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International Journal of Modern Physics B

SPIN DYNAMICS IN STRONGLY CORRELATED ELECTRON SYSTEMS

A. Sherman, Michael Schreiber

Published Feb 20, 2007• 2 citations
Publisher

Abstract

Magnetic properties of the two-dimensional t-J model are reviewed. Some of these properties are close to those observed in cuprate perovskites. In particular, the magnetic response of the model is characterized by the intensive peak at the antiferromagnetic wave vector and at some transfer frequency. The peak splits into several incommensurate maxima for lower and higher frequencies. We discuss mechanisms which are responsible for these peculiarities in the model, which might also refer to cuprates.

DOI
10.1142/s0217979207036692

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Magnetic properties of the two-dimensional t-J model are reviewed. Some of these properties are close to those observed in cuprate perovskites. In particular, the magnetic response of the model is characterized by the intensive peak at the antiferromagnetic wave vector and at some transfer frequency. The peak splits into several incommensurate maxima for lower and higher frequencies. We discuss mechanisms which are responsible for these peculiarities in the model, which might also refer to cuprates.
Abstract Using the strong-coupling diagram technique, low-temperature spectral properties of the two-dimensional fermionic Hubbard model are considered for strong and moderate Hubbard repulsions U . The electron hopping to the nearest, second and third neighbors is taken into account with hopping constants t , t ′ = − 0.3 t and t ″ = 0.2 t , respectively. The nonzero values of t ′ and t ″ lead to strong asymmetry in magnetic properties with respect to the hole and electron doping—for U = 8 t strong antiferromagnetic correlations are retained up to the electron concentration n ¯ ≈ 1.25 , while they are destroyed completely at n ¯ ≈ 0.87 . When the temperature is decreased to T ≲ 0.1 t , in a wide range of electron concentrations there appear narrow and intensive peaks at the Fermi level (FL) in densities of states. For U ≲ 6 t the peaks are seen even at half-filling, while for larger U they arise as the FL leaves the Mott gap. The peaks are connected with a narrow band emerging at low temperatures. We identify states forming the band with spin-polaron excitations—bound states of correlated electrons and mobile spin excitations. Obtained low-temperature spectral functions are used for interpreting the peak-dip-hump structure observed in the photoemission of Nd 2− x Ce x CuO 4 . In the case of hole doping, the calculated Fermi contour contains arcs near nodal points with pseudogaps near antinodal points, while for electron doping the spectral intensity is suppressed at hot spots, in agreement with experimental observations in cuprate perovskites.
Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial directions (t(x) not equal to t(y) and Jx not equal to J(y)). Incommensurate peaks in the spin structure factor show up only in the presence of a lattice anisotropy, whereas charge correlations, indicating enhanced fluctuations at incommensurate wave vectors, are present but almost unaffected with respect to the isotropic case.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
The one-electron spectral function $\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})$ for the large-N\mathcal{N}N $t\ensuremath{-}J$ model typically consists of two distinct peaks: a dispersive quasiparticle and a lower-energy incoherent structure. This is reminiscent of the spectral function of the weak coupling Hubbard model in which the electron is coupled to antiferromagnetic spin fluctuations. In both theories, the two-peaked pattern can be traced to the frequency dependence of the (normal) electron self-energy $\ensuremath{\Sigma}(\mathit{k},\ensuremath{\omega})$. What interaction causes this particular $\ensuremath{\omega}$ dependence of $\ensuremath{\Sigma}$? In the weak coupling case it is clearly the emission and absorption of an antiferromagnetic spin fluctuation by the electron. In the slave boson formulation of the large-N\mathcal{N}N $t\ensuremath{-}J$ model, there are six bosonic excitations: the slave bosons, the constraint field, and the real and imaginary parts of the hopping amplitudes in both the x and y directions. None of these are obviously related to a spin fluctuation propagator. These bosons have the unusual property of transmuting in flight---that is, they are not eigenstates. In order to try to make physical sense of the interaction that is primarily responsible for the frequency dependence of $\ensuremath{\Sigma}$ and the structure of $\ensuremath{\rho}(\mathit{k},\ensuremath{\omega})$, we investigate the transformation to a representation in which the boson propagator matrix is diagonal and extract the contributions of the slave bosons and the constraint field, which appear to be of particular importance.
One of the central issues in the study of high-temperature superconducting cuprates which are composed of two-dimensional (2D) CuO 2 planes is whether the 2D systems with strong electron correlation behave as a Fermi liquid or a non-Fermi-liquid-like one-dimensional (1D) system with electron correlation. In this article, we start with the detailed examination of the electronic structure in cuprates and study theoretically the spin and charge dynamics in 1D and 2D cuprates. The theoretical background of spin-charge separation in the 1D model systems including the Hubbard and t - J models is presented. The first direct observation of collective modes of spin and charge excitations in a 1D cuprate, which are called spinons and holons respectively, in angle-resolved photoemission spectroscopy (ARPES) experiments is reviewed in the light of the theoretical results based on the numerically exact-diagonalization method. The charge and spin dynamics in 1D insulating cuprates is also discussed in connection with the spin-charge separation. The arguments are extended to the 2D cuprates, and the unique aspects of the electronic properties of high-temperature superconductors are discussed. Special emphasis is placed on the d-wave-like excitations in insulating 2D cuprates observed in ARPES experiments. We explain how the excitations are caused by the spin-charge separation. The charge stripes observed in the underdoped cuprates are examined in connection with spin-charge separation in real space.
The discovery of high-Tc superconductivity in cuprates in 1986 moved strongly correlated systems from exotic worlds interesting only for pure theorists to the focus of solid-state research. In recent decades, the majority of hot topics in condensed matter physics (high-Tc superconductivity, colossal magnetoresistance, multiferroicity, ferromagnetism in diluted magnetic semiconductors, etc.) have been related to strongly correlated transition metal compounds. The highly successful electronic structure calculations based on density functional theory lose their predictive power when applied to such compounds. It is necessary to go beyond the mean field approximation and use the many-body theory. The methods and models that were developed for the description of strongly correlated systems are reviewed together with the examples of response function calculations that are needed for the interpretation of experimental information (inelastic neutron scattering, optical conductivity, resonant inelastic X-ray scattering, electron energy loss spectroscopy, angle-resolved photoemission, electron spin resonance, and magnetic and magnetoelectric properties). The peculiarities of (quasi-) 0-, 1-, 2-, and 3- dimensional systems are discussed.