  Inducing magnetism in graphene holds great promises, such as controlling the
exchange interaction with a gate electrode and generating exotic magnetic
phases. Coating graphene with magnetic molecules or atoms has so far mostly
lead to decreased graphene mobility. In the present work, we show that
Pt-porphyrins adsorbed on graphene lead to an enhanced mobility and to
gate-dependent magnetism. We report that porphyrins can be donor or acceptor,
depending on graphene s initial doping. The porphyrins transfer charge and
ionize around the charged impurities on graphene, decreasing the graphene
doping and increasing its mobility. In addition, ionized porphyrins carry a
magnetic moment. Using the sensitivity of mesoscopic transport to magnetism, in
particular the superconducting proximity effect and conductance fluctuations,
we explore the magnetic order induced in graphene by the interacting magnetic
moments of the ionized porphyrins. Among the signatures of magnetism, we find
two-terminal-magnetoresistance fluctuations with an odd component, a tell-tale
sign of time reversal symmetry breaking at zero field, that does not exist in
uncoated graphene sample. When graphene is connected to superconducting
electrodes, the induced magnetism leads to a gate-voltage-dependent suppression
of the supercurrent, modified magnetic interference patterns, and
gate-voltage-dependent magnetic hysteresis. The magnetic signatures are
greatest for long superconductor graphene superconductor junctions and for
samples with the highest initial doping, compatible with a greater number of
ionized and thus magnetic porphyrins. Our findings suggest that long-range
magnetism is induced through graphene by the ionized porphyrins magnetic
moment. This magnetic interaction is controlled by the density of carriers in
graphene, a tunability that could be exploited in spintronic applications.
