  In this paper, we have done a comparative study of electronic and magnetic
properties of iron phthalocyanine (FePc) and cobalt phthalocyanine (CoPc)
molecules physisorbed on monolayer of MoS$_2$ and graphene by using density
functional theory. Various different types of physisorption sites have been
considered for both surfaces. Our calculations reveal that the $M$Pc molecules
prefer the S-top position on MoS$_2$. However, on graphene, FePc molecule
prefers the bridge position while CoPc molecule prefers the top position. The
$M$Pc molecules are physisorbed strongly on the MoS$_2$ surface than the
graphene ($\sim$ 2.5 eV higher physisorption energy). Analysis of magnetic
properties indicates the presence of strong spin dipole moment opposite to the
spin moment and hence a huge reduction of effective spin moment can be
observed. Our calculations of magnetic anisotropy energies using both
variational approach and $2^{nd}$ order perturbation approach indicate no
significant changes after physisorption. In case of FePc, an out-of-plane easy
axis and in case of CoPc, an in-plane easy axis can be seen. Calculations of
work function indicate a reduction of MoS$_2$ work function $\sim$ 1 eV due to
physisorption of $M$Pc molecules while it does not change significantly in case
of graphene.
