Spin ices are ferromagnetic media that are magnetised in a special way at low temperature. They then form a structure similar to that in water ice.
Water molecules have a dipole moment that can be represented by a vector. When water freezes it forms a structure in which the water molecules are oriented to form a kind of crystal lattice with tetrahedra.
In the case of spin ices, a lattice also forms with tetrahedra which have magnetic moments that are represented in the form of vectors, organised according to the same rules as the dipole moments of water molecules in ice.
As these magnetic moments are related to angular momentums, spins, it is referred to as spin ice and it is this structure that can be seen in the diagram below. The rule for forming spin ice with a lattice of tetrahedra is simple: at the vertices of the tetrahedra there must always be two spins pointing inwards and two others pointing outwards. This can easily be seen in the diagram below.
In 2009 magnetic monopoles were discovered in a certain spin ice.
Analogy between the structure of ice and a spin ice. Credit: Nature