Abstract Motivated by the on-going discussion on the nature of magnetism in the quantum Ising chain CoNb 2 O 6 , we present a first-principles-based analysis of its exchange interactions with additional modeling, addressing drawbacks of a purely density functional theory ansatz. This method allows us to extract and understand the origin of the magnetic couplings—including all symmetry-allowed terms - and resolve conflicting model descriptions in CoNb 2 O 6 . We find that the twisted Kitaev chain and transverse-field ferromagnetic Ising chain views are mutually compatible, although additional off-diagonal exchanges are required for a complete picture. We show that the dominant exchange interaction is a ligand-centered process—involving e g electrons -, rendered anisotropic by low-symmetry crystal fields in CoNb 2 O 6 , resulting in dominant Ising exchange. Smaller bond-dependent anisotropies are found to originate from d − d kinetic exchange processes involving t 2 g electrons. We demonstrate the validity of our low-energy model by comparing its predictions to measured THz and INS spectra.
Abstract Motivated by the on-going discussion on the nature of magnetism in the quantum Ising chain CoNb 2 O 6 , we present a first-principles-based analysis of its exchange interactions with additional modeling, addressing drawbacks of a purely density functional theory ansatz. This method allows us to extract and understand the origin of the magnetic couplings—including all symmetry-allowed terms - and resolve conflicting model descriptions in CoNb 2 O 6 . We find that the twisted Kitaev chain and transverse-field ferromagnetic Ising chain views are mutually compatible, although additional off-diagonal exchanges are required for a complete picture. We show that the dominant exchange interaction is a ligand-centered process—involving e g electrons -, rendered anisotropic by low-symmetry crystal fields in CoNb 2 O 6 , resulting in dominant Ising exchange. Smaller bond-dependent anisotropies are found to originate from d − d kinetic exchange processes involving t 2 g electrons. We demonstrate the validity of our low-energy model by comparing its predictions to measured THz and INS spectra.
For many years, CoNb_{2}O_{6} has served as an exemplar of the one-dimensional Ising model. However, recent experimental and theoretical analyses challenge its applicability to this material. Prior to that, a tailored spin model for 3d^{7} systems such as Co^{2+}, known as the JKΓ model, has emerged, featuring Heisenberg (J), Kitaev (K), and Gamma (Γ) interactions. While these interactions are permitted by the symmetry of the system, their role in CoNb_{2}O_{6} remains enigmatic. We present a microscopic theory based on spin-orbit entangled J_{eff}=1/2 states, aimed at elucidating the roles of Kitaev and Gamma interactions in shaping Ising anisotropy. Leveraging strong coupling theory, we identify a dominant ferromagnetic Kitaev interaction. Furthermore, by comparing dynamical structure factors obtained via exact diagonalization with those from inelastic neutron scattering experiments, we find an antiferromagnetic Γ interaction, which dictates the Ising axis and explains the mechanism behind moment pinning. Our theory provides a microscopic origin for Ising behavior in spin-orbit coupled one-dimensional chains and posits CoNb_{2}O_{6} as a rare Kitaev chain.
The identification of microscopic models describing the low-energy properties of correlated materials has been a central goal of spectroscopic measurements. We demonstrate how 2D non-linear spectroscopy can be used to distinguish effective spin models whose linear responses show similar behavior. Motivated by recent experiments on the quasi-1D Ising magnet CoNb2O6, we focus on two proposed models, the ferromagnetic twisted Kitaev chain with bond dependent interactions and the transverse field Ising model. The dynamical spin structure factor probed in linear response displays similar broad spectra for both models from their fermionic domain wall excitations. In sharp contrast, the 2D non-linear spectra of the two models show clear qualitative differences: those of the twisted Kitaev model contain off-diagonal peaks originating from the bond dependent interactions and transitions between different fermion bands absent in the transverse field Ising model. We discuss the different signatures of spin fractionalization in integrable and non-integrable regimes of the models and their connection to experiments.
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.
Evolution from Kitaev to XXZ spin chains via distortion: Application to BaCo2V2O8
BaCo2V2O8 is a prototypical spin-orbit-coupled Ising-chain antiferromagnet that provides a unique platform for studying field-induced quantum magnetism. Under a transverse magnetic field, it exhibits unusual magnetic properties, including an anomalous staggered magnetization and a pronounced anisotropy of the critical field with respect to the in-plane field direction. While these phenomena have been attributed phenomenologically to a site-dependent anisotropic g-tensor, a recent microscopic theory has shown that spin-orbit coupling naturally generates bond-dependent Heisenberg, Kitaev, and Γ exchange interactions. Here, we unify these two pictures by extending the microscopic theory to incorporate distortions of the CoO6 octahedra. We show that the distortions not only generate the site-dependent anisotropic g-tensor but also renormalize the staggered exchange interactions through a distortion-induced contribution that partially compensates the Kitaev-derived staggered term. Using point-charge calculations to estimate the g-tensor of BaCo2V2O8, we demonstrate that the strong anisotropy of the critical field originates from the combined effects of the modified exchange interactions and the anisotropic g-tensor. Our work provides a unified microscopic framework for understanding the magnetic anisotropy of spin-orbit-coupled Ising-chain materials.
The Ising chain in a transverse field stands out as a paradigmatic example for a quantum phase transition. CoNb2O6 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 CoNb2O6, 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.
Abstract With recent advances in terahertz (THz) sources and detection, two-dimensional coherent spectroscopy (2DCS), which allows one to probe nonlinear responses, now reaches the meV regime relevant for quasiparticle excitations in magnetic materials. This opens a promising route to reveal many-body phenomena that evade linear-response probes. To date, most experimental applications have focused on classical magnets, and a solid demonstration in a quantum magnet has yet to be established. Here we present a theoretical study of 2DCS in CoNb 2 O 6 , a quasi-one-dimensional Ising magnet that is believed to host fractionalized spinons which at low temperatures are confined by weak interchain coupling. Our analysis, which builds on an experimentally constrained effective S = 1/2 Hamiltonian, is found to reveal unambiguous 2DCS signatures of spinon deconfinement above the low-temperature ordered phase. Using a four-spinon approximation, we track these 2DCS signatures by sequentially building a faithful microscopic model for CoNb 2 O 6 , starting from the exactly solvable one-dimensional transverse-field Ising model (1 d TFIM) and successively adding additional interactions. In particular, adding a bond-dependent staggered YZ interaction to the 1 d -TFIM already reproduces many key spectral features of the full material Hamiltonian. Within this TFIM+YZ model, we find a series of bound states, including a four-spinon bound state that is distinct from the familiar two-spinon bound states. We further find that introducing a confinement potential suppresses sharp spinon-echo features, which are thought to reflect an underlying continuum of fractionalized excitations. Our results provide concrete predictions for future THz 2DCS experiments on CoNb 2 O 6 and related quasi-one-dimensional quantum magnets.