Observation of Bose–Einstein Condensation of Triplons in Quasi 1D Spin-Gap System Pb2V3O9

Waki, Takeshi; Morimoto, Yuko; Michioka, Chishiro; Kato, Masaki; Kageyama, Hiroshi; Yoshimura, Kazuyoshi; Nakatsuji, Satoru; Sakai, Osamu; Maeno, Y.; Mitamura, Hiroyuki; Goto, T.

doi:10.1143/jpsj.73.3435

Cited by 40 publications

(31 citation statements)

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“…This compound is composed of isolated spin dimer chains of V 4+ ͑S =1/ 2͒ ions, with no evidence of a bulk phase transition down to 20 mK in zero field. In applied fields, the Zeeman splitting of the excited triplet state reduces the singlet-triplet excitation energy and induces a transition to a possible BEC that was first documented by Waki et al 11 However, the initial reports on this material were made on polycrystalline samples and the power-law description of the phase boundary could not confirm that a BEC-type state indeed exists. We have recently grown single crystals of Pb 2 V 3 O 9 to resolve this controversy, characterizing the magnetic properties through dc susceptibility, torque-magnetometry, heat-capacity, and muon-spinrelaxation ͑SR͒ experiments.…”

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confidence: 93%

Possible Bose-Einstein condensate of magnons in single-crystallinePb2V3O9

Conner

Zhou

et al. 2010

Phys. Rev. B

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Possible Bose-Einstein condensate of magnons in single-crystallinePb2V3O9

Conner

Zhou

et al. 2010

Phys. Rev. B

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“…Equation (2) or (3) gives the critical behavior near the QCP characteristic of the magnon BEC. The BEC of magnons has been studied extensively in many gapped spin systems [5][6][7][8][9][10][11][12] and the power law behavior of the phase boundary was confirmed.TlCuCl 3 is an S ¼ 1=2 interacting spin dimer system in which a chemical dimer Cu 2 Cl 6 forms a antiferromagnetic spin dimer. The interactions between neighboring dimers are three-dimensional.…”

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confidence: 99%

Magnetic-Field Induced Bose–Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl₃

et al. 2008

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Magnetization measurements were performed to investigate the critical behavior of the field-induced magnetic ordering in gapped spin system TlCuCl 3 . The critical density of the magnons was obtained as a function of temperature and the magnon-magnon interaction constant was evaluated. The experimental phase boundary for T < 5 K agrees almost perfectly with the magnon Bose-Einstein condensation (BEC) theory based on the Hartree-Fock approximation with realistic dispersion relations. The phase boundary can be described by the power law ½H N ðTÞ À H c / T . With decreasing fitting temperature range, the critical exponent decreases and converges at BEC ¼ 3=2 predicted by the magnon BEC theory.KEYWORDS: TlCuCl 3 , spin dimer system, magnons, quantum phase transition, Bose-Einstein condensation, critical behavior DOI: 10.1143/JPSJ.77.013701Quantum spin system composed of antiferromagnetic spin dimer often shows a gapped singlet ground state. In an external magnetic field exceeding the energy gap Á, S z ¼ 1 component of the spin triplet is created in the system. The field-induced S z ¼ 1 component has the characteristics of boson and is called magnon or triplon. Magnons move to neighboring dimers and interact with one another due to the transverse and longitudinal components of the interdimer exchange interactions, respectively. Consequently, the spin dimer system in the magnetic field can be represented as an interacting boson system. 1) Magnons can undergo BoseEinstein condensation (BEC) in a magnetic field higher than the critical field H c ¼ Á=g B , which leads to field-induced magnetic ordering (FIMO).2,3) Nikuni et al.2) discussed the FIMO observed in TlCuCl 3 , 4) applying the Hartree-Fock (HF) approximation to a simplified modelwhere " k is the kinetic energy determined by the curvature of the dispersion around the lowest excitation, the chemical potential given by ¼ g B ðH À H c Þ, U the interaction constant and N the number of dimers. If a parabolic isotropic dispersion relation " k ¼ ðh " kÞ 2 =2m is used, then the critical chemical potential is given byThis relation leads to the phase boundary described by the power lawwith critical exponent BEC ¼ 3=2, 2) where H N ðTÞ is the transition field at temperature T. A point given by T ¼ 0 and H ¼ H c on the temperature vs field diagram denotes the quantum critical point (QCP). Equation (2) or (3) gives the critical behavior near the QCP characteristic of the magnon BEC. The BEC of magnons has been studied extensively in many gapped spin systems [5][6][7][8][9][10][11][12] and the power law behavior of the phase boundary was confirmed.TlCuCl 3 is an S ¼ 1=2 interacting spin dimer system in which a chemical dimer Cu 2 Cl 6 forms a antiferromagnetic spin dimer. The interactions between neighboring dimers are three-dimensional. The lowest excitation occurs at Q ¼ ð0; 0; 1Þ and its equivalent reciprocal points. [13][14][15] The magnitude of the excitation gap is Á=k B ¼ 7:5 K. 4,16) In the previous magnetization and specific heat measurements in magnetic fields on Tl...

