Magnetism
The material CoNb2O6 contains loosely bound zigzag chains of magnetic cobalt ions and is considered to be a model system for the so-called one-dimensional transverse field Ising model (TFIM). In this iconic model of quantum criticality, a string of particles with spin ½ orders with all of the spins pointing in the same direction, this ferromagnetic state melts at a critical value of an external transverse magnetic field. Morris et al. re-examined the applicability of this model to CoNb2O6 using time–domain terahertz spectroscopy and found that some of their results could not be explained by TFIM. Instead, the data fit what the authors dubbed a twisted Kitaev chain model, in which the Ising direction alternates along the chain.
Nat. Phys. 10.1038/s41567-021-01208-0 (2021).
CoNb2O6 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+ acts as a pseudospin
1/2 with anisotropic exchange interactions that are largely Ising-like, enabling the realization of the TFIM. However, the behavior of
CoNb2O6 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-
1/2 Hamiltonian. These terms are expected to be controlled in part by single-ion physics, namely the wave function for the pseudospin-
1/2 angular momentum doublet. Here, we present the results of both inelastic neutron scattering measurements and electron paramagnetic resonance spectroscopy on
CoNb2O6, which elucidate the single-ion physics of
Co2+ in
CoNb2O6 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
g tensor. We provide the approximate wave functions for this doublet, which we expect will be useful in theoretical investigations of the anisotropic exchange interactions.
The concept of T = 0 quantum phase transi-tions has emerged as an overarching theme in strongly correlated electron physics [1–9]. The nature of quantum fluctuations near the quantum critical point, however, remains enigmatic [10]. How well does the quantum criticality account for finite temperature properties? How high in tem-perature does the effect of the quantum critical point persist?[10, 11] The dearth of appropriate model materials has not permitted experimental-ists to address these fundamental questions even for the transverse field Ising chain (TFIC), a cel-ebrated textbook example of quantum criticality [6]. Here we use NMR (Nuclear Magnetic Res-onance) to map the evolution of quantum spin fluctuations in CoNb2O6 [12–14], which has re-cently been proposed as an ideal model material for the TFIC [15, 16]. We will demonstrate that the effect of the quantum critical point persists to a remarkably high temperature, T ∼ 0.4J, where the exchange coupling J is the only energy scale in the problem.
The dynamical structure factor of the transverse field Ising model (TFIM) shows universal power-law divergence at its quantum critical point, signatures of which have been arguably observed in inelastic neutron scattering studies of quantum spin chain materials, for example CoNb 2 O 6 . However, it has recently been suggested that its microscopic description is better captured in terms of a twisted Kitaev spin chain (TKSC) with bond-anisotropic couplings. Here, we present exact results for the dynamical structure factor of the TKSC across its quantum critical point, analyzing both the universal low-frequency response and the non-universal high-energy features. In addition, we explore extensions of the model including broken glide symmetry as well as the case of random, and incommensurate magnetic fields. Notably, in the latter case, the fermionic excitations exhibit a localization-delocalization transition, which is manifest in the dynamical response as a distinct signature at finite frequency. We discuss the relevance of these features for the observation of quantum critical response in experiments.
Kink bound states in the one-dimensional ferromagnetic Ising chain compound CoNb2O6 have been studied using high-resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schrödinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near 2 times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states--two pairs of kinks on neighboring chains.
Quantum phase transitions take place between distinct phases of matter at zero temperature. Near the transition point, exotic quantum symmetries can emerge that govern the excitation spectrum of the system. A symmetry described by the E8 Lie group with a spectrum of eight particles was long predicted to appear near the critical point of an Ising chain. We realize this system experimentally by using strong transverse magnetic fields to tune the quasi-one-dimensional Ising ferromagnet CoNb2O6 (cobalt niobate) through its critical point. Spin excitations are observed to change character from pairs of kinks in the ordered phase to spin-flips in the paramagnetic phase. Just below the critical field, the spin dynamics shows a fine structure with two sharp modes at low energies, in a ratio that approaches the golden mean predicted for the first two meson particles of the E8 spectrum. Our results demonstrate the power of symmetry to describe complex quantum behaviors.
The Ising chain in a transverse field stands out as a paradigmatic example for a quantum phase transition. CoNb
2O
6 has been discussed as a material realization of this physics, but it was later realized that its magnetic exchange couplings are more complicated, taking the form of twisted Kitaev chains. Here we study a three-dimensional model for CoNb
2O
6, taking into account both Kitaev physics and frustrated interchain coupling, in applied magnetic field. Using semiclassical techniques at zero temperature, we map out the sequence of field-driven phases for arbitrary field direction; these include phases with commensurate and incommensurate interchain order. As a result of spin-orbit coupling, the phase diagram is extremely sensitive to small changes in the field angle. We compute static observables as well as magnetic excitation spectra in the various phases and connect our results to existing experimental data.