Competing ferro- and antiferromagnetic exchange drives shape-selective $$\hbox{Co}_3\hbox{O}_4$$ nanomagnetism

We have synthesized three different shapes of [Formula: see text] nanoparticles to investigate the relationships between the surface Co[Formula: see text] and Co[Formula: see text] bonding quantified by exploiting the known exposed surface planes, terminations, and coordiations of [Formula: see text] nanoparticle spheres, cubes and plates. Subsequently this information is related to the unusual behaviour observed in the magnetism. The competition of exchange interactions at the surface provides the mechanism for different behaviours in the shapes. The cubes display weakened antiferromagnetic interactions in the form of a spin-flop that occurs at the surface, while the plates show distinct ferromagnetic behaviour due to the strong competition between the interactions. We elucidate the spin properties which are highly sensitive to bonding and crystal field environments. This work provides a new window into the mechanisms behind surface magnetism.