Antiferromagnetic and spiral phases in at-t’-Jmodel

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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 (π,π), i.e., Néel modulation of the spin configuration and an unusual (π,-π) 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.