Magnetic Frustration

Abstract: Frustration, or the inability to simultaneously satisfy all interactions, frequently lead to a macroscopically degenerate ground state, as well as exotic excitations above this ground state. The spin ice family of materials, with rare-earth ions residing on the pyrochlore lattice of corner-sharing tetrahedra, is a prime example of this phenomenology. The ground state maps onto Pauling's celebrated disordered proton ground state in water ice, and the excitations share many properties with the fundamental magnetic monopole proposed by Dirac in 1931. With the strongest interactions frustrated small perturbations may, at very low temperature, cause a recovery of the lost entroy through a non-trivial ordering of the material. In addition, we have found magnetic analogues of the well-known special temperatures in classical gases such as the Joule-Thompson temperature, which underpins a vast low-temperature technology. I will review the theory and experiments that describe the low-temperature behavior of the spin ice materials including the monopole-like excitations, degenerate ground state and possible eventual fate of the lost entropy.