Observation of Field-Induced Transverse Néel Ordering in the Spin Gap System TlCuCl₃

Abstract

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...

Field-induced effects of anisotropic magnetic interactions in SrCu2(BO3)2

“…A generic example is the Bose-Einstein condensation of triplets when the field exceeds the critical value at which the excitation energy vanishes. This results in an antiferromagnetic order with the staggered moment perpendicular to the field, as has been observed, e.g., in TlCuCl 3 [2]. Another possibility is the formation of a superlattice of localized triplets due to repulsive interactions, which translates into magnetization plateaus at fractional values of the saturated magnetization.…”

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“…While a quantitative synthesis of theory and experiment in the superconducting materials remains elusive, much progress has been made in describing a number of antiferromagnetic Mott insulators. A number of such insulators have been studied extensively in the past decade, with a few prominent examples being CaV 4 O 9 [1], (C 5 H 12 N 2 ) 2 Cu 2 Cl 4 [2,3,4], SrCu 2 (BO 3 ) 2 [5,6], TlCuCl 3 [7,8,9,10], and Cs 2 CuCl 4 [11,12]. In some cases, it has even been possible to tune these insulators across quantum phase transitions by applied pressure [8] or by an applied magnetic field [3,4,7,9].…”

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“…In absence of anisotropy, this new phase is critical in the purely one-dimensional (1D) case and exhibits long-range order in the presence of a weak 3D coupling. Experimentally, field-induced ordering has been studied for several substances, one of the better understood examples being the dimer material TlCuCl 3 [15,16,17,18].Consider an interacting 3D system of spin-1 2 dimers described by the following Hamiltonian:where J > 0 and J ′ > 0 are the intra-and interdimer exchange couplings, respectively, and H is the external magnetic field directed along the z axis. The vector r labels the dimers located at the sites of a lattice with coordination number Z, and .. denotes summation only over neighboring dimers.…”

“…In absence of anisotropy, this new phase is critical in the purely one-dimensional (1D) case and exhibits long-range order in the presence of a weak 3D coupling. Experimentally, field-induced ordering has been studied for several substances, one of the better understood examples being the dimer material TlCuCl 3 [15,16,17,18].…”