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arXiv:2303.15639 · Physical review. B./Physical review. B

Refined spin-wave model and multimagnon bound states in Li2CuO2

Eli Zoghlin, M. B. Stone, Stephen D. Wilson

Published Aug 9, 2023• 5 citations
arXivHTMLPDF

Abstract

Quasi-one-dimensional materials serve as both testbeds for tractable magnetic models and as a perennial source of intriguing physics. An excellent example is the emergence of multimagnon bound states in ferromagnetic (FM) spin chains, which provide a platform for probing a few-body quantum phenomenon. Despite being studied for many years, the exchange anisotropy-driven bound state of a FM chain has yet to be observed by inelastic neutron scattering (INS). As INS provides a unique window into the nature of magnon-magnon interactions, this represents a substantive gap in the literature. Here, the authors rectify this gap by presenting detailed INS data on the $S$=\textonehalf{} spin chain Li${}_{2}$CuO${}_{2}$. Their data allows for determination of a refined spin Hamiltonian which fully describes the one-magnon dispersion. With these details in hand, they demonstrate the existence of two-magnon and, potentially, three-magnon bound states in Li${}_{2}$CuO${}_{2}$, with the potential three-magnon bound state showing anomalous behavior.

DOI
10.1103/physrevb.108.064408

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Quasi-one-dimensional materials serve as both testbeds for tractable magnetic models and as a perennial source of intriguing physics. An excellent example is the emergence of multimagnon bound states in ferromagnetic (FM) spin chains, which provide a platform for probing a few-body quantum phenomenon. Despite being studied for many years, the exchange anisotropy-driven bound state of a FM chain has yet to be observed by inelastic neutron scattering (INS). As INS provides a unique window into the nature of magnon-magnon interactions, this represents a substantive gap in the literature. Here, the authors rectify this gap by presenting detailed INS data on the SSS=\textonehalf{} spin chain Li2{}_{2}2​CuO2{}_{2}2​. Their data allows for determination of a refined spin Hamiltonian which fully describes the one-magnon dispersion. With these details in hand, they demonstrate the existence of two-magnon and, potentially, three-magnon bound states in Li2{}_{2}2​CuO2{}_{2}2​, with the potential three-magnon bound state showing anomalous behavior.
Few-magnon physics in the spin-SSS periodic XXZXXZXXZ chain
Few-magnon excitations in Heisenberg-like models play an important role in understanding magnetism and have long been studied by various approaches. However, the quantum dynamics of magnon excitations in a finite-size spin-SSS XXZXXZXXZ chain with single-ion anisotropy remains unsolved. Here, we exactly solve the two-magnon (three-magnon) problem in the spin-SSS XXZXXZXXZ chain by reducing the few-magnons to a fictitious single particle on a one-dimensional (two-dimensional) effective lattice. Such a mapping allows us to obtain both the static and dynamical properties of the model explicitly. The zero-energy-excitation states and various types of multimagnon bound states are manifested, with the latter being interpreted as edge states on the effective lattices. Moreover, we study the real-time multimagnon dynamics by simulating single-particle quantum walks on the effective lattices.
Here we report on the formation of a three-magnon bound state in the quasi-one-dimensional antiferromagnet α-NaMnO_{2}, where the single-ion, uniaxial anisotropy inherent to the Mn^{3+} ions in this material provides a binding mechanism capable of stabilizing higher order magnon bound states. While such states have long remained elusive in studies of antiferromagnetic chains, neutron scattering data presented here demonstrate that higher order n>2 composite magnons exist, and, specifically, that a weak three-magnon bound state is detected below the antiferromagnetic ordering transition of NaMnO_{2}. We corroborate our findings with exact numerical simulations of a one-dimensional Heisenberg chain with easy-axis anisotropy using matrix-product state techniques, finding a good quantitative agreement with the experiment. These results establish α-NaMnO_{2} as a unique platform for exploring the dynamics of composite magnon states inherent to a classical antiferromagnetic spin chain with Ising-like single ion anisotropy.
Quasiparticles are physically motivated mathematical constructs for simplifying the seemingly complicated many-body description of solids. A complete understanding of their dynamics and the nature of the effective interactions between them provides rich information on real material properties at the microscopic level. In this paper, we explore the dynamics and interactions of magnon quasiparticles in a ferromagnetic spin-1 Heisenberg chain with easy-axis on-site anisotropy, a model relevant for the explanation of recent terahertz optics experiments on NiNb2O6{\mathrm{NiNb}}_{2}{\mathrm{O}}_{6}NiNb2​O6​ [P. Chauhan et al., Phys. Rev. Lett. 124, 037203 (2020)], and nonequilibrium dynamics in ultracold-atomic settings [W. C. Chung et al., Phys. Rev. Lett. 126, 163203 (2021)]. We build a picture for the properties of clouds of a few magnons with the help of