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.
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.
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.
We present a study of a t-t'-J model on a square lattice, where t' denotes hopping along the diagonal, within a suitable 1/N expansion. The T=0 phase diagram consists of conventional ferromagnetic and incommensurate (Q,Q) and (Q,0) spiral phases, in addition to an unconventional antiferromagnetic (AF) phase characterized by the usual (\ensuremath{\pi},\ensuremath{\pi}), i.e., N\'eel modulation of the spin configuration and an unusual (\ensuremath{\pi},-\ensuremath{\pi}) phase modulation. We obtain the spectrum of elementary excitations for all these phases and explicitly display the associated Goldstone-mode structure. A detailed analysis of the AF phase including leading quantum-fluctuation effects shows that it remains locally stable at small finite doping, in agreement with the observed behavior in doped antiferromagnets, as well as globally stable against phase separation for sufficiently large t'. A characteristic feature of this AF phase is an anisotropy in the velocities of its elementary excitations which is suppressed, however, at half-filling. Finally, the spin-spin dynamical structure factor in the AF phase is found to exhibit a double peak at finite doping, which reflects hybridization between the relevant transverse (magnonlike) and longitudinal (holonlike) modes, one of the peaks also being suppressed at half-filling.
We calculate the real part of the finite-frequency conductivity, i.e., the optical absorption, in the canted antiferromagnetic phase of a t-J model using a suitable 1/N expansion. We find that below a characteristic crossover frequency \ensuremath{\Delta} the absorption is very small, while above \ensuremath{\Delta} it rises sharply to a broad maximum, in qualitative agreement with recent infrared absorption experiments in doped antiferromagnets. This crossover frequency is identified with an energy gap developing upon hole doping in one of the two branches of elementary excitations, at the corner of the square Brillouin zone.
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.
Uniform and staggered chiral order are investigated in the two-dimensional t-J model at arbitrary doping fractions. Equal-time and dynamical correlations are calculated on a 4\ifmmode\times\else\texttimes\fi{}4 cluster by using a Lanczos algorithm. We found that static uniform correlations are suppressed with increasing doping and t/J while static staggered correlations seem enhanced, in agreement with previous mean-field studies. The plaquette-plaquette correlation function falls off rapidly with distance, and, thus, we obtain an upper bound on the plaquette order parameter, which is very small. However, our numerical results show that doping for t/J\ensuremath{\ge}1 induces large chiral fluctuations at low energy, which may become important even in the absence of long-range order. The staggered order parameter exhibits low-energy fluctuations of energy \ensuremath{\sim}2J, while for the uniform case fluctuations also occur at a higher energy \ensuremath{\sim}2t.
We discuss a pseudospin representation of the two-dimensional $t\text{\ensuremath{-}}J$ model. We introduce pseudospins associated with empty sites, deriving a representation of the $t\text{\ensuremath{-}}J$ model that consists of local spins and spinless fermions. We show, within a mean-field approximation, that our representation of $t\text{\ensuremath{-}}J$ model corresponds to the isotropic antiferromagnetic Heisenberg model in an effective magnetic field. The strength and the direction of the effective field are determined by the hole doping $\ensuremath{\delta}$ and the orientation of pseudospins associated with empty sites, respectively. We find that the staggered magnetization in the standard representation corresponds to the component of magnetization perpendicular to the effective field in our pseudospin representation. Using a many-body Green's function method, we show that the staggered magnetization decreases with increasing hole doping $\ensuremath{\delta}$ and disappears at $\ensuremath{\delta}\ensuremath{\approx}0.06--0.12$ for t∕J=2.5−−5. Our results are in good agreement with experiments and numerical calculations in contradistinction to usual mean-field methods.