  We study the electronic structure of the Pd-terminated surface of the
non-magnetic delafossite oxide metal PdCoO$_2$. Combining angle-resolved
photoemission spectroscopy and density-functional theory, we show how an
electronic reconstruction driven by surface polarity mediates a Stoner-like
magnetic instability towards itinerant surface ferromagnetism. Our results
reveal how this leads to a rich multi-band surface electronic structure, and
provide spectroscopic evidence for an intriguing sample-dependent coupling of
the surface electrons to a bosonic mode which we attribute to electron-magnon
interactions. Moreover, we find similar surface state dispersions in PdCrO$_2$,
suggesting surface ferromagnetism persists in this sister compound despite its
bulk antiferromagnetic order.
