  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.
