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arXiv:0908.2557 · Physical Review B

Dynamic spin susceptibility in the t−J model

Artem Vladimirov, Dieter Ihle, Nikolay M. Plakida

Published Sep 21, 2009• 45 citations
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Abstract

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.

DOI
10.1103/physrevb.80.104425

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A relaxation-function theory for the dynamic spin susceptibility in the t\ensuremath-Jt\text{\ensuremath{-}}Jt\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 La2\ensuremath−\ensuremathδSr\ensuremathδCuO4{\text{La}}_{2\ensuremath{-}\ensuremath{\delta}}{\text{Sr}}_{\ensuremath{\delta}}{\text{CuO}}_{4}La2\ensuremath−\ensuremathδ​Sr\ensuremathδ​CuO4​. 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 \ensuremathω/T\ensuremath{\omega}/T\ensuremathω/T scaling behavior are calculated in a reasonable agreement with experimental and ED data.
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic t - J Heisenberg model on the honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures and hole dopings, the electronic spectrum of excitations, the spin-excitation spectrum and thermodynamic quantities (two-spin correlation functions, staggered magnetization, magnetic susceptibility, correlation length) are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature and doping dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. Our results on the doping dependencies of the magnetization and susceptibility are analyzed in comparison with previous results for the t - J model on the square lattice.
We present a spin-rotation-invariant Green-function theory for the dynamic spin susceptibility in the spin-1/2 antiferromagnetic t-J Heisenberg model on the honeycomb lattice. Employing a generalized mean-field approximation for arbitrary temperatures and hole dopings, the electronic spectrum of excitations, the spin-excitation spectrum and thermodynamic quantities (two-spin correlation functions, staggered magnetization, magnetic susceptibility, correlation length) are calculated by solving a coupled system of self-consistency equations for the correlation functions. The temperature and doping dependence of the magnetic (uniform static) susceptibility is ascribed to antiferromagnetic short-range order. Our results on the doping dependencies of the magnetization and susceptibility are analyzed in comparison with previous results for the t-J model on the square lattice.
We consider the slave-fermion--Schwinger-boson decomposition of a t-J model for a two-dimensional antiferromagnet in which the next-nearest-neighbor hopping is taken into account by an explicit t' term. This technique is particularly suitable to describe systems with low hole density, as in the parent phases of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconducting (HTSC) materials, and we examine the experimental consequences of the model. Using mean-field states which admit finite spiral and off-diagonal order, we compute first the dynamic susceptibility \ensuremath{\chi}(q,\ensuremath{\omega}) from fluctuations in the boson (spin) degrees of freedom, and investigate a selected parameter regime for the model to seek features consistent with inelastic neutron scattering experiments on underdoped HTSC crystals. We find peaks in the scattered intensity at incommensurate wave vectors (\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2k0{\mathit{k}}_{0}k0​,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}) and (\ensuremath{\pi},\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}\ifmmode\pm\else\textpm\fi{}2k0{\mathit{k}}_{0}k0​), but within our approximation the q-integrated susceptibility as a function of frequency and temperature resembles that from spin-wave theory, which does not contain the scaling behavior over all values of \ensuremath{\omega}/T found experimentally. We show also the form of the nuclear magnetic resonance relaxation time ${\mathit{T}}_{1}^{\mathrm{\ensuremath{-}}1}$(T), which measures the zero-frequency limit of the susceptibility. The imaginary part of the physical electron Green function is a convolution of both fermionic (hole) and bosonic Green functions, and so incorporates the effect of spin dynamics on the charge motion. We calculate the photoemitted intensity, a direct experimental measurement of this quantity, focusing on its behavior near the hole pockets at (\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2) which characterize this type of model. The peak photocurrent occurs not at the hole Fermi surface, but at points separated from it by k0{\mathbf{k}}_{0}k0​ due to the boson incommensuration.
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.
Finite-temperature spin dynamics in the planar $t\ensuremath{-}J$ model are studied using a method based on the Lanczos diagonalization of small systems. The dynamical spin structure factor at moderate dopings shows the coexistence of free-fermion-like and spin-fluctuation time scales. At T<JT<JT<J, low-frequency and static susceptibilities show a pronounced TTT dependence, supporting a scenario related to the marginal Fermi liquid one, for the explanation of neutron-scattering and NMR relaxation experiments in cuprates. Calculated NMR relaxation rates reasonably reproduce experimental ones.
The dynamic charge susceptibility and the optical conductivity are calculated in the planar $t\ensuremath{-}J$ model within the memory function method, working directly in terms of Hubbard operators. The density fluctuation spectrum consists of a damped soundlike mode for small wave vectors and a broad high energy peak $(\ensuremath{\sim}t)$ for large momenta. The study of the optical conductivity shows that electron scattering from spin fluctuations leads to the Drude-frequency dependent relaxation rate which exhibits a crossover from ${\ensuremath{\omega}}^{3/2}$ behavior at low frequencies $(\ensuremath{\omega}<2|\ensuremath{\mu}|),$ to a linear $\ensuremath{\omega}$ dependence for frequencies larger than $2|\ensuremath{\mu}|.$ Due to the spin-polaron nature of charge carriers, extra absorptions arise starting at a frequency $\ensuremath{\omega}\ensuremath{\gtrsim}J.$ The obtained results are in a good agreement with exact diagonalization studies.