Field-induced three-dimensional magnetic ordering in the spin-gap system

Oosawa, Akira; Ishii, M.; Tanaka, Hidekazu

doi:10.1088/0953-8984/11/1/021

Cited by 192 publications

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“…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.…”

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

et al. 2001

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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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“…9. Since a precise structural analysis for TlCuCl 3 has not been reported, we performed the single-crystal X-ray diffraction.…”

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

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“…For example, it results in a discontinuous drop in the magnetization at the critical point as we increase the temperature, whereas we only see a dip in experiments. 47 Another apparent disagreement is of the estimate of the exponent φ. Experiments seemed to indicate a larger value for the exponent φ for the QCP than the HF theory does.…”

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Critical Properties of Condensation of Field‐Induced Triplet Quasiparticles

Kawashima

2005

ChemInform

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A review on the field-induced magnetic ordering is given, together with some results of a quantum Monte Carlo simulation focused on the critical behevior near the quantum critical point.KEYWORDS: quantum spin system, Heisenberg model, quantum Monte Carlo, XY model, XXZ model, cluster algorithm, loop algorithm, worm algorithm, directed-loop algorithm IntroductionIn this article we discuss phenomena observed in systems with a singlet ground state with triplet excitations separated by a finite spin gap. The focus of researchers' attention has been on the magnetic phase transition induced by a magnetic field and/or a pressure. While the field-(or pressure-) induced magnetic ordering were observed in various materials, the character of the phase transition, in particular the one at the quantum critical point (QCP) seems to be insensitive to the the nature of the ground state and to the origin of the gap. In one class of materials, localized magnetic spins are bound strongly in pairs to form singlet dimers, and the inter-dimer interaction is not strong enough to induce any long-range magnetic ordering. In these materials, the excited states consist of excitations of quasiparticles, recently often referred to as tripletons or triplons. They originate from the triplet states at each site. The magnetic ordering in the dimer systems with a sufficiently strong magnetic field was suggested based on a mean-field theory. 1, 2 Later, two possibilities were suggested 3 depending on the relative strength of the repulsive interaction among the quasiparticles and their kinetic energy. If the kinetic term dominates, the system may undergo a condensation transition as suggested by the mean-field theory 1, 2 and later also by the Hartree-Fock (HF) theory with the bosonic representation. 4 On the other hand, when the repulsive force dominates, the ordered state is the super lattice where the quasiparticles are located periodically to form a lattice with a larger unit cell than that of the original lattice, which gives rise to magnetization plateaus in the magnetization-field curve. This scenario is realized in materials for which the effective dimer-dimer couplings vanish due to the cancellation among the exchange couplings and higher order interactions play essential roles. 5 A well-known example is SrCu 2 (BO 3 ) 2 . 6-8 In the rest of the present article, however, we only discuss the first case, i.e., the case where the kinetic-term is dominant.

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“…In particular, a class of spin-gapped antiferromagnets has provided rich macroscopic quantum phenomena such as spin-Peierls transition and impurity-induced magnetic ordering in CuGeO 3 , 2,3,4,5 and Bose-Einstein condensation of magnons in TlCuCl 3 . 6,7,8 Microscopic aspects of the spin-gapped phase in lowdimensional antiferromagnets have been extensively discussed on the basis of the antiferromagnetic (AFM) Heisenberg model. In general, a spin gap is defined as the energy difference between singlet ground and triplet first-excited states.…”

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Spin-orbital gap of multiorbital antiferromagnet with geometrical frustration

Onishi

Hotta

2007

Phys. Rev. B

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In order to discuss the spin-gap formation in a multiorbital system, we analyze an eg-orbital Hubbard model on a geometrically frustrated zigzag chain by using a density-matrix renormalization group method. Due to the appearance of a ferro-orbital arrangement, the system is regarded as a one-orbital system, while the degree of spin frustration is controlled by the spatial anisotropy of the orbital. In the region of strong spin frustration, we observe a finite energy gap between ground and first-excited states, which should be called a spin-orbital gap. The physical meaning is clarified by an effective Heisenberg spin model including correctly the effect of the orbital arrangement influenced by the spin excitation.

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Field-induced three-dimensional magnetic ordering in the spin-gap system

Cited by 192 publications

References 24 publications

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

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

Critical Properties of Condensation of Field‐Induced Triplet Quasiparticles

Spin-orbital gap of multiorbital antiferromagnet with geometrical frustration

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Field-induced three-dimensional magnetic ordering in the spin-gap system

Cited by 192 publications

References 24 publications

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

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

Critical Properties of Condensation of Field‐Induced Triplet Quasiparticles

Spin-orbital gap of multiorbital antiferromagnet with geometrical frustration

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

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