Quantum magnetism on a frustrated lattice: rare earth pyrochlores

 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.