The spin response functions for a doped strongly correlated quantum Heisenberg antiferromagnet, in the form of a t–J model, on low-dimensional lattices have been explored. In particular, the spin stiffness constant and the spin diffusion coefficient have been calculated as functions of doping concentration by different approaches for this model on a chain and on a square lattice. The occurrences of various possible magnetic phases, namely with long range and short range orders, and also a novel paramagnetic phase, have been predicted at zero temperature. Our conclusions regarding the phase diagram agree remarkably well with those from other recent theoretical approaches. Our results are discussed in the light of experimental results from the cuprates.

The generalized spin stiffness constant for a doped quantum antiferromagnet has been investigated both analytically and numerically as a function of doping concentration at zero temperature, based on the strongly correlated t-J model on two-dimensional square lattice. The nature of the theoretical dependence of the stiffness constant on doping shows a striking similarity with that of the effective exchange constant, obtained from the combination of other theoretical and experimental techniques in the low doping region. This correspondence once again establishes that spin stiffness can very well play the role of an effective exchange constant even in the strongly correlated semi-itinerant systems. Our theoretical plot of the stiffness constant against doping concentration in the whole doping region exhibits the various characteristic features like a possible crossover in the higher doping regions and persistence of short range ordering even for very high doping with the complete vanishing of spin stiffness occurring only close to 100% doping. Our results receive very good support from various other theoretical approaches and also brings out a few limitations of some of them. Our detailed analysis highlights the crucial importance of the study of spin stiffness for the proper understanding of magnetic correlations in a semi-itinerant magnetic system described by the strongly correlated t-J model. Moreover, our basic formalism can also be utilized for determination of the effective exchange constant and magnetic correlations for itinerant magnetic systems, in general in a novel way.

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A theoretical study has been carried out to analyze the available results from the inelastic neutron scattering experiment performed on a quasi-two dimensional spin-1 2 ferromagnetic material K 2 CuF 4 . Our formalism is based on a conventional semi-classical like treatment involving a model of an ideal gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results for dynamical structure functions for our model corresponding to spin-1 2 , show occurrence of negative values in a large range of energy transfer even encompassing the experimental range, when convoluted with a realistic spectral window function. This result indicates failure of the conventional theoretical framework to be applicable to the experimental situation corresponding to low spin systems. A full quantum formalism seems essential for treating such systems. PACS: 78.70.Nx-inelastic neutron scattering in condensed matter, 75.10.Jm-Heisenberg model, 75.30.Kz-Kosterlitz-Thouless transition in magnetic systems *

The possibility of existence of topological excitations in the anisotropic quantum Heisenberg model in one and two spatial dimensions is studied using coherent state method. It is found that a part of the Wess-Zumino term contributes to the partition function, as a topological term for ferromagnets in the long wavelength limit in both one and two dimensions. In particular, the XY limit of the two-dimensional anisotropic ferromagnet is shown to retain the topological excitations, as expected from the quantum Kosterlitz-Thouless scenario. a) ranjan@boson.bose.res.in b) smr@boson.bose.res.in