Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3

Abstract

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 such compounds (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 (total spin zero), separated by an energy gap from the excited triplet state (total spin one). In these dimer compounds, Bose-Einstein condensation becomes theoretically possible. At a critical external magnetic field, the energy of one of the Zeeman split triplet components (a type of boson) 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 report an experimental investigation of the excitation spectrum in such a field-induced magnetically ordered state, using inelastic neutron scattering measurements of TlCuCl3 single crystals. We verify unambiguously the theoretically predicted gapless Goldstone mode characteristic of the Bose-Einstein condensation of the triplet states.

Doping-induced spin-manipulation in complex trimer system Ca3Cu3(PO4)4: A density functional investigation

“…[7] Inelastic Neutron scattering experiments and successive analysis of exchange integrals have enabled to obtain an understanding of many such systems where the magnetic interactions within a geometric cluster of atoms are orders of magnitude larger than the inter-cluster interactions. [8,9] The ground-state properties of such systems are very much sensitive of intra and inter cluster interactions. One such quasi-two-dimensional weakly coupled system is the triangle spin-1/2 trimer system La 4 Cu 3 Mo 3 O 12 , which can be well modelled by isolated Heisenberg spin-triangle model.…”

Evidence of a field-induced Berezinskii–Kosterlitz–Thouless scenario in a two-dimensional spin–dimer system

“…The system, crystallizing in a triclinic structure (space group P 1) has a layered structure where planes, containing polymeric chains along the crystallographic a axis, are separated by CF 3 SO 3 À groups, cf. Fig.…”

“…Prominent examples include the Bose-Einstein condensation (BEC) of magnetic triplet excitations (triplons), first observed in TlCuCl 3 (refs 2,3) and subsequently in a variety of related compounds, see ref. 4 for a recent review.…”

Universal postquench coarsening and aging at a quantum critical point

“…A realization for N = 3 is the quantum dimer antiferromagnet TlCuCl 3 shown in Fig. 1(b), which can be driven across the quantum phase transition by either changing pressure 85 or magnetic field 96 .…”