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arXiv:1705.01259 · Physical review. B./Physical review. B

Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet

Anup Kumar Bera, B. Lake, Fabian H. L. Eßler, Laurens Vanderstraeten, Claudius Hubig, Ulrich Schollwöck, A. T. M. N. Islam, A. Schneidewind, Diana Lucia Quintero-Castro

Published Aug 17, 2017• 96 citations
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Abstract

Confinement -- the process by which particles with fractional quantum numbers bind to form quasiparticles with integer quantum numbers -- is as important to condensed matter as to particle physics. By a combination of inelastic neutron scattering experiments and theoretical calculations, the authors establish the compound SrCo${}_{2}$V${}_{2}$O${}_{8}$ as a beautiful paradigm for spinon confinement in a quasi-one-dimensional quantum magnet. In particular, using state-of-the-art theoretical techniques, the authors provide a quantitative and macroscopic explanation for the existence of free spinons above the ordering temperature. They also explain how those spinons get confined into pairs with transverse and longitudinal polarizations by interchain interactions as well as how these bound pairs evolve with temperature.

DOI
10.1103/physrevb.96.054423

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Confinement -- the process by which particles with fractional quantum numbers bind to form quasiparticles with integer quantum numbers -- is as important to condensed matter as to particle physics. By a combination of inelastic neutron scattering experiments and theoretical calculations, the authors establish the compound SrCo2{}_{2}2​V2{}_{2}2​O8{}_{8}8​ as a beautiful paradigm for spinon confinement in a quasi-one-dimensional quantum magnet. In particular, using state-of-the-art theoretical techniques, the authors provide a quantitative and macroscopic explanation for the existence of free spinons above the ordering temperature. They also explain how those spinons get confined into pairs with transverse and longitudinal polarizations by interchain interactions as well as how these bound pairs evolve with temperature.
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.
The research presented here focuses on the theoretical investigation of spinons in quasi one-dimensional quantum spin chains from the perspective of neutron scattering, with emphasis placed on the calculation of dynamic spin structure factors for both unpolarised and polarised incident neutrons. Two anisotropic versions of the Heisenberg spin chain are considered for such an examination: the spin-1/21/21/2 antiferromagnetic XXZXXZXXZ model and the spin-1/21/21/2 ferromagnetic XYZXYZXYZ model.The XYZXYZXYZ model supports spinon scattering (modelled at finite temperature) and is related to the so-called Villain mode. The introduction of a perturbation in the form of an external transverse magnetic field or Dzyaloshinskii-Moriya interaction (DMI) leads to the emergence of incommensurability in the system; such a result is a signature of fractional excitations. The presence of these interactions also give rise to a chiral response associated with the spinons in the polarised term of the scattering cross section. The inelastic scattering cross section is computed for both unpolarised and polarised neutrons.In relation to the antiferromagnetic XXZXXZXXZ model, emphasis is on spinon pair creation (modelled at T=0rmKT = 0 {rm K}T=0rmK). Motivated by the presence of a chiral response in the case of the XYZXYZXYZ model mentioned above, a new technique is developed in order to incorporate DMI and the transverse magnetic field so that one can determine if there is a chiral property associated with the two-spinon system. This technique is numerical in nature and is based on Green function methods. Using the results produced by the Green function approach, the inelastic cross section in the presence of an external transverse magnetic field is computed for the first time. The result is compared with experimental neutron scattering data; good agreement is demonstrated between theory and experiments on rmCsCoBr3{rm CsCoBr}_3rmCsCoBr3​.Finally, the Green function approach is generalised to account for the interactions between spin chains in magnetic compounds described by a staggered field. Various dynamic structure factors are computed for this scenario with results compared to experiment; good agreement between the theory and experiments on rmRbCoCl3{rm RbCoCl}_3rmRbCoCl3​ is shown.
Magnetic excitations in the spin chain candidate Sr2V3O9{\mathrm{Sr}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{9}Sr2​V3​O9​ have been investigated by inelastic neutron scattering on a single crystal sample. A spinon continuum with a bandwidth of $\ensuremath{\sim}22$ meV is observed along the chain formed by alternating magnetic V4+{\mathrm{V}}^{4+}V4+ and nonmagnetic V5+{\mathrm{V}}^{5+}V5+ ions, which reveals the importance of the orbital degree of freedom in determining the chain axis as identified by prior electronic structure calculations. Incipient magnetic Bragg peaks due to weak ferromagnetic interchain couplings emerge when approaching the magnetic transition at ${T}_{N}\ensuremath{\sim}5.3$ K, while the excitations remain gapless within the instrumental resolution. Comparisons to the Bethe ansatz, density matrix renormalization group calculations, and effective field theories confirm Sr2V3O9{\mathrm{Sr}}_{2}{\mathrm{V}}_{3}{\mathrm{O}}_{9}Sr2​V3​O9​ as a host of weakly coupled S=1/2S=1/2S=1/2 chains dominated by antiferromagnetic intrachain interactions of $\ensuremath{\sim}7.1$(1) meV.
Spinon confinement is key to the understanding of quantized excitation spectra in quasi-one-dimensional SSS = \textonehalf{} spin systems. The authors investigate the quantization of the excitation continuum in quasi-one-dimensional S=1S=1S=1 antiferromagnetic spin systems with single-ion anisotropy DDD. When DDD 0, the magnon continuum is quantized by the interchain interactions. This is due to magnon confinement. The present study suggests the possibility for observation of quantized spectra in many S=1S=1S=1 antiferromagnetic spin-chain compounds.
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.
We report on spectroscopy study of elementary magnetic excitations in an Ising-like antiferromagnetic chain compound SrCo2V2O8{\mathrm{SrCo}}_{2}{\mathrm{V}}_{2}{\mathrm{O}}_{8}SrCo2​V2​O8​ as a function of temperature and applied transverse magnetic field up to 25 T. An optical as well as an acoustic branch of confined spinons, the elementary excitations at zero field, are identified in the antiferromagnetic phase below the N\'eel temperature of 5 K and described by a one-dimensional Schr\"odinger equation. The confinement can be suppressed by an applied transverse field and a quantum disordered phase is induced at 7 T. In this disordered paramagnetic phase, we observe three emergent fermionic excitations with different transverse-field dependencies. The nature of these modes is clarified by studying spin dynamic structure factor of a 1D transverse-field Heisenberg-Ising (XXZ)(XXZ)(XXZ) model using the method of infinite time evolving block decimation. Our work reveals emergent quantum phenomena and provides a concrete system for testifying theoretical predications of one-dimension quantum spin models.