Geometrically-frustrated magnetism on triangular and tetrahedral lattices

The combination of simple, nearest neighbor antiferromagnetic interactions and certain lattice symmetries leads to phenomena known broadly as frustration. In such systems, the formation of a collinear magnetic structure cannot occur at low temperature. The material may undergo a phase transition to an unusual magneticallyordered state, or it may not undergo a conventional transition at all-entering a glass-like state as the temperature is lowered.This paper will review recent work, mostly from neutron scattering studies, on three such magnetic materials. CsMnBr3 and CsCoBr3 are XY-like and Ising-like stacked-triangular lattice antiferromagnets, respectively. Both undergo magnetic phase transitions with interesting properties due to the presence of geometricalfrustration within the triangular layers. TD2Mo2O7 is a pyrochlore antiferromagnet, in which the magnetic moments reside on a network of corner-sharing tetrahedra. This material enters a magnetic glass-like state at low temperature.