Spin ices are geometrically frustrated magnetic systems. While frustration is usually associated with triangular or tetrahedral arrangements of magnetic moments coupled via antiferromagnetic exchange interactions, as in Andersons Ising model, spin ices are frustrated ferromagnets.  It is the very strong local magnetic anisotropy from the crystal field forcing the magnetic moments to point either in or out of a tetrahedron that renders ferromagnetic interactions frustrated in spin ices. Most importantly, it is the long-range magnetostatic dipole–dipole interaction, and not' the nearest-neighbor exchange, that causes the frustration and the consequential two-in, two-out rule that leads to the spin ice phenomenology.
For a tetrahedron in a two-in, two-out state, the magnetization field is divergent-free; there is as much "magnetization intensity" entering a tetrahedron as there is leaving (see figure 3). In such a divergent-free situation, there exists no source or sink for the field. According to Gauss theorem (also known as Ostrogradskys theorem), a nonzero divergence of a field is caused, and can be characterized, by a real number called "charge". In the context of spin ice, such charges characterizing the violation of the two-in, two-out magnetic moment orientation rule are the aforementioned monopoles.
In Autumn 2009, researchers reported experimental observation of low-energy quasiparticles resembling the predicted monopoles in spin ice. A single crystal of the dysprosium titanate spin ice candidate was examined in the temperature range of 0.6–2.0K. Using neutron scattering, the magnetic moments were shown to align in the spin ice material into interwoven tube-like bundles resembling Dirac strings. At the defect formed by the end of each tube, the magnetic field looks like that of a monopole. Using an applied magnetic field, the researchers were able to control the density and orientation of these strings. A description of the heat capacity of the material in terms of an effective gas of these quasiparticles was also presented.
The effective charge of a magnetic monopole, Q (see figure 3) in both the dysprosium and holmium titanate spin ice compounds is approximately  (Bohr magnetons per angstrom). The elementary magnetic constituents of spin ice are magnetic dipoles, so the emergence of monopoles is an example of the phenomenon of fractionalization.
The microscopic origin of the atomic magnetic moments in magnetic materials is quantum mechanical; the Planck constant enters explicitly in the equation defining the magnetic moment of an electron, along with its charge and its mass. Yet, the magnetic moments in the dysprosium titanate and the holmium titanate spin ice materials are effectively described by classical statistical mechanics, and not quantum statistical mechanics, over the experimentally relevant and reasonably accessible temperature range (between 0.05K and 2K) where the spin ice phenomena manifest themselves. Although the weakness of quantum effects in these two compounds is rather unusual, it is believed to be understood. There is current interest in the search of quantum spin ices, materials in which the laws of quantum mechanics now become needed to describe the behavior of the magnetic moments. Magnetic ions other than dysprosium (Dy) and holmium (Ho) are required to generate a quantum spin ice, with praseodymium (Pr), terbium (Tb) and ytterbium (Yb) being possible candidates. One reason for the interest in quantum spin ice is the belief that these systems may harbor a quantum spin liquid, a state of matter where magnetic moments continue to wiggle (fluctuate) down to absolute zero temperature. The theory describing the low-temperature and low-energy properties of quantum spin ice is akin to that of vacuum quantum electrodynamics, or QED. This constitutes an example of the idea of emergence.