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Physical review. B, Condensed matter

Antiferromagnetic and spiral phases in at-t’-Jmodel

G. C. Psaltakis, N. Papanicolaou

Published Jul 1, 1993• 24 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.48.456

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Abstract. Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t–J model. This model possesses the global discrete Z2 symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t–J model, usually referred to as the t–Jz model, the global SU(2) invariance is fully restored at Jz = 0, so that only the spin-spin interaction has in that model the true Ising form. We discuss a relationship between those two models and the standard isotropic t–J model. We show that the low-energy quasiparticles in all three models share the qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t–J model over the t–Jz one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10 3 sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next nearest neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no double occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed. PACS numbers: 71.10.Fd, 71.10.Pm, 74.25.JbIsing t–J model close to half filling: A Monte Carlo study 2 1.

•Nov 20, 2012•2 citations
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.
The phase diagram of a t-t'-J model on a square lattice has been determined within a suitable 1/N expansion and shown to exhibit a phase-modulated antiferromagnetic (AF) ground state close to half-filling. Here we calculate the real part of the finite-frequency conductivity \ensuremath{\sigma}(\ensuremath{\omega}), i.e., the optical absorption, in the AF state and find a structureless broadband regime at low frequencies, in qualitative agreement with infrared absorption experiments in doped antiferromagnets. In particular, the limiting value \ensuremath{\sigma}(\ensuremath{\omega}\ensuremath{\rightarrow}0) is finite, at finite hole doping, due to the diffusion character of the relevant low-energy quasiparticle states at the corner of the square Brillouin zone.
A real spin-charge separation scheme is found based on a saddle-point state of the t-J model. In the one-dimensional (1D) case, such a saddle-point reproduces the correct asymptotic correlations at the strong-coupling fixed point of the model. In the two-dimensional (2D) case, the transverse gauge field confining spinon and holon is shown to be gapped at finite doping so that a spin-charge deconfinement is obtained for its first time in 2D. The gap in the gauge fluctuation disappears at half-filling limit, where a long-range antiferromagnetic order is recovered at zero temperature and spinons become confined. The most interesting features of spin dynamics and transport are exhibited at finite doping where exotic residual couplings between spin and charge degrees of freedom lead to systematic anomalies with regard to a Fermi-liquid system. In spin dynamics, a commensurate antiferromagnetic fluctuation with a small, doping-dependent energy scale is found, which is characterized in momentum space by a Gaussian peak at (\ensuremath{\pi}/a,\ensuremath{\pi}/a) with a doping-dependent width (\ensuremath{\propto} \ensuremath{\surd}\ensuremath{\delta} , \ensuremath{\delta} is the doping concentration). This commensurate magnetic fluctuation contributes a non-Korringa behavior for the NMR spin-lattice relaxation rate. There also exists a characteristic temperature scale below thich a pseudogap behavior appears in the spin dynamics. Furthermore, an incommensurate magnetic fluctuation is also obtained at a finite energy regime. In the transport, a strong-range phase intereference leads to an effective holon Lagrangian which can give rise to a series of interesting phenomena including linear-T resistivity and a T2{\mathit{T}}^{2}T2 Hall angle. We discuss the striking similarities of these theoretical features with those found in the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates and give a consistent picture for the latter. Electronic properties like Fermi surface and superconducting pairing in this framework are also discussed.
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.
Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.
Using a path-integral formalism and decomposing the Hubbard interaction into charge and spin order parameters, we develop a 1/S loop expansion of the two-dimensional Hubbard model. At the saddle-point level, we present a detailed study of the energetics of twisted antiferromagnetic order. Doping the antiferromagnetic state leads to a rich mean-field phase diagram at zero temperature, which includes spiral phases, a column phase, and ferromagnetism. The on-site magnetization, the density of states, the plasma frequency, and the quasiparticle weights are evaluated for the twisted spin-density-wave (SDW) states as a function of doping and U/t. Doping-induced frustration remarkably leads to a closure of the Mott-Hubbard band gap for any U/t. At one-loop order, we delineate the collective spin and charge fluctuations of the mean-field SDW state. The action for the two transverse spin modes at half-filling maps to a nonlinear \ensuremath{\sigma} model, which tends to disorder upon doping. Twisted magnetic ground states exhibit a third Goldstone mode due to the complete breaking of rotational invariance. For the commensurate SDW, the charge fluctuations couple only to longitudinal spin fluctuations, whereas, for the incommensurate metallic SDW states, the charge modes are coupled nontrivially to the massless spin waves. This suggests a metallic state quite unlike traditional Fermi liquids.
Abstract. Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t–J model. This model possesses the global discrete Z2 symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t–J model, usually referred to as the t–Jz model, the global SU(2) invariance is fully restored at Jz = 0, so that only the spin-spin interaction has in that model the true Ising form. We discuss a relationship between those two models and the standard isotropic t–J model. We show that the low-energy quasiparticles in all three models share the qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t–J model over the t–Jz one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10 3 sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next nearest neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no double occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed. PACS numbers: 71.10.Fd, 71.10.Pm, 74.25.JbIsing t–J model close to half filling: A Monte Carlo study 2 1.