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Physical review. B, Condensed matter

Spin-wave spectral properties of the Mott-Hubbard antiferromagnet: The intermediate-coupling regime

Avinash Singh

Published Sep 1, 1993• 10 citations
Publisher

Abstract

Spectral properties of spin-wave excitations in the Mott-Hubbard antiferromagnet are studied in the intermediate-coupling regime, wherein extended-range spin couplings are present in the equivalent spin-1/2 Heisenberg model. A systematic expansion in powers of ${\mathit{t}}^{2}$/${\mathit{U}}^{2}$ is developed for the spin-wave propagator in the random-phase approximation, and its quantitative usefulness is investigated. In two dimensions the spin-wave density of states exhibits a peak structure, resembling the broadening effect of spin-wave damping. Implications for recent light-pair scattering experiments in ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ wherein the complete spin-wave spectrum is accessible in principle, are discussed.

DOI
10.1103/physrevb.48.6668

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Spectral properties of spin-wave excitations in the Mott-Hubbard antiferromagnet are studied in the intermediate-coupling regime, wherein extended-range spin couplings are present in the equivalent spin-1/2 Heisenberg model. A systematic expansion in powers of t2{\mathit{t}}^{2}t2/U2{\mathit{U}}^{2}U2 is developed for the spin-wave propagator in the random-phase approximation, and its quantitative usefulness is investigated. In two dimensions the spin-wave density of states exhibits a peak structure, resembling the broadening effect of spin-wave damping. Implications for recent light-pair scattering experiments in {\mathrm{La}}_{2}$${\mathrm{CuO}}_{4} wherein the complete spin-wave spectrum is accessible in principle, are discussed.
A perturbation-theoretic diagrammatic scheme is developed for systematically studying the two-magnon Raman scattering in a Mott-Hubbard antiferromagnet. The fermionic structure of the magnon interaction vertex is obtained at order-1N\frac{1}{\mathcal{N}}N1​ level in an inverse-degeneracy expansion, and the relevant two-magnon propagator is obtained by incorporating magnon interactions at a ladder-sum level. Evaluation of the magnon interaction vertex in the large-UUU limit yields a nearest-neighbor instantaneous interaction with interaction energy $\ensuremath{-}J$. Application of this approach to the intermediate-UUU regime, which is of relevance for cuprate antiferromagnets, is also discussed. Incorporating the zero-temperature magnon damping, which is estimated in terms of quantum spin fluctuations, the two-magnon Raman scattering intensity is evaluated and compared with experiments on La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{O}}_{4}O4​.
The spectrum of spin-wave and single-particle excitations is studied in a half-filled-band Hubbard antiferromagnet for interaction strength values in the intermediate and weak-coupling regimes. The spin-wave-energy scale, which goes essentially as t2{\mathit{t}}^{2}t2/U in the strong- and intermediate-coupling regimes, exhibits a crossover and goes down with decreasing interaction strength in the weak-coupling regime. This crossover is found to occur at U/t=3.26, and it demarcates the Heisenberg behavior in the strong- and intermediate-coupling regimes from the spin-density-wave behavior in the weak-coupling regime. The spin-wave-energy scale gets compressed by the charge gap in the weak-coupling regime, and consequently the spin-wave branch, which approaches the single-particle excitation band quite closely, never actually merges into it.
We present a comprehensive study of the spin excitations---as measured by the dynamical spin structure factor $S(q,\ensuremath{\omega})$---of the so-called block-magnetic state of low-dimensional orbital-selective Mott insulators. We realize this state via both a multi-orbital Hubbard model and a generalized Kondo-Heisenberg Hamiltonian. Due to various competing energy scales present in the models, the system develops periodic ferromagnetic islands of various shapes and sizes, which are antiferromagnetically coupled. The $2\ifmmode\times\else\texttimes\fi{}2$ particular case was already found experimentally in the ladder material BaFe2Se3\mathrm{Ba}{\mathrm{Fe}}_{2}{\mathrm{Se}}_{3}BaFe2​Se3​ that becomes superconducting under pressure. Here we discuss the electronic density as well as Hubbard and Hund coupling dependence of $S(q,\ensuremath{\omega})$ using density matrix renormalization group method. Several interesting features were identified: (1) An acoustic (dispersive spin-wave) mode develops. (2) The spin-wave bandwidth establishes a new energy scale that is