Fig. 7-13 Pressure-induced quantum phase transition between the dimer phase and the magnetically ordered phase

Fig. 7-14 Temperature dependence of the magnetic Bragg scattering intensities from TlCuCl3 at P=1.48 GPa

There are magnetic systems in which the magnetism can be interpreted as the ordering of an ensemble of magnetic moment vectors. These systems are generally known as "classical spin systems." On the other hand, many "quantum spin systems" have also been discovered recently. In quantum spin systems, novel magnetism appears as a consequence of strong quantum fluctuations. The title compound Thallium Copper Trichloride (TlCuCl3) has a "spin gap," wherein magnetic order does not appear even at T=0K. The spin gap cannot be understood in terms of classical spin systems. Quite recently, we have observed pressure-induced magnetic quantum phase transitions in the spin gap system TlCuCl3. TlCuCl3 has a crystal structure composed of chemical dimers of Cu2+ ions, which have a spin of ½. Due to strong intra-dimer antiferromagnetic exchange interactions, the ground state of this system is a spin singlet with an excitation gap. What happens to the dimer singlet ground state under hydrostatic pressure? When hydrostatic pressure is applied to a dimer system, the distance between the dimers is reduced so that inter-dimer interactions become larger. Thus, if inter-dimer correlations develop significantly, the ground state may change from a spin gap state to a magnetically ordered state. Such an effect is a quantum phase transition from the dimer phase to the magnetically ordered phase (Fig. 7-13). In general, magnetic ordering can be observed through magnetic Bragg reflections. In this way we have observed a pressure-induced magnetic ordering in TlCuCl3 below TN=16.9K at the hydrostatic pressure P=1.48 GPa, as shown in Fig. 7-13. We have also observed another magnetic phase transition at TSR=10K by means of polarized neutron scattering experiments, as shown in Fig. 7-14. Using polarized neutron scattering, the spin components in and out of the scattering plane (in this case <Sac> and <Sb>, respectively) can be completely separated by measuring the spin-flip and non-spin-flip scatterings. From these properties, we have been able to conclude that this additional transition is associated with spin reorientation. Pressure-induced magnetic quantum phase transitions can be also interpreted as follows. The increase of the interdimer exchange interactions due to the applied pressure widens out the dispersion relation of the excited triplets. At some point the spin gap may vanish so that the ground state becomes magnetic. This mechanism is the same as that of magnetic field-induced quantum phase transitions in spin gap systems, in which the Zeeman splitting of the energy dispersion induces a vanishing of the spin gap. Because it has also been found that a magnetic field-induced quantum phase transition can be interpreted as a "Bose-Einstein condensation (BEC) of magnons" in TlCuCl3, the pressure-induced magnetic quantum phase transition may be also identified as a BEC of magnons. This is a problem for future investigation.

Reference A. Oosawa et al., Pressure-Induced Successive Magnetic Phase Transitions in the Spin Gap System TlCuCl3, J. Phys. Soc. Jpn., 73, 1446 (2004).

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