The recent observation [Oosawa et al. J. Phys. : Condens. Matter 11, 265 (1999)] of the field-induced Néel ordering in a spin-gap magnetic compound TlCuCl3 is interpreted as a Bose-Einstein Condensation of magnons. A mean-field calculation based on this picture is shown to describe well the temperature dependence of the magnetization. The present system opens a new area for studying Bose-Einstein condensation of thermodynamically large number of particles in a grand-canonical ensemble.PACS number 75.10.Jm

The temperature and field variations of the magnetization have been measured for which has a singlet ground state with an excitation gap. It is found that undergoes three-dimensional ordering in magnetic fields. The phase boundaries between the paramagnetic and ordered states are determined for and . The phase boundaries for these field directions coincide when normalized by the g-factor. The excitation gap at zero temperature is re-evaluated as .

Neutron elastic scattering experiments have been performed on the spin gap system TlCuCl 3 in magnetic fields parallel to the b-axis. The magnetic Bragg peaks which indicate the fieldinduced Néel ordering were observed for the magnetic field higher than the gap field H g ≈ 5.5 T at Q = (h, 0, l) with odd l in the a * − c * plane. The spin structure in the ordered phase was determined. The temperature and field dependence of the Bragg peak intensities and the phase boundary obtained were discussed in connection with a recent theory which describes the field-induced Néel ordering as a Bose-Einstein condensation of magnons.KEYWORDS: TlCuCl 3 , spin gap, field-induced magnetic ordering, spin structure, neutron elastic scattering, BoseEinstein condensation of magnonsThe singlet ground state with the excitation gap (spin gap) is a notable realization of the macroscopic quantum effect in quantum spin systems. When a magnetic field is applied in the spin gap system, the gap Δ is suppressed and closes completely at the gap field H g = Δ/gμ B . For H > H g the system can undergo magnetic ordering due to three-dimensional (3D) interactions. Such field-induced magnetic ordering was studied first for Cu(NO 3 ) 2 · 5 2 H 2 O. 1) However, the magnetic properties near H = H g have not been investigated because of the very low ordering temperature, the maximum of which is 0.18 K. Recently, the study of fieldinduced magnetic ordering has been revived, because the spin gap has been found in many quantum spin systems. Field-induced 3D ordering has been observed in several quasi-one-dimensional spin gap systems. [2][3][4][5][6] This paper is concerned with field-induced magnetic ordering in TlCuCl 3 . This compound has a monoclinic structure (space group P 2 1 /c). 7) TlCuCl 3 contains planar dimers of Cu 2 Cl 6 , in which Cu 2+ ions have spin-1 2 . These dimers are stacked on top of one another to form infinite double chains parallel to the crystallographic aaxis. These double chains are located at the corners and center of the unit cell in the b−c plane, and are separated by Tl + ions. The magnetic ground state is the spin singlet with the excitation gap Δ/k B ≈ 7.5 K. 8, 9) The magnetic excitations in TlCuCl 3 were investigated by Oosawa et al., 10) who found that the lowest excitation occurs at Q = (0, 0, 1) and its equivalent reciprocal points, as observed in KCuCl 3 . 11, 12) The origin of the gap is the strong antiferromagnetic interaction J = 5.26 meV on the planar dimer Cu 2 Cl 6 in the double chain. The * E-mail: tanaka@lee.phys.titech.ac.jp neighboring dimers couple magnetically along the chain and in the (1, 0, −2) plane.Our previous magnetic measurements revealed that TlCuCl 3 undergoes 3D magnetic ordering in magnetic fields higher than the gap field H g ≈ 5.5 T. 9) The magnetization exhibits a cusplike minimum at the ordering temperature T N . The phase boundary on the temperature vs field diagram is independent of the field direction when normalized by the g-factor, and can be represented by the power lawwith φ = 2.2...

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The field induced magnetic phase transitions of Cs 2 CuBr 4 were investigated by means of magnetization process and neutron scattering experiments. This system undergoes magnetic phase transition at Neél temperature T N = 1.4 K at zero field, and exhibits the magnetization plateau at approximately one third of the saturation magnetization for the field directions H b and H c. In the present study, additional symptom of the two-third magnetization plateau was found in the field derivative of the magnetization process. The magnetic structure was found to be incommensurate with the ordering vector Q = (0, 0.575, 0) at zero field. With increasing magnetic field parallel to the c-axis, the ordering vector increases continuously and is locked at Q = (0, 0.662, 0) in the plateau field range 13.1 T < H < 14.4 T. This indicates that the collinear up-up-down spin structure is stabilized by quantum fluctuation at the magnetization plateau. a c b Figure 2. Antiferromagnetic interactions J 1 and J 2 within the bc-plane. The open circles denote Cu 2+ -ions.