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1

CAVADINI, N., CH RüEGG, A. FURRER, H. U. GüDEL, K. KRäMER, H. MUTKA, A. WILDES, K. HABICHT, and P. VORDERWISCH. "TRIPLET MODES IN A QUANTUM SPIN LIQUID ACROSS THE CRITICAL FIELD." International Journal of Modern Physics B 16, no. 20n22 (August 30, 2002): 3302–5. http://dx.doi.org/10.1142/s0217979202014243.

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S = 1/2 TlCuCl3 is a magnetic insulator with a singlet ground state and a finite spin gap to triplet excited states. At finite fields, the degeneracy of the triplet states is lifted according to the Zeeman interaction term. Field-induced magnetic ordering occurs in TlCuCl3 at the critical field Hc ~ 6 T , when the Zeeman interaction overcomes the spin gap at the antiferromagnetic zone center. A detailed characterization of the elementary excitations realized at H > Hc is obtained by means of inelastic neutron scattering on single crystals. The general framework of field-induced quantum criticality in a three-dimensional spin liquid is illustrated on the complete dynamic range for the first time.
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2

Sirker, Jesko, Alexander Weiße, and Oleg P. Sushkov. "The Field-Induced Magnetic Ordering Transition in TlCuCl3." Journal of the Physical Society of Japan 74, Suppl (January 2005): 129–34. http://dx.doi.org/10.1143/jpsjs.74s.129.

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3

Johannsen, N., A. Oosawa, H. Tanaka, A. Vasiliev, and T. Lorenz. "Uniaxial pressure dependencies of the phase boundary of TlCuCl3." Physica B: Condensed Matter 378-380 (May 2006): 1043–44. http://dx.doi.org/10.1016/j.physb.2006.01.526.

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4

Kato, T., A. Oosawa, K. Takatsu, H. Tanaka, W. Shiramura, K. Nakajima, and K. Kakurai. "Magnetic excitations in the spin gap system KCuCl3 and TlCuCl3." Journal of Physics and Chemistry of Solids 60, no. 8-9 (September 1999): 1125–28. http://dx.doi.org/10.1016/s0022-3697(99)00072-4.

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5

Kudo, K., M. Yamazaki, T. Kawamata, T. Noji, Y. Koike, T. Nishizaki, N. Kobayashi, and H. Tanaka. "Thermal conductivity in the Bose–Einstein condensed state of TlCuCl3." Journal of Magnetism and Magnetic Materials 272-276 (May 2004): 214–15. http://dx.doi.org/10.1016/j.jmmm.2003.12.419.

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6

Takatsu, K., W. Shiramura, H. Tanaka, T. Kambe, H. Nojiri, and M. Motokawa. "ESR of quantum double-spin-chain systems KCuCl3 and TlCuCl3." Journal of Magnetism and Magnetic Materials 177-181 (January 1998): 697–98. http://dx.doi.org/10.1016/s0304-8853(97)00442-3.

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7

Normand, B., M. Matsumoto, O. Nohadani, S. Wessel, S. Haas, T. M. Rice, and M. Sigrist. "Pressure- and field-induced magnetic quantum phase transitions in TlCuCl3." Journal of Physics: Condensed Matter 16, no. 11 (March 4, 2004): S867—S873. http://dx.doi.org/10.1088/0953-8984/16/11/042.

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8

TANAKA, H. "Magnetic ordering under high pressure in the quantum spin system TlCuCl3." Physica B: Condensed Matter 329-333 (May 2003): 697–98. http://dx.doi.org/10.1016/s0921-4526(02)02009-4.

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9

Rüegg, Ch, N. Cavadini, A. Furrer, H. U. Güdel, K. Krämer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch. "Bose–Einstein condensation of the triplet states in the magnetic insulator TlCuCl3." Nature 423, no. 6935 (May 2003): 62–65. http://dx.doi.org/10.1038/nature01617.

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10

Oosawa, A., H. Tanaka, T. Takamasu, H. Abe, N. Tsujii, and G. Kido. "Field-induced Néel ordering in the spin gap systems TlCuCl3 and KCuCl3." Physica B: Condensed Matter 294-295 (January 2001): 34–38. http://dx.doi.org/10.1016/s0921-4526(00)00602-5.

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11

Oosawa, Akira, Kazuhisa Kakurai, Toyotaka Osakabe, Mitsutaka Nakamura, Masayasu Takeda, and Hidekazu Tanaka. "Pressure-Induced Successive Magnetic Phase Transitions in the Spin Gap System TlCuCl3." Journal of the Physical Society of Japan 73, no. 6 (June 15, 2004): 1446–49. http://dx.doi.org/10.1143/jpsj.73.1446.

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12

Goto, Kenji, Masashi Fujisawa, Toshio Ono, Hidekazu Tanaka, and Yoshiya Uwatoko. "Pressure-induced Magnetic Quantum Phase Transition from Gapped Ground State in TlCuCl3." Journal of the Physical Society of Japan 73, no. 12 (December 15, 2004): 3254–57. http://dx.doi.org/10.1143/jpsj.73.3254.

