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arXiv:cond-mat/0511459 · Physical Review B

Spin correlations and magnetic susceptibilities of lightly doped antiferromagnets

F. Carvalho Dias, Iveta R. Pimentel

Published Jun 21, 2005• 1 citation
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Abstract

We calculate the spin correlation function and the magnetic longitudinal and transverse susceptibilities of a two-dimensional antiferromagnet doped with a small concentration of holes, in the $t\text{\ensuremath{-}}J$ model. We find that the motion of holes generates spin fluctuations that add to the quantum fluctuations, the spin correlations decaying with the inverse of the spin distance, while increasing with doping as the critical hole concentration, where the long-range order disappears, is approached. Moreover, the longitudinal susceptibility becomes finite in the presence of doping due to the strong damping effects induced by the hole motion, while the transverse susceptibility is renormalized by softening effects. Both the longitudinal and transverse susceptibilities increase with doping, the former more significantly than the latter. Our results imply that doping destroys the long-range order while local antiferromagnetic spin correlations persist. This is consistent with experiments on doped copper oxide superconductors.

DOI
10.1103/physrevb.71.224412

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We calculate the spin correlation function and the magnetic longitudinal and transverse susceptibilities of a two-dimensional antiferromagnet doped with a small concentration of holes, in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model. We find that the motion of holes generates spin fluctuations that add to the quantum fluctuations, the spin correlations decaying with the inverse of the spin distance, while increasing with doping as the critical hole concentration, where the long-range order disappears, is approached. Moreover, the longitudinal susceptibility becomes finite in the presence of doping due to the strong damping effects induced by the hole motion, while the transverse susceptibility is renormalized by softening effects. Both the longitudinal and transverse susceptibilities increase with doping, the former more significantly than the latter. Our results imply that doping destroys the long-range order while local antiferromagnetic spin correlations persist. This is consistent with experiments on doped copper oxide superconductors.
The two dimensional (2D) t - J model is studied in a Green's function decoupling scheme, which is an extension of the Kondo and Yamaji's theory (KY theory). The KY theory was originally proposed for spin systems, and is applicable to cases in which there is no symmetry breaking. We derive the lowest order corrections by the electron hopping energy t to self-consistent equations for the correlation function. Hole concentration dependences of the antiferromagnetic (AF) long-range-order (LRO) and spin correlation length at zero temperature are obtained. It is found that they decrease sensitively with doping holes even in a situation very favorable for the antiferromagnetism. The critical hole concentration at which AF LRO vanishes is estimated to be much smaller than in the three-dimensional case. A characteristic feature of 2D electron systems with strong correlations is discussed.
We analyze the density dependence of the spin stiffnesses and the stability of magnetic order with respect to quantum fluctuations in the two-dimensional Hubbard model close to half-filling. The stiffnesses are computed from the spin susceptibility obtained from a random-phase approximation in a magnetically ordered state. For a sizable next-to-nearest-neighbor hopping amplitude and a moderate Hubbard interaction, the mean-field ground state is a Néel antiferromagnet in the electron-doped regime at and above half-filling and a planar circular spiral state in the hole-doped regime below half-filling. Upon electron doping, the Néel stiffness decreases smoothly and not very steeply. By contrast, the in-plane and out-of-plane stiffnesses in the spiral state drop abruptly at half-filling. The out-of-plane stiffness even drops to zero and then increases again very slowly upon increasing hole doping. At finite temperatures, the Néel-to-spiral transition is shifted into the hole-doped regime, the stiffnesses are continuous functions of the density, and they vanish at the transition. For small hole doping, the spin stiffnesses describe the quantum fluctuations only in a small momentum range, which shrinks to zero upon approaching half-filling. Using the above results, we show that the quantum ground state of the lightly electron-doped Hubbard model remains Néel ordered, while quantum fluctuations probably destroy the spiral long-range order in the hole-doped regime, giving rise to a quantum disordered state with a spin gap.
The dynamics of magnetic fluctuations in the canted antiferromagnetic phase of a t-J model is studied within a suitable 1/N expansion. We calculate the dynamical structure factor and assess the effect of hole doping on the excitation spectrum, the staggered antiferromagnetic moment, and the perpendicular uniform ferromagnetic moment. The average long-wavelength excitation energies in the transverse direction are shown to soften with increasing hole concentration, in qualitative agreement with recent neutron-scattering experiments in doped antiferromagnets.
Abstract We investigate the spin dynamics in weakly doped high‐temperature superconductors. The system is described by the two‐dimensional t‐J model. Our focus is on the interaction between mobile holes and spin waves. The calculations are based on a recently introduced cumulant method for computing the ground state energy of correlated electronic systems. Contrary to previous works using dynamical quantities like correlation functions or spectral densities our approach contains a static view to the system. This new method treats spin and hole dynamics on the same basis and allows for the calculation of static and dynamical quantities. We present results for spin‐wave energies and transverse static susceptibilities for small hole concentrations and various values of t/J. We find a strong renor‐malization of the spin‐wave energies due to the spin‐hole interaction. In agreement with neutron scattering experiments the spin‐wave velocity vanishes at a critical hole density of a few percent which is equivalent to the instability of the antiferromagnetic order.
A relaxation-function theory for the dynamic spin susceptibility in the $t\text{\ensuremath{-}}J$ model is presented. By a sum-rule-conserving generalized mean-field approximation (GMFA), the two-spin correlation functions of arbitrary range, the staggered magnetization, the uniform static susceptibility, and the antiferromagnetic correlation length are calculated in a wide region of hole doping and temperatures. A good agreement with available exact diagonalization (ED) data is found. The correlation length is in reasonable agreement with neutron-scattering experiments on ${\text{La}}_{2\ensuremath{-}\ensuremath{\delta}}{\text{Sr}}_{\ensuremath{\delta}}{\text{CuO}}_{4}$. Going beyond the GMFA, the self-energy is calculated in the mode-coupling approximation. The spin dynamics at arbitrary frequencies and wave vectors is studied for various temperatures and hole doping. At low doping a spin-wave-type behavior is found as in the Heisenberg model, while at higher doping a strong damping caused by hole hopping occurs, and a relaxation-type spin dynamics is observed in agreement with the ED results. The local spin susceptibility and its $\ensuremath{\omega}/T$ scaling behavior are calculated in a reasonable agreement with experimental and ED data.
We reconsider some of the previous studies of the interactions between the holes and the spin background in the Hubbard model in the small-doping limit. We show that the hole-hole interaction due to the transverse magnetization fluctuations (i.e., spin waves) is finite at arbitrarily small hole density. It may be comparable to the coupling due to the longitudinal magnetization fluctuations (which are the essence of the ``spin-bag'' mechanism of Schrieffer, Wen, and Zhang). This suggests that the two couplings should be considered simultaneously when studying the phase diagram of the lightly doped quantum antiferromagnets at the values of U/t relevant to the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting materials. We also show that in the large-(U/t) limit the Hubbard-model expressions for the coupling of holes reduce to those given by Shraiman and Siggia for the t-J model. This provides a link between the weak- and the strong-coupling theories of the doped quantum antiferromagnets, in the small-doping limit.