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arXiv:2205.05130 · Physical review. B./Physical review. B

Single-ion properties of the transverse-field Ising model material CoNb2O6

John Ringler, Alexander I. Kolesnikov, Kate A. Ross

Published Jun 27, 2022• 15 citations
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Abstract

$\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$ 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 ${\mathrm{Co}}^{2+}$ 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 $\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$ 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 $\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$, which elucidate the single-ion physics of ${\mathrm{Co}}^{2+}$ in $\mathrm{Co}{\mathrm{Nb}}_{2}{\mathrm{O}}_{6}$ 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.

DOI
10.1103/physrevb.105.224421

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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.
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).
We present experimental and theoretical evidence that an interesting quantum many-body effect---quasiparticle breakdown---occurs in the quasi-one-dimensional spin-12\frac{1}{2}21​ Ising-like ferromagnet CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ 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 CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ 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 Z2{\mathbb{Z}}_{2}Z2​ spin inversion symmetry of the Hamiltonian.
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.
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.
We present experimental and theoretical evidence of novel bound state formation in the low transverse field ordered phase of the quasi-one-dimensional Ising-like material CoNb2O6{\text{CoNb}}_{2}{\text{O}}_{6}CoNb2​O6​. High-resolution single-crystal inelastic neutron scattering measurements observe that small transverse fields lead to a breakup of the spectrum into three parts, each evolving very differently upon increasing field. This can be naturally understood starting from the excitations of the ordered phase of the transverse field Ising model, domain wall quasiparticles (solitons). Here, the transverse field and a staggered off-diagonal exchange create one-soliton hopping terms with opposite signs. We show that this leads to a rich spectrum and a special field, when the strengths of the off-diagonal exchange and transverse field match, at which solitons become localized; the highest field investigated is very close to this special regime. We solve this case analytically and find three two-soliton continua, along with three novel bound states. Perturbing away from this novel localized limit, we find very good qualitative agreement with the experimental data. We also present calculations using exact diagonalization of a recently refined Hamiltonian model for CoNb2O6{\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}CoNb2​O6​ and using diagonalization of the two-soliton subspace, both of which provide a quantitative agreement with the observed spectrum. The theoretical models qualitatively and quantitatively capture a variety of nontrivial features in the observed spectrum, providing insight into the underlying physics of bound state formation.
Transition metal compounds have been central to the study of quantum magnetism in recent years. The multi-orbital nature of these compounds together with the interplay between electron-electron interactions, crystal field effects and spin-orbit coupling leads to spin-orbit entangled wave functions, known as pseudospins. Pseudospins depend highly on the electron filling of the transition metal, and are highly spatially anisotropic which leads to frustrated, bond-dependent exchange interactions. These interactions manifest themselves in a variety of non-trivial ways, depending on the structure and dimensionality of the underlying lattice, which we explore in this thesis. In one dimension we show that CoNb2O6, thought to be the best known candidate for the 1D transverse field Ising model, is an example of a rare 1D Kitaev chain where the bond-dependent pseudospin interactions are responsible for the transverse field Ising behaviour. On the two dimensional honeycomb lattice we propose a mechanism to generate the bond-dependent, exactly solvable, Yao-Lee interaction among others. We show at the exactly solveable point of our model, the ground state is a quantum spin-orbital liquid with emergent fermionic octupolar excitations. Finally, we study the three dimensional 5d double-perovskites (DPs), which have been proposed to be the first d-orbital candidates exhibiting hidden octupolar order. We develop a microscopic theory for these materials, and determine several microscopic mechanisms that may be responsible for stabilizing octupolar order.