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“…Furthermore, it is found that every κ(14T)/κ(0) clearly exhibits a kink at a low temperature around 4 K corresponding to the BEC transition temperature shown by arrows in Figs. 2(d)-(f) [3,4,6,7]. This indicates that the BEC transition temperature is independent of the applied-field direction and that the thermal conductivity is more or less enhanced at low temperatures in the BEC state.…”

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confidence: 99%

“…1, VO 6 octahedra are connected with each other by sharing an oxygen at the corner along the [101] direction, forming a S = 1/2 bond-alternating spin-chain. It has been reported that the ground state is of spin-singlets with a spin gap ∆ ∼ 7 K and that the spin gap disappears by the application of magnetic field, followed by the appearance of a BEC state of triplons [3].The anisotropy of the magnetic interaction of the one-dimensional (1D) spin system Pb 2 V 3 O 9 is stronger than that of the 3D spin system TlCuCl 3 . Considering that the value of κ triplon is related to the magnitude of the magnetic interaction and that κ phonon is comparatively isotropic, the origin of the enhancement of the thermal conductivity in the BEC state of field-induced…”

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Anisotropic Behavior of Thermal Conductivity in the Bose-Einstein Condensed State of the Bond-Alternating Spin-Chain System Pb₂V₃O₉

Sato¹,

Naruse²,

Kudo³

et al. 2012

J. Phys.: Conf. Ser.

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Abstract.We have systematically measured the thermal conductivity along the [101], [101] and b * directions, κ [101] , κ [101] and κ b * , respectively, of the S = 1/2 bond-alternating spinchain system Pb2V3O9 in magnetic fields parallel and perpendicular to the heat current. It has been found that κ [101] along the spin chains is markedly enhanced in the BEC state, which has been concluded to be due to the enhancement of the thermal conductivity due to triplons. Furthermore, it has been found that the enhancement of κ [101] in the BEC state is more marked in magnetic fields parallel to the [101] direction than perpendicular to the [101] direction. The BEC state may be weakened or broken in magnetic fields perpendicular to the [101] direction on account of the breaking of the rotational symmetry. IntroductionThermal conductivity is recognized as a good probe detecting a change of the spin state in a spin system, because the scattering rate of heat carries, such as electrons, phonons and magnetic excitations, is affected sensitively by the change of the spin state. For example, a drastic enhancement of the thermal conductivity has been observed in the Bose-Einstein condensed (BEC) state of field-induced magnetic excitations, namely, triplons in the three-dimensional (3D) spin-dimer system TlCuCl 3 with the spin quantum number S = 1/2 [1], which is analogous to that observed in the BEC superfluid state of liquid 4 He [2]. However, it has not yet been clarified whether the enhancement in the BEC state is due to thermal conductivity due to phonons, κ phonon , or that due to triplons, κ triplon .The compound Pb 2 V 3 O 9 contains both two nonmagnetic V 5+ ions located in VO 4 tetrahedra and one V 4+ ion with S = 1/2 in VO 6 octahedra in the unit cell. As shown in Fig. 1, VO 6 octahedra are connected with each other by sharing an oxygen at the corner along the [101] direction, forming a S = 1/2 bond-alternating spin-chain. It has been reported that the ground state is of spin-singlets with a spin gap ∆ ∼ 7 K and that the spin gap disappears by the application of magnetic field, followed by the appearance of a BEC state of triplons [3].The anisotropy of the magnetic interaction of the one-dimensional (1D) spin system Pb 2 V 3 O 9 is stronger than that of the 3D spin system TlCuCl 3 . Considering that the value of κ triplon is related to the magnitude of the magnetic interaction and that κ phonon is comparatively isotropic, the origin of the enhancement of the thermal conductivity in the BEC state of field-induced

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Observation of Bose–Einstein Condensation of Triplons in Quasi 1D Spin-Gap System Pb₂V₃O₉

Cited by 40 publications

References 11 publications

Possible Bose-Einstein condensate of magnons in single-crystallinePb2V3O9

Possible Bose-Einstein condensate of magnons in single-crystallinePb2V3O9

Magnetic-Field Induced Bose–Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl₃

Anisotropic Behavior of Thermal Conductivity in the Bose-Einstein Condensed State of the Bond-Alternating Spin-Chain System Pb₂V₃O₉

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Observation of Bose–Einstein Condensation of Triplons in Quasi 1D Spin-Gap System Pb2V3O9

Cited by 40 publications

References 11 publications

Possible Bose-Einstein condensate of magnons in single-crystallinePb2V3O9

Possible Bose-Einstein condensate of magnons in single-crystallinePb2V3O9

Magnetic-Field Induced Bose–Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl3

Anisotropic Behavior of Thermal Conductivity in the Bose-Einstein Condensed State of the Bond-Alternating Spin-Chain System Pb2V3O9

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Observation of Bose–Einstein Condensation of Triplons in Quasi 1D Spin-Gap System Pb₂V₃O₉

Magnetic-Field Induced Bose–Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl₃

Anisotropic Behavior of Thermal Conductivity in the Bose-Einstein Condensed State of the Bond-Alternating Spin-Chain System Pb₂V₃O₉