Bose–Einstein condensation in magnetic materials

Bose–Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In magnetic insulators, the magnetic properties are due to the unpaired shell electrons that have half-integer spin. However, in some magnetic compounds (e.g., TlCuCl3) two Cu2+ ions are antiferromagnetically coupled to form a spin singlet with total spin S=0S=0, separated by an energy gap from the excited triplet states with total spin S=1S=1. In such dimer compounds, Bose–Einstein condensation becomes possible when the energy of one of the triplet components intersects the ground-state singlet, resulting in long-range magnetic order; this transition represents a quantum critical point at which Bose–Einstein condensation occurs. Here we summarize recent neutron scattering investigations of the excitation spectrum in TlCuCl3, for which the quantum critical point was realized by the application of both an external magnetic field and hydrostatic pressure. The theoretically predicted gapless Goldstone mode characteristic of the Bose–Einstein condensation of the triplet states was verified.