2009/03/16 by Michel J. P. Gingras, Gingras, Michel J. P. · 12 citations
Decision Sciences · Physics and Astronomy · #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Personal Information Management and User Behavior #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.0903.2772
33 pages, 6 figures. Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mila
arxiv created 2009/03/16 · openalex publication_date 2009/03/16 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
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 (Ho3+, Dy3+) 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.