Half metals: from formal theory to real material issues.

At the basic level of collinear spin density functional theory, half metallic ferromagnets represent a fundamentally different state of matter: for low-energy physics the spin degree of freedom is absent, although the system is spin polarized. This makes such systems highly attractive for spintronics applications, but also introduces fundamental new phenomena such as a superconducting state in which the concept of 'spin-pairing' never appears. A fully relativistic theory introduces spin-orbit coupling and destroys the precise aspect of half metallicity; does this make 'half metals' a half truth? Obviously not in any real sense: spin-orbit coupling arises as a perturbative effect, and although necessitating reconsideration from the formal viewpoint, leaves half metallicity as a qualitatively distinct state. We provide a simple model that suggests that in appropriate circumstances this qualitative distinction may even survive strong spin-orbit coupling.