The ability to manipulate the surface and interface properties of correlated electron systems underpins the burgeoning field of designer quantum matter. In this context, electronic reconstructions arising from polar interfaces have been widely discussed as a way to drastically modify the interface electronic properties of complex oxide heterostructures [1]. Here, we show that an electronic reconstruction occurs at the polar surfaces of delafossite oxides, an emerging class of oxide materials [2]. Using angle-resolved photoemission, we demonstrate how this leads to a Stoner-instability towards itinerant ferromagnetism at the Pd-terminated surface of the non-magnetic PdCoO₂ [3], thereby stabilising a magnetic environment which does not exist in the bulk. We also show that this occurs for the Pd-terminated surface of PdCrO₂, an antiferromagnet in the bulk, thus leading to a ferromagnetic-antiferromagnetic heterostructure at its surface. For the PdCoO₂ states, we also uncover a strong coupling of the surface electrons with magnons. Our work paves the way for the creation, control and manipulation of magnetic states in oxide surfaces and heterostructures. [1] Hwang et al. Nature Mater. 11, 103 (2012) [2] Mackenzie, Rep. Prog. Phys. 80, 32501 (2017) [3] Mazzola et al., arXiv1710.05392