  Randomness and frustration are considered to be the key ingredients for the
existence of spin glass (SG) phase. In a canonical system, these ingredients
are realized by the random mixture of ferromagnetic (FM) and antiferromagnetic
(AF) couplings. The study by Bartolozzi {\it et al.} [Phys. Rev. B{\bf 73},
224419 (2006)] who observed the presence of SG phase on the AF Ising model on
scale free network (SFN) is stimulating. It is a new type of SG system where
randomness and frustration are not caused by the presence of FM and AF
couplings. To further elaborate this type of system, here we study Heisenberg
model on AF SFN and search for the SG phase. The canonical SG Heisenberg model
is not observed in $d$-dimensional regular lattices for ($d \leq 3$). We can
make an analogy for the connectivity density ($m$) of SFN with the
dimensionality of the regular lattice. It should be plausible to find the
critical value of $m$ for the existence of SG behaviour, analogous to the lower
critical dimension ($d_l$) for the canonical SG systems. Here we study system
with $m=2,3,4$ and $5$. We used Replica Exchange algorithm of Monte Carlo
Method and calculated the SG order parameter. We observed SG phase for each
value of $m$ and estimated its corersponding critical temperature.
