Electrically charged particles, such as the electron, are ubiquitous. In contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches (see ref. 1 for example). We pursue an alternative strategy, namely that of realizing them not as elementary but rather as emergent particles-that is, as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice: the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This would account for a mysterious phase transition observed experimentally in spin ice in a magnetic field, which is a liquid-gas transition of the magnetic monopoles. These monopoles can also be detected by other means, for example, in an experiment modelled after the Stanford magnetic monopole search.

Sources of magnetic fields-magnetic monopoles-have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes-classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

The spin ice compounds Dy2Ti2O7 and Ho2Ti2O7 are highly unusual magnets that epitomize a set of concepts of great interest in modern condensed matter physics: Their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles that arise from the fractionalization of the microscopic magnetic spin degrees of freedom. In this review, we provide an elementary introduction to these concepts and we survey the thermodynamics, statics, and dynamics—in and out of equilibrium—of spin ice from these vantage points. Along the way, we touch on topics such as emergent Coulomb plasmas, observable Dirac strings, and irrational charges. We close with the outlook for these unique materials.

Electrically charged particles, such as the electron, are ubiquitous. By contrast, no elementary particles with a net magnetic charge have ever been observed, despite intensive and prolonged searches 1 . We pursue an alternative strategy, namely that of realising them not as elementary but rather as emergent particles, i.e., as manifestations of the correlations present in a strongly interacting many-body system. The most prominent examples of emergent quasiparticles are the ones with fractional electric charge e/3 in quantum Hall physics 2 . Here we show that magnetic monopoles do emerge in a class of exotic magnets known collectively as spin ice 3,4,5 : the dipole moment of the underlying electronic degrees of freedom fractionalises into monopoles. This enables us to account for a mysterious phase transition observed experimentally in spin ice in a magnetic field 6,7 , which is a liquid-gas transition of the magnetic monopoles. These monopoles can also be detected by other means, e.g., in an experiment modelled after the celebrated Stanford magnetic monopole search 8 .