Ferromagnetism —the ability of materials such as iron to form permanent magnets—arises from the spontaneous alignment of atomic spins when atoms interact with each other. But some magnetic solids, especially ones that are geometrically frustrated, exhibit rich and complex effects of those interactions. The behavior of a solid depends not just on the positions of its atoms but also on their local properties—the electric, magnetic, or rotational degrees of freedom. So when the energetically preferred alignment of magnetic moments in a lattice is incompatible with the underlying crystal geometry, exotic phases can emerge (see the article by Roderich Moessner and Art Ramirez in Physics Today, Physics Today 0031-9228 59 2 2006 24 https://doi.org/10.1063/1.2186278 February 2006, page 24).
One of those phases, spin ice, is a strange magnetic state in a material whose ions reside on the vertices of the pyrochlore lattice, a network of corner-sharing tetrahedra. A strong crystal...