Magnetic excitations in the quantum spin system ${\mathrm{TlCuCl}}_3$

The $S=\frac{1}{2}$ quantum system ${\mathrm{TlCuCl}}_3$ has a nonmagnetic singlet ground state and a finite-energy gap to triplet excited states. At $H_c\sim 6\mathrm{T}$ it undergoes field-induced three-dimensional magnetic ordering. Its dynamical spin properties in zero field were studied by inelastic neutron scattering on single crystals. The elementary spectrum consists of well-defined triplet waves of dimer origin. From the observed energy dispersion, the underlying spin-exchange coupling scheme is rationalized. Appreciable three-dimensional correlations are reported, in accordance with the high-field phase. An antiferromagnetic Heisenberg model in the strong-coupling approximation satisfactorily accounts for the energy and intensity dependence of the triplet excitations in the whole reciprocal space. ${\mathrm{TlCuCl}}_3$ is characterized as a strongly coupled spin system in the vicinity of a quantum critical point. A comparison with the parent compound ${\mathrm{KCuCl}}_3$ is proposed.