  Recently, porphyrin units have been attached to graphene nanoribbons
(Por-GNR) enabling a multitude of possible structures. Here we report first
principles calculations of two prototypical, experimentally feasible, Por-GNR
hybrids, one of which displays a small band gap relevant for its use as
electrode in a device. Embedding a Fe atom in the porphyrin causes spin
polarization with a spin ground state $S=1$. We employ density functional
theory and nonequilibrium Green's function transport calculations to examine a
2-terminal setup involving one Fe-Por-GNR between two metal-free, small band
gap, Por-GNR electrodes. The coupling between the Fe-$d$ and GNR band states
results in a Fano anti-resonance feature in the spin transport close to the
Fermi energy. This feature makes transport highly sensitive to the Fe spin
state. We demonstrate how mechanical strain or chemical adsorption on the Fe
give rise to a spin-crossover to $S=1$ and $S=0$, respectively, directly
reflected in a change in transport. Our theoretical results provide a clue for
the on-surface synthesis of Por-GNRs hybrids, which can open a new avenue for
carbon-based spintronics and chemical sensing.
