Spin ice

Abstract: A frustrated system is one whose symmetry precludes the possibility that every pairwise interaction (“bond”) in the system can be satisfied at the same time. Such systems are common in all areas of physical and biological science. In the most extreme cases, they can have a disordered ground state with “macroscopic” degeneracy; that is, one that comprises a huge number of equivalent states of the same energy. Pauling9s description of the low-temperature proton disorder in water ice was perhaps the first recognition of this phenomenon and remains the paradigm. In recent years, a new class of magnetic substance has been characterized, in which the disorder of the magnetic moments at low temperatures is precisely analogous to the proton disorder in water ice. These substances, known as spin ice materials, are perhaps the “cleanest” examples of such highly frustrated systems yet discovered. They offer an unparalleled opportunity for the study of frustration in magnetic systems at both an experimental and a theoretical level. This article describes the essential physics of spin ice, as it is currently understood, and identifies new avenues for future research on related materials and models.

Abstract: We are familiar with elementary particles that carry either negative or positive electric charge, such as electrons and protons, but there is no evidence of elementary particles with a net magnetic charge. Magnets tend to come with inseparable north and south poles, and there are no known magnetic monopoles despite concerted efforts to find them. But an intriguing theoretical study now proposes that magnetic monopoles may exist, not as elementary particles, but as emergent particles in exotic condensed matter magnetic systems such as 'spin ice'. The theory, based on an analogy to fractional electric charges seen, for example, in quantum Hall systems in two dimensions, can explain a mysterious phase transition that has been observed experimentally in spin ice. The cover, by Alessandro Canossa, depicts a magnetic monopole (red sphere) emerging from break-up of the dipole moment (arrows) of the underlying electronic degrees of freedom in spin ice. A theoretical study proposes that magnetic monopoles may appear not as elementary but as emergent particles in complex, strongly-correlated magnetic systems such as spin ice, in analogy to fractional electric charges in quantum Hall systems. This theory explains a mysterious phase transition in spin ice that has been observed experimentally. 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 physics2. Here we propose that magnetic monopoles emerge in a class of exotic magnets known collectively as spin ice3,4,5: 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 field6,7, 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 search8.

Abstract: Within the past 20 years or so, there has occurred an explosion of interest in the magnetic behavior of pyrochlore oxides of the type $A_{2}^{3+}$$B_{2}^{4+}$O$_{7}$ where $A$ is a rare-earth ion and $B$ is usually a transition metal. Both the $A$ and $B$ sites form a network of corner-sharing tetrahedra which is the quintessential framework for a geometrically frustrated magnet. In these systems the natural tendency to form long range ordered ground states in accord with the Third Law is frustrated, resulting in some novel short range ordered alternatives such as spin glasses, spin ices and spin liquids and much new physics. This article attempts to review the myriad of properties found in pyrochlore oxides, mainly from a materials perspective, but with an appropriate theoretical context.