Indications of incommensurate spin fluctuations in doped triangular antiferromagnets

The incommensurate spin fluctuation of the doped triangular antiferromagnet is studied within the t-J model. It is shown that the commensurate peak near the half-filling is split into six incommensurate peaks in the underdoped and optimally doped regimes. The incommensurability increases with the hole concentration at lower dopings, and saturates at higher dopings. Although the incommensurability is almost energy independent, the weight of these incommensurate peaks decreases with energy and temperature. 74.25.Ha, 75.50.-y, 74.72.-h Typeset using REVTEX 1 The high-Tc cuprate superconductors exhibit many unusual properties [1,2], one of the most striking being the anomalous incommensurate antiferromagnetism in the normal state in the underdoped regime [3,4]. These unusual properties are closely related to the fact that cuprate superconductors are doped Mott insulators, obtained by chemically adding charge carriers to a strongly correlated antiferromagnetic (AF) insulating state [1,2]. Neutronscattering measurements show that when the commensurate AF long-range-order (AFLRO) phase is suppressed and the hole concentration exceeds 3%, incommensurate dynamical short-range magnetic correlations appear [3,4], with four peaks located at the reciprocal space positions [(1±δ)π, π] and [π, (1±δ)π] (square lattice notations, unit lattice constant). Even more remarkable is that for very low dopings the incommensurability δ varies almost linearly with the concentration x, but saturates at higher dopings. Moreover, the incommensurate peaks broaden and weaken in amplitude as the energy increases. This incommensurate antiferromagnetism of doped cuprates results from special microscopic conditions [3,4]: (1) Cu ions situated in a square-planar arrangement and bridged by oxygen ions, (2) weak coupling between neighboring layers, and (3) doping in such a way that the Fermi level lies near the middle of the Cu-O σ bond. One common feature of these doped cuprates is the square-planar Cu arrangement. However, some materials with a two-dimensional (2D) spin arrangements on non-square lattices have been synthetized. In particular, it has been reported [5] that there is a class of doped cuprates, RCuO2+δ, R being a rare-earth element, where the Cu ions sites sit not on a square-planar, but on a triangular-planar lattice, therefore allowing a test of the geometry effect on the spin fluctuations, while retaining some other unique microscopic features of the Cu-O bond. In other words, the question is whether the incommensurate magnetic fluctuations observed on the doped square antiferromagnet exist also in the doped triangular antiferromagnet? In addition, the doped triangular antiferromagnet, where geometric frustration is present, is also of theoretical interest by himself, with many unanswered fascinating theoretical questions [6]. Historically the undoped triangular antiferromagnet was firstly proposed to be a model for microscopic realization of the resonating valence bond spin liquid due to the strong frustration [7]. It has been argued [8] 2 that this spin liquid state plays a crucial role in the superconductivity of doped cuprates. Moreover, it has been shown [9] that the doped and undoped triangular antiferromagnets present a pairing instability in an unconventional channel. The incommensurate antiferromagnetism of the doped square antiferromagnet has been extensively studied, and some fundamentally different microscopic mechanisms have been proposed [10–12] to explain the origin of the incommensurate antiferromagnetism, where there is a general consensus that incommensurate antiferromagnetism emerges due to doped charge carriers. Recently, it has been shown very clearly [13] that if the strong electron correlation is treated properly and strong spinon-holon interaction is taken into account, the t-J model can correctly reproduce all main features of the incommensurate antiferromagnetism in the underdoped square antiferromagnets, including the doping dependence of the incommensurate peak position and the energy dependence of the amplitude of these peaks. Since the strong electron correlations are present in both doped square and triangular antiferromagnets, it is expected that the unconventional incommensurate antiferromagnetism existing in the doped square antiferromagnet may also be seen in the doped triangular antiferromagnet. In this paper, the purpose is to apply the successful approach [13] for the doped square lattice antiferromagnet to triangular lattice. We hope that the information from the present work may induce further experimental works in doped antiferromagnets on the non-square lattice. As in the doped square antiferromagnet, the essential physics of the doped triangular antiferromagnet is well described by the t-J model on the triangular lattice, H = −t ∑ iη̂σ C iσCi+η̂σ + h.c.− μ ∑