exact diagonalization and density matrix renormalization group calculations supported by physically motivated Jastrow wave functions. We show how the binding energy of magnons effectively reduces with their number and explain how this energy scale is of direct relevance for dynamical magnetic susceptibility measurements. This understanding is used to make predictions for ultracold-atomic platforms, which are ideally suited to study the thermalization of multimagnon states. We simulate the nonequilibrium dynamics of these chains using the matrix product state based time-evolution block decimation algorithm and explore the dependence of revivals and thermalization on magnon density and easy-axis on-site anisotropy (which controls the strength of effective magnon interactions). We observe behaviors akin to those reported for many-body quantum scars, which we explain with an analytic approximation that is accurate in the limit of small anisotropy.
Few-magnon bound states in quantum spin chains have been long studied and attracted much recent attention. For a higher-spin ferromagnetic XXZ chain with single-ion anisotropy, several features regarding the evolution of the low-lying two-magnon bound states with varying wave number were observed in the literature. However, most of these observations are only qualitatively understood due to the lack of analytical tools. By combining a set of exact two-magnon Bloch states and a plane-wave ansatz, we achieve a complete solution of the two-magnon problem in such a system. We identify parameter regions that support different types of two-magnon bound states, with the boundaries defined by algebraic equations. We discover a narrow region in which two single-ion bound states coexist. We show that the phase diagrams for distinct wave numbers are similar to each other, which enables us to map the evolution of the bound states to the rectilinear movement of a representative point for given parameters in a rescaled phase diagram. This dynamic picture provides quantitative interpretations of the observed features.
This thesis describes the neutron scattering measurements of magnetic excitations in \nspin-chains and ladders. The first part discusses an experimental investigation of the copper oxide family Srâ â Cuâ â Oâ â composed of edge-sharing chains and spin-ladders. \nThe study of Laâ Srâ â Cuâ â Oâ â comprises a slightly hole-doped chain and an undoped ladder structure where the chain can be modeled by a ferromagnetic nearest and an \nantiferromagnetic next-nearest neighbor coupling. The hole effects are apparent in gaps in the dispersion relation and can be described by a charge-density wave agreeing with the commensuration of the dispersion. Investigating the undoped ladder establishes \nthe exchange constants including a cyclic exchange manifested by the two-magnon \ncontinuum and the suppression of the S = 1 bound mode. An orbital consideration \nprovides an explanation for the exchanges including the different sizes of rung and \nleg coupling. The excitation spectrum of the doped ladder in Caâ .â Srâ â .â Cuâ â Oâ â can be \ndescribed by a direct comparison with the undoped ladder and the differences consisting \nof a higher energy mode and subgap scattering can be successfully modeled by the charge spectrum of the ladder calculated from the free electron model. The second part of the thesis investigates the alternating chain material Cu(NOâ )â · 2.5D2O and establishes the gapped one-magnon dispersion, the two-magnon continuum and for the first time the S =1 bound mode. Applying magnetic field drives the system through two critical field transitions, condensation of magnons into the ground state and saturation. The modes beyond saturation can be modeled by spin wave theory and the excitations at the first critical field follow Luttinger Liquid behavior. Additionally investigated are the temperature effects with the excitations being of a different nature but containing the signature of a strong correlated system. For an outlook the measurements including temperature and field are provided with further theoretical descriptions necessary.
Magnetic systems composed of weakly coupled spin-1/2 chains are fertile ground for hosting the fractional magnetic excitations that are intrinsic to interacting fermions in one-dimension (1D). However, the exotic physics arising from the quantum many-body interactions beyond 1D are poorly understood in materials of this class. Spinons and psinons are two mutually exclusive low-energy magnetic quasiparticles; the excitation seen depends on the ground state of the spin chain. Here, we present inelastic neutron scattering and neutron diffraction evidence for their coexistence in SrCo2_{2}2​V2_{2}2​O8_{8}8​ at milli-Kelvin temperatures in part of the N\'eel phase (2.4 T ≤\leq≤ μ0\mu_\mathrm{{0}}μ0​H <<< 3.9 T) and possibly also the field-induced spin density wave phase up to the highest field probed (μ0\mu_\mathrm{{0}}μ0​H ≥\geq≥ 3.9 T, μ0\mu_\mathrm{{0}}μ0​Hmax_\mathbf{\mathrm{{max}}}max​ = 5.5 T). These results unveil a novel spatial phase inhomogeneity for the weakly coupled spin chains in this compound. This quantum dynamical phase separation is a new phenomenon in quasi-1D quantum magnets, highlighting the non-trivial consequences of inter-chain coupling.