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13

Kuroe, H., A. Oosawa, T. Sekine, F. Yamada, H. Tanaka, and M. Matsumoto. "Anticrossing effect between magnon and phonon in Bose-Einstein condensation phase of TlCuCl3." Journal of Physics: Conference Series 150, no. 4 (March 1, 2009): 042104. http://dx.doi.org/10.1088/1742-6596/150/4/042104.

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14

Tanaka, Hidekazu, Akira Oosawa, Tetsuya Kato, Hidehiro Uekusa, Yuji Ohashi, Kazuhisa Kakurai, and Andreas Hoser. "Observation of Field-Induced Transverse Néel Ordering in the Spin Gap System TlCuCl3." Journal of the Physical Society of Japan 70, no. 4 (April 15, 2001): 939–42. http://dx.doi.org/10.1143/jpsj.70.939.

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15

Kudo, Kazutaka, Mitsuhiro Yamazaki, Takayuki Kawamata, Takashi Noji, Yoji Koike, Terukazu Nishizaki, Norio Kobayashi, and Hidekazu Tanaka. "Drastic Enhancement of Thermal Conductivity in the Bose–Einstein Condensed State of TlCuCl3." Journal of the Physical Society of Japan 73, no. 9 (September 15, 2004): 2358–61. http://dx.doi.org/10.1143/jpsj.73.2358.

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16

Tanaka, H., T. Takatsu, W. Shiramura, T. Kambe, H. Nojiri, T. Yamada, S. Okubo, H. Ohta, and M. Motokawa. "High-frequency high-field ESR of quantum double spin chain systems KCuCl3 and TlCuCl3." Physica B: Condensed Matter 246-247 (May 1998): 545–48. http://dx.doi.org/10.1016/s0921-4526(97)00982-4.

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17

Tanaka, H., W. Shiramura, T. Takatsu, B. Kurniawan, M. Takahashi, K. Kamishima, K. Takizawa, H. Mitamura, and T. Goto. "High-field magnetization processes of quantum double spin chain systems KCuCl3, TlCuCl3 and NH4CuCl3." Physica B: Condensed Matter 246-247 (May 1998): 230–33. http://dx.doi.org/10.1016/s0921-4526(97)00983-6.

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18

VYASELEV, O. "Field-induced magnetic ordering in TlCuCl3: lattice deformation and features of first-order transition." Physica B: Condensed Matter 329-333 (May 2003): 892–93. http://dx.doi.org/10.1016/s0921-4526(02)02572-3.

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19

Rüegg, Ch, N. Cavadini, A. Furrer, K. Krämer, H. U. Güdel, P. Vorderwisch, K. Habicht, H. Mutka, and A. Wildes. "Spin dynamics in the BEC phase of the S=1/2 quantum spin system TlCuCl3." Journal of Magnetism and Magnetic Materials 272-276 (May 2004): 195–96. http://dx.doi.org/10.1016/j.jmmm.2003.11.075.

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20

Higemoto, W., H. Tanaka, I. Watanabe, S. Ohira, A. Fukaya, and K. Nagamine. "Anomalous magnetic field dependence of muon spin relaxation in double-chain system KCuCl3 and TlCuCl3." Physica B: Condensed Matter 289-290 (August 2000): 172–75. http://dx.doi.org/10.1016/s0921-4526(00)00354-9.

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21

Oosawa, Akira, Masashi Fujisawa, Toyotaka Osakabe, Kazuhisa Kakurai, and Hidekazu Tanaka. "Neutron Diffraction Study of the Pressure-Induced Magnetic Ordering in the Spin Gap System TlCuCl3." Journal of the Physical Society of Japan 72, no. 5 (May 15, 2003): 1026–29. http://dx.doi.org/10.1143/jpsj.72.1026.

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22

Chang, Chih-Chun, and Lee Lin. "The finite-temperature binary collision method for treating spin-dimer systems: Taking TlCuCl3 as an example." Annals of Physics 327, no. 2 (February 2012): 264–82. http://dx.doi.org/10.1016/j.aop.2011.09.004.

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23

Yamada, Fumiko, Toshio Ono, Hidekazu Tanaka, Grégoire Misguich, Masaki Oshikawa, and Toshiro Sakakibara. "Magnetic-Field Induced Bose–Einstein Condensation of Magnons and Critical Behavior in Interacting Spin Dimer System TlCuCl3." Journal of the Physical Society of Japan 77, no. 1 (January 15, 2008): 013701. http://dx.doi.org/10.1143/jpsj.77.013701.

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24

Ryu, Gihun, and Kwanghyo Son. "Surface defect free growth of a spin dimer TlCuCl3 compound crystals and investigations on its optical and magnetic properties." Journal of Solid State Chemistry 237 (May 2016): 358–63. http://dx.doi.org/10.1016/j.jssc.2016.02.048.

