Effective electromagnetism in rare-earth pyrochlore oxides

Rare-earth pyrochlore oxides show a fabulously diverse range of different forms of magnetism, including both classical and quantum spin-liquid phases. Here we develop a unified picture of ordered and disordered states in a pyrochlore magnet with anisotropic exchange interactions. We find that the great majority of these phases can be understood in terms of a simple classical field theory, reminiscent of electromagnetism.