RbCoCl_{3}. The structure and magnetic interactions in this material conspire to produce two magnetic phase transitions at low temperatures, presenting an ideal opportunity for thermal control of the chain environment. The high-resolution spectra we measure of two-domain-wall excitations therefore characterize precisely both the continuum response of isolated chains and the "Zeeman-ladder" bound states of chains in three different effective staggered fields in one and the same material. We apply an extended Matsubara formalism to obtain a quantitative description of the entire dataset, Monte Carlo simulations to interpret the magnetic order, and finite-temperature density-matrix renormalization-group calculations to fit the spectral features of all three phases.

DOI
10.1103/physrevlett.124.257201

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We have used neutron spectroscopy to investigate the spin dynamics of the quantum (S=1/2) antiferromagnetic Ising chains in RbCoCl_{3}. The structure and magnetic interactions in this material conspire to produce two magnetic phase transitions at low temperatures, presenting an ideal opportunity for thermal control of the chain environment. The high-resolution spectra we measure of two-domain-wall excitations therefore characterize precisely both the continuum response of isolated chains and the "Zeeman-ladder" bound states of chains in three different effective staggered fields in one and the same material. We apply an extended Matsubara formalism to obtain a quantitative description of the entire dataset, Monte Carlo simulations to interpret the magnetic order, and finite-temperature density-matrix renormalization-group calculations to fit the spectral features of all three phases.
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The lowest-lying excited states in the S=1/2 one-dimensional Ising-like antiferromagnet CsCoCl3{\mathrm{CsCoCl}}_{3}CsCoCl3​ consist of domain-wall (soliton) pair states. Although the dynamical response function S(Q,\ensuremath{\omega}) has been calculated for these states, it has not proved possible to explain the results of neutron scattering and Raman experiments without recourse to the introduction of extra terms in the spin Hamiltonian. We argue against the two modifications to the Hamiltonian of CsCoCl3{\mathrm{CsCoCl}}_{3}CsCoCl3​ proposed in previous papers, a staggered field term arising from a mean field approach to exchange mixing, and next-nearest-neighbor intrachain coupling, as being unphysical. Instead we derive a nearest-neighbor effective Hamiltonian, which takes account of the mixing of higher Co2+{\mathrm{Co}}^{2+}Co2+ ion crystal-field levels in a self-consistent manner. We also present a high-resolution inelastic neutron scattering experiment on CsCoCl3{\mathrm{CsCoCl}}_{3}CsCoCl3​, which has allowed the dispersion of the excited states across the Brillouin zone to be studied more carefully than before. These results give a direct measure of S(Q,\ensuremath{\omega}) in the one-dimensional phase where there is a continuum of excited states, and in the three-dimensionally ordered phases, where weak interchain interactions split the continuum into a ``Zeeman ladder'' of discrete states. The predictions of our theory are found to be in quantitative agreement with experiment.
Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the S=1/2S=1/2S=1/2 Heisenberg spin chain compound K2CuSO4Cl2{\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}K2​CuSO4​Cl2​ at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted z=2,d=1z=2,\phantom{\rule{0.16em}{0ex}}d=1z=2,d=1 quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent nonuniversal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.
We use the density matrix renormalization group method to compute the frequency and momentum-resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero-temperature case, the finite-temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one-dimensional quantum chains.
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