Bose-Einstein condensation denotes the formation of a collective quantum ground state of identical particles with integer spin or intrinsic angular momentum. In compounds like KCuCl₃ and TlCuCl₃, two Cu²⁺ ions are antiferromagnetically coupled to form a dimer in a crystalline network: the dimer ground state is a spin singlet, separated by an energy gap from the excited triplet state.
At a critical external magnetic field, the energy of one of the Zeeman split 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.

This work was carried out in the groups of Prof. Hans Ulrich Güdel / Dr. Karl Krämer.

References:

• Ch. Rüegg, N. Cavadini, A. Furrer, H.-U. Güdel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, P. Vorderwisch;
  "Bose-Einstein condensation of the triplet states in the magnetic insulator TlCuCl₃"
  Nature, 423, 62-65, (2003); doi:10.1038/nature01617.