Magnetism and Colossal Negative Magnetoresistance

I discuss recent experimental data concerning ferromagnetism, a metal-insulator transition and colossal negative magnetoresistance in Eu_x Ca_{1-x} B_6 collected in the group of my colleague H.-R. Ott at ETH Zurich. I then propose a phenomenological model enabling me to interpret those data. In connection with this model, I discuss mathematical problems related to itinerant ferromagnetism (Zener's mechanism) and Anderson localization caused by random exchange interactions between electrons in a conduction band and localized spins. I indicate solutions to these problems and show how such solutions qualitatively explain the experimental data.