Magnetic relaxation in rare-earth oxide pyrochlores

A theory of magnetic relaxation is developed for geometrically frustrated three-dimensional magnets that can be described by an antiferromagnetic Ising model. These magnetic materials are exemplified by some of the recently synthesized rare-earth oxide pyrochlores, such as Dy₂Ti₂O₇, Ho₂Ti₂O₇, or Yb₂Ti₂O₇. A model based on an analogy between the spin ordering in Ising magnets and proton ordering in ice is proposed. In this model, magnetic point defects treated as noninteracting quasiparticles characterized by well-defined energies, mobilities, and effective magnetic charges play a fundamental role analogous to that of ion defects in the physics of ice or by electrons and holes in semiconductors. The proposed model is used to derive expressions for magnetic susceptibility as a function of frequency and temperature.