Microscopic aspects of insulating rare-earth pyrochlore magnets

Abstract

In this tutorial, we will review the microscopic aspects of rare-earth magnets relevant for quantum spin ice. We first discuss the single-ion properties of the variety of rare-earth atoms that appear in quantum spin ice candidate materials. Second, we consider the origin of the two-ion exchange interactions, including electric and magnetic multipolar interactions, super-exchange and virtual crystal field mediated interactions. We provide a detailed microscopic basis for the super-exchange interaction and discuss the implications of its multipolar structure for models of rare-earth materials. Finally, we introduce the generic symmetry allowed anisotropic exchange model for rare-earth pyrochlore magnets.