  Spin-manipulated doping with magnetic (Ni) and non-magnetic (Mg) dopants
constitutes the experimental attempts to obtain a singlet ground state system
from the linear chain Heisenberg antiferromagnetic Cu-based $d^{9}$ spin-1/2
trimer compound Ca$_{3}$Cu$_{3}$(PO$_{4}$)$_{4}$ with doublet ground state. The
present study is a first-principles based investigation of the effects of such
doping on the spin-exchange mechanism and electronic structure of the parent
compound. Site-selective doping with zero-spin dopants like Mg is proved to be
more efficient than an integral spin dopant Ni in obtaining a spin-gap system
with singlet ground state, as also observed in the experimental studies. Doping
induced dimerized state is found to be the lowest in ground-state energy.
Calculated spin exchange values along various possible paths resemble nicely
with earlier experimental results.