strongly dependent on the size of the magnetic island and becomes abnormally small for large clusters. (3) Optical (dispersionless spin excitation) modes are present for all block states studied here. In addition, a variety of phenomenological spin Hamiltonians have been investigated but none matches entirely our results that were obtained primarily at intermediate Hubbard UUU strengths. Our comprehensive analysis provides theoretical guidance and motivation to crystal growers to search for appropriate candidate materials to realize the block states, and to neutron scattering experimentalists to confirm the exotic dynamical magnetic properties unveiled here, with a rich mixture of acoustic and optical features.
Spin-only descriptions of the half-filled one-band Hubbard model are relevant for a wide range of Mott insulators. In addition to the usual Heisenberg exchange, many other types of interactions, including ring exchange, appear in the effective Hamiltonian in the intermediate coupling regime. In order to improve on the quantitative description of magnetic excitations in the insulating antiferromagnetic phase of copper-oxide (cuprate) materials, and to be consistent with band-structure calculations and photoemission experiments on these systems, we include second- and third-neighbor hopping parameters, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, into the Hubbard Hamiltonian. A unitary transformation method is used to find systematically the effective Hamiltonian and any operator in the spin-only representation. The results include all closed four-hop electronic pathways in the canonical transformation. The method generates many ring exchange terms that play an important role in the comparison with experiments on La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. Performing a spin-wave analysis, we calculate the magnon dispersion as a function of UUU, ttt, ${t}^{\ensuremath{'}}$, and ${t}^{\ensuremath{''}}$. The four parameters are estimated by fitting the magnon dispersion to the experimental results of Coldea et al. [Phys. Rev. Lett. 86, 5377 (2001)] for La2CuO4{\text{La}}_{2}{\text{CuO}}_{4}La2​CuO4​. The ring exchange terms are found essential, in particular to determine the relative sign of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, with the values found in good agreement with independent theoretical and experimental estimates for other members of the cuprate family. The zero-temperature sublattice magnetization is calculated using these parameters and also found to be in good agreement with the experimental value estimated by Lee et al. [Phys. Rev. B 60, 3643 (1999)]. We find a value of the interaction strength $U\ensuremath{\simeq}8t$ consistent with Mott insulating behavior.
Abstract We numerically investigate spectroscopic properties for a two-dimensional Mott insulator described by a half-filled Hubbard model on the square lattice. Firstly, we examine the spectral shape of the optical conductivity by using time-dependent density-matrix renormalization group implemented by the Legendre polynomial expansion. We find a shape peak resembling to an excitonic peak at absorption edge, whose origin is attributable to antiferromagnetic correlation in the spin background. We next investigate momentum-dependent transient charge and spin dynamics after photoirradiation by using time-dependent Lanczos-type exact diagonalization. We find a temporal oscillation in the intensity of the dynamical spin structure factor, which exhibits an antiphase behavior between, for example, two orthogonal momentum directions parallel and perpendicular to the electric field of a pump pulse. Observing such antiphase oscillations will be a big challenge for time-resolved resonant-inelastic x-ray scattering experiments.
Elucidating the physics of the single-orbital Hubbard model in its intermediate-coupling regime is a key missing ingredient to our understanding of metal-insulator transitions in real materials. Using recent nonperturbative many-body techniques that are able to interpolate between the spin-fluctuation-dominated Slater regime at weak coupling and the Mott insulator at strong coupling, we obtain the momentum-resolved spectral function in the intermediate regime and disentangle the effects of antiferromagnetic fluctuations and local electronic correlations in the formation of an insulating state. This allows us to identify the Slater and Heisenberg regimes in the phase diagram, which are separated by a crossover region of competing spatial and local electronic correlations. We identify the crossover regime by investigating the behavior of the local magnetic moment, shedding light on the formation of the insulating state at intermediate couplings.