  The effective interaction between the itinerant spin degrees of freedom in
the paramagnetic phases of hole doped quantum Heisenberg antiferromagnets is
investigated theoretically, based on the single-band t-J model on 1D lattice,
at zero temperature. The effective spin-spin interaction for this model in the
strong correlation limit, is studied in terms of the generalized spin stiffness
constant as a function of doping concentration. The plot of this generalized
spin stiffness constant against doping shows a very high value of stiffness in
the vicinity of zero doping and a very sharp fall with increase in doping
concentration, signifying the rapid decay of original coupling of
semi-localized spins in the system. Quite interestingly, this plot also shows a
maximum occurring at a finite value of doping, which strongly suggests the
tendency of the itinerant spins to couple again in the unconventional
paramagnetic phase. As the doping is further increased, this new coupling is
also suppressed and the spin response becomes analogous to almost Pauli-like.
The last two predictions of ours are quite novel and may be directly tested by
independent experiments and computational techniques in future. Our results in
general receive good support from other theoretical works and experimental
results extracted from the chains of YBa$_2$Cu$_3$O$_{6+x}$.
