Spin Ice

Geometric frustration usually arises in systems that comprise magnetic moments (spins) which reside on the sites of a lattice made up of elementary triangular or tetrahedral units and which interact via antiferromagnetic nearest-neighbor exchange. Albeit much less common, geometric frustration can also arise in systems with strong non-collinear single-ion easy-axis (Ising-like) anisotropy and ferromagnetically} coupled spins. This is what happens in some pyrochlore oxide materials where Ising-like magnetic rare earth moments (Ho$^{3+}$, Dy$^{3+}$) sit on a lattice of corner-shared tetrahedra and are coupled via effectively ferromagnetic (dipolar) interactions. These systems possess a macroscopic number of quasi-degenerate classical ground states and display an extensive low-temperature entropy closely related to the extensive proton disorder entropy in common water ice. For this reason, these magnetic systems are called {\it spin ice}. This chapter reviews the essential ingredients of spin ice phenomenology in magnetic pyrochlore oxides.