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Physical review. B, Condensed matter

Electron correlations in stripe phases for doped antiferromagnets

Dariusz Gora, Krzysztof Rościszewski, Andrzej M. Oleś

Published Sep 1, 1999• 26 citations
Publisher

Abstract

We present the charge and magnetization density distribution in various stripe phases obtained for two-dimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped $(\ensuremath{\delta}=1/8)$ and overdoped $(\ensuremath{\delta}=1/4)$ systems. At intermediate values of U in underdoped systems $(\ensuremath{\delta}=1/8)$ local correlations stabilize the vertical (01) antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped $(\ensuremath{\delta}=1/4)$ systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the (11) direction. These findings agree qualitatively with the experimental results.

DOI
10.1103/physrevb.60.7429

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We present the charge and magnetization density distribution in various stripe phases obtained for two-dimensional models of correlated electrons solved within the Hartree-Fock approximation and a variational local ansatz. Apart from the Hubbard model with local Coulomb interaction U, we investigate its two extensions by adding either static Peierls electron-lattice coupling, or the correlated hopping term in the so-called Hirsch model. It has been found that the stripe ordering is robust and occurs in underdoped (\ensuremathδ=1/8)(\ensuremath{\delta}=1/8)(\ensuremathδ=1/8) and overdoped (\ensuremathδ=1/4)(\ensuremath{\delta}=1/4)(\ensuremathδ=1/4) systems. At intermediate values of U in underdoped systems (\ensuremathδ=1/8)(\ensuremath{\delta}=1/8)(\ensuremathδ=1/8) local correlations stabilize the vertical (01) antiferromagnetic domains, separated by nonmagnetic domain walls filled by one doped hole per two wall atoms. A stripe phase with the same size of magnetic domains and an increased filling of one hole per one wall atom is stable for overdoped (\ensuremathδ=1/4)(\ensuremath{\delta}=1/4)(\ensuremathδ=1/4) systems. At larger values of U, both structures are replaced by more extended magnetic domain walls oriented along the (11) direction. These findings agree qualitatively with the experimental results.
Applying the dynamical mean-field theory to the two-dimensional Hubbard model, we calculate self-consistent solutions of doped antiferromagnets with spatially varying spin density ‹ n iσ › using realistic tight-binding parameters. The local self-energy of the supercell includes transverse and longitudinal spin fluctuations with an effective local potential due to short-range electron-electron correlations. It is found that metallic stripes are stabilized by a pseudogap. The stripes along (1,0) direction filled by one hole per two-domain wall unit cells change with increasing Coulomb interaction U to the more extended stripes along (1,1) direction consisting of four atoms filled by 1/4 doped hole each. These findings agree qualitatively with the experimental observations in the superconducting cuprates, and predict a qualitative difference between various compounds due to differences in the extended hopping parameters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Magnetic and charge order in half-filled and doped finite two-dimensional (8 × 8) clusters described by the extended Hubbard Hamiltonian with medium to large on-site ( U ) and intersite ( V ) Coulomb repulsion were investigated using correlated wavefunctions. The treatment of spatially inhomogeneous correlations was possible thanks to a combination of the local ansatz and the local increments expansion methods. The surprising result is that in the half-filled case the correlations do not influence the transition from the antiferromagnetic (AF) to charge order (CO) phase found in the Hartree–Fock approximation. For the doped systems we found a variety of stripe or superlattice-like structures for small values of V , while for larger V we identified robust CO phases. For smaller doping (δ = 1/8 and 1/4) the charge-majority sublattice has typically inhomogeneous charge distribution and is decorated by various magnetic patterns, while for larger doping (δ = 1/2) the co-phase is homogeneous (ideal) and with superimposed AF order.
We investigate the formation of charge domain walls in an electron-doped extended Hubbard model for the superconducting cuprates. Within an unrestricted Hartree-Fock approach, extended by slave bosons to obtain a better treatment of strong correlations, we demonstrate the occurrence of stripes in the (1,1) and (1,-1) directions having one doped electron per stripe site. The different filling, direction, and width of these electron-doped stripes with respect to those obtained in the hole-doped systems have interesting observable consequences.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
The internal structure of stripes in the two-dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes with inhomogeneous magnetization and charge along the stripe core, consistent with experimental observations, are stabilized by quantum fluctuations, included through the configuration interaction method. Similar configurations result to be stable for filled stripes, and have a lower energy than the standard paramagnetic core solution. Away from half-filling, solitonlike solutions show up within the Hartree-Fock approximation. The hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The hole-hole correlation shows maxima along the stripe direction, while the integrated value of ${n}_{\stackrel{\ensuremath{\rightarrow}}{k}}$ compares satisfactorily with experimental results.
Using a variational Monte Carlo approach with a recently proposed stripe wave function, we showed that the strong correlation included in a $t\text{\ensuremath{-}}J$-type model has essentially all the necessary ingredients to form these stripes with modulations of charge density, spin magnetization, and pair field. If a perturbative effect of electron-phonon coupling to renormalize the effective mass or the hopping rate of holes is considered with the model, we find the half-doped stripes, which has on the average one half of a hole in one period of charge modulation, to be most stable energetic wise in the underdoped region, $1/12\ensuremath{\le}\ensuremath{\delta}\ensuremath{\le}1/8$. This is in good agreement with the observation in the neutron-scattering experiments. We also find long-range Coulomb interaction to be less effective in the formation of half-doped stripes.