Spin Ice

TL;DR

Spin ice refers to magnetic pyrochlore oxides with Ising-like moments on a tetrahedral lattice, exhibiting geometric frustration and extensive low-temperature entropy similar to water ice.

Contribution

This paper reviews the fundamental phenomenology of spin ice in magnetic pyrochlore oxides, highlighting its unique frustration and entropy properties.

Findings

Spin ice systems exhibit macroscopic degeneracy of ground states.

They display extensive residual entropy at low temperatures.

The magnetic behavior is analogous to proton disorder in water ice.

Abstract

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.