Pressure-Induced Quantum Phase Transition in the Spin-Liquid TlCuCl3
Ch. Rüegg1, A. Furrer1, D. Sheptyakov1, Th. Strässle2, K. Krämer3, H.-U. Güdel3 and L. Mélési4
Laboratory for Neutron Scattering, ETHZ & PSI, CH-5232 Villigen PSI, Switzerland
Physique des Milieux Condensés, Université Pierre et Marie Curie, F-75252 Paris, France
Department for Chemistry and Biochemistry, University of Berne, Freiestrasse 3, CH-3000 Bern 9, Switzerland
Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9, France
The novel pressure-induced quantum phase transition in the dimer spin-liquid TlCuCl3 has been investigated by
means of elastic and inelastic neutron scattering. The latter demonstrates the softening of the relevant triplet
excitations at the critical pressure pc . The former provides the pressure-temperature phase diagram with long-range
antiferromagnetic order above pc .
The condensation of magnetic quasi-particles (triplet pressure-cell (aluminum/TiZr, p=7.3(5) kbar) and a tunable
excitations with total spin S=1) into the non-magnetic He-gas pressure-cell (p<5 kbar).
ground state (singlet with S=0) has been used to explain The pressure-dependence of the singlet-triplet spin energy
novel magnetic ordering phenomena observed in quantum gap Δ(p) has been measured up to p=2.0 kbar. The results
spin systems [1,2]. The neutron scattering results across the are summarized in Fig. 2. We observe a softening of the gap
pressure-induced quantum phase transition and for the novel for increasing 0<p<pc . The INS spectra at pc <p<2 kbar are
ordered phase of the magnetic insulator TlCuCl3 are consistent, within instrumental resolution, with a gapless
consistent with the theoretically predicted two degenerate excitation spectrum and the spin waves at p=7.3 kbar show
"gapless" Goldstone modes, similar to the low-energy spin an increased stiffness.
excitations in the field-induced case. These experimental Neutron diffraction experiments have been performed to
findings complete the field-induced Bose-Einstein observe long-range magnetic order above pc . The Néel
condensate picture and supports the recently proposed field- temperature as a function of pressure TN(p) is extracted
pressure phase diagram common for quantum spin systems from the characteristic temperature-dependence of magnetic
with an energy gap of singlet-triplet nature, see Fig. 1. Bragg peaks. A combined fit to Δ(p) and T N(p) yields
pc =1.07(1) kbar, see Fig. 1.
14 These results clearly demonstrate that dimer quantum spin
5 systems with a spin energy gap of singlet-triplet nature can
be driven to an ordered phase by external pressure. The
Magnetic field [T]
c driving mechanism for the quantum phase transition is
8 2 hereby the change in the exchange interactions closing the
e spin gap at p c . A detailed discussion of the present study can
6 b 0 be found in Ref. .
-0.5 0.0 0.5
AF Momentum (0 qk 0) [r.l.u]
2 pc=1.07(1) kbar 10
a SL d
0.00 0.50 1.00 1.50 8.00 0.6
Pressure [kbar] 6
0.4 Δ(p), T=1.85 K 4
Figure 1: Magnetic field versus pressure phase diagram for
the dimer compound TlCuCl 3 at T=0 K. A square root phase 0.2
SL AF 2
boundary separates the spin-liquid phase (SL) from the
antiferromagnetic phase (AF). Insets: Spin dynamics around
the AF zone center , Q=q+τ=(0 qk 0)+(0 4 0) in 0 0
0 1 2 3 4 5
reciprocal lattice units [r.l.u.]. Common scale for (a)-(e), Pressure [kbar]
possible anisotropy gaps are not considered. (a) Degenerate
triplet modes. (b) Zeeman split triplet modes at Hc . (c) Spin Figure 2: Pressure-induced quantum phase transition in
dynamics in the field-induced ordered phase . (d) TlCuCl3 between spin-liquid (SL) and antiferromagnetic
Degenerate and linear triplet modes close the spin energy (AF) phase. Singlet-triplet gap Δ(p) and Néel temperature
gap at the critical pressure pc . (e) Spin dynamics in the TN(p) measured at Q=(0 0 1) r.l.u.
pressure-induced ordered phase . Two degenerate
transverse Goldstone modes (solid line) and a longitudinal  M. Matsumoto et al., Phys. Rev. B 69, 054423 (2004).
amplitude mode (dashed line) are expected .  Ch. Rüegg et al., Nature 423, 62 (2003).
 Ch. Rüegg et al., Phys. Rev. Lett. 93, 257201 (2004).
Elastic and inelastic neutron scattering experiments have
been performed on the triple-axis spectrometer TASP
(SINQ, PSI) to investigate the novel pressure-induced Work fully performed at SINQ
quantum phase transition in TlCuCl3. Single crystals Proposal-number: II/04-S100, II/03-S59
(sample masses 0.5 g and 2.0 g) were mounted in a clamp Instruments: TASP