Electron correlations in stripe phases for doped antiferromagnets

Abstract

We present the charge and magnetization density distribution in various stripe phases obtained for twodimensional 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 ( d51/8) and overdoped (d51/4) systems. At intermediate values of U in underdoped systems (d51/8) 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 (d51/4) 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. @S0163-1829~99!13733-0# Nonhomogeneous charge and spin ordering in real space, so-called stripe phases, attracted much attention due to their possible role in the high-temperature superconductivity of the cuprates. In contrast to the high-temperature superconductivity itself, the stripe instability of the effective Hubbard model describing a normal phase of the cuprates was first predicted in the theory within Hartree-Fock ~HF! calculations on finite clusters with periodic boundary conditions, 1 and later verified experimentally. The theoretical discovery was soon followed by the experimental observation of incommensurate spin correlations in La22xSrxCuO4 by neutron scattering experiments. 2 However, a clear identification of a stripe phase was possible only more recently in La1.62xNd0.4SrxCuO4, where the stripe structures are pinned. Neutron scattering experiments 3‐5 performed on La1.62xNd0.4SrxCuO4 demonstrate the existence of the stripe phases, with antiferromagnetic ~AF! spin domains, separated by charged domain walls. Neutron diffraction measurements on single crystals with the hole doping ratio d.1/8 revealed the existence of two kinds of incommensurate superlattices peaks. 4 In the reciprocal space the magnetic peaks are satellites of the AF Bragg reflection at k5(p,p); they are displaced along the (10) and (01) directions to k5@p(1 62h),p# and k5@p,p(162h)#, respectively, while at the same time the charge-order x-ray satellite diffraction peaks are displaced by 4h with respect to the peak at k5(0,0) found for a uniform distribution. Experiments at low temperature for La1.62xNd0.4SrxCuO4 showed that h.d at small doping d<1/8, while h is almost constant at higher doping. 5 The appearance of peaks in neutron scattering at incommensurate positions points out toward two possibilites: either ~i! there are two types of twin domains, half of them with the modulation wave vector aligned along the x axis and the other half with the modulation along the y axis or ~ii! only a single type of domain with the modulation both along the x and the y axes is formed. The experiments are usually interpreted within the first scenario, which is also supported by numerous theoretical papers devoted to the study of striped