Magnetic Frustration in Spinels, Spin Ice Compounds, A 3 B 5 O 12 Garnet, and Multiferroic Materials

Abstract Frustrated magnets are materials in which localized magnetic moments, or spin, interact through competing exchange interactions that cannot be simultaneously satisfied, giving rise to a large degeneracy of the system ground state. Study of frustration began with antiferromagnets, in which frustration usually has a simple geometric origin. In addition to the fact that real magnetic materials are often frustrated due to several kinds of interactions, frustrated spin systems have their own interest in statistical mechanics. Recent studies show that many established statistical methods and theories have encountered many difficulties in dealing with frustrated systems. Since the mechanisms of many phenomena are not understood in real system (disordered systems, systems with long‐range interaction, three‐dimensional systems, etc.), it is worth to search for the origins of those phenomena in exactly solved systems. These exact results will help to understand qualitatively the behavior of real systems that are in general much more complicated. We survey how the discovery of new materials and improved experimental probes, together with complementary advances in theory, have reinvigorated the study of spin liquids and frustrated magnetism in general. We begin with several concepts in magnetic frustration: Geometric Frustration in Simple Atomic Systems, Fluctuations of the Spins in a Spin Liquid–Classical or Quantum, Spin Vice. After describing their basic physics, we discuss the experimental situation and Interesting Magnetic Frustrated Materials: Highly Frustrated Magnetism in Spinels, Spin Ice Compounds: Ho 2 Ti 2 O 7 and Dy 2 Ti 2 O 7 , A 3 B 5 O 12 Garnet Structure, and Magnetic Frustration in Multiferroic Materials.