Quantum magnetism on a frustrated lattice: rare earth pyrochlores

Abstract:

 Why are the pyrochlore crystals R2Ti2O7 "quantum" magnets?  Beginning with this question,this talk will introduce concepts of quantum magnetism on the pyrochlore lattice. The symmetry of the lattice and of quantum mechanical spin states will be described. Using symmetry arguments, the most general form of a spin=1/2 quantum exchange model for the pyrochlore crystal can be written down.  Symmetry considerations also yield a map between rare earth spin states and spin=1/2 states, leading to a universal model of "anisotropic exchange" for rare earth pyrochlores. This model contains four coupling constants, which have been determined experimentally for various rare earth pyrochlores.