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25

Misguich, Grégoire, and Masaki Oshikawa. "Bose–Einstein Condensation of Magnons in TlCuCl3: Phase Diagram and Specific Heat from a Self-consistent Hartree–Fock Calculation with a Realistic Dispersion Relation." Journal of the Physical Society of Japan 73, no. 12 (December 15, 2004): 3429–34. http://dx.doi.org/10.1143/jpsj.73.3429.

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26

Sirker, J., A. Weiße, and O. P. Sushkov. "Bose–Einstein condensation of magnons in TlCuCl." Physica B: Condensed Matter 359-361 (April 2005): 1318–20. http://dx.doi.org/10.1016/j.physb.2005.01.392.

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27

Saha-Dasgupta, T., and R. Valentí. "Comparative study between two quantum spin systems KCuCl 3 and TlCuCl 3." Europhysics Letters (EPL) 60, no. 2 (October 2002): 309–15. http://dx.doi.org/10.1209/epl/i2002-00351-x.

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28

Oosawa, A., T. Kato, H. Tanaka, K. Kakurai, M. M�ller, and H. J. Mikeska. "Magnetic excitations and exchange interactions in the spin-gap system TlCuCl 3." Applied Physics A: Materials Science & Processing 74 (December 1, 2002): s846—s849. http://dx.doi.org/10.1007/s003390201591.

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29

Shiramura, Wakako, Ken-ichi Takatsu, Hidekazu Tanaka, Kenji Kamishima, Mitsue Takahashi, Hiroyuki Mitamura, and Tsuneaki Goto. "High-Field Magnetization Processes of Double Spin Chain Systems KCuCl 3 and TlCuCl 3." Journal of the Physical Society of Japan 66, no. 7 (July 15, 1997): 1900–1903. http://dx.doi.org/10.1143/jpsj.66.1900.

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30

Takatsu, Ken-ichi, Wakako Shiramura, and Hidekazu Tanaka. "Ground States of Double Spin Chain Systems TlCuCl 3, NH 4CuCl 3 and KCuBr 3." Journal of the Physical Society of Japan 66, no. 6 (June 15, 1997): 1611–14. http://dx.doi.org/10.1143/jpsj.66.1611.

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31

R�egg, Ch, N. Cavadini, A. Furrer, K. Kr�mer, H. U. G�del, P. Vorderwisch, and H. Mutka. "Spin dynamics in the high-field phase of quantum-critical S =1/2 TlCuCl 3." Applied Physics A: Materials Science & Processing 74 (December 1, 2002): s840—s842. http://dx.doi.org/10.1007/s003390101156.

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32

Kimura, Shojiro, Kento Kakihata, Yuya Sawada, Kazuo Watanabe, Masashige Matsumoto, Masayuki Hagiwara, and Hidekazu Tanaka. "Magnetoelectric effect in the quantum spin gap system TlCuCl3." Physical Review B 95, no. 18 (May 17, 2017). http://dx.doi.org/10.1103/physrevb.95.184420.

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33

Sakurai, Kyosuke, Shojiro Kimura, Staoshi Awaji, Masashige Matsumoto, and Hidekazu Tanaka. "Spin-driven ferroelectricity in the quantum magnet TlCuCl3 under high pressure." Physical Review B 102, no. 6 (August 14, 2020). http://dx.doi.org/10.1103/physrevb.102.064104.

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34

Rakhimov, Abdulla, Mukhtorali Nishonov, Luxmi Rani, and Bilal Tanatar. "Characteristic temperatures of a triplon system of dimerized quantum magnets." International Journal of Modern Physics B, December 19, 2020, 2150018. http://dx.doi.org/10.1142/s0217979221500181.

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Exploiting the analogy between ultracold atomic gases and the system of triplons, we study magneto-thermodynamic properties of dimerized quantum magnets in the framework of Bose–Einstein condensation (BEC). Particularly, introducing the inversion (or Joule–Thomson) temperature [Formula: see text] as the point where Joule–Thomson coefficient of an isenthalpic process changes its sign, we show that for a simple paramagnet, this temperature is infinite, while for three-dimensional (3D) dimerized quantum magnets it is finite and always larger than the critical temperature [Formula: see text] of BEC. Below the inversion temperature [Formula: see text], the system of triplons may be in a liquid phase, which undergoes a transition into a superfluid phase at [Formula: see text]. The dependence of the inversion temperature on the external magnetic field [Formula: see text] has been calculated for quantum magnets of TlCuCl3 and Sr3Cr2O8.
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35

Zhou, X. G., Yuan Yao, Y. H. Matsuda, A. Ikeda, A. Matsuo, K. Kindo, and H. Tanaka. "Particle-Hole Symmetry Breaking in a Spin-Dimer System TlCuCl3 Observed at 100 T." Physical Review Letters 125, no. 26 (December 31, 2020). http://dx.doi.org/10.1103/physrevlett.125.267207.

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36

Rakhimov, Abdulla, Asliddin Khudoyberdiev, and B. Tanatar. "Effects of exchange and weak Dzyaloshinsky–Moriya anisotropies on thermodynamic characteristics of spin-gapped magnets." International Journal of Modern Physics B 35, no. 25 (October 8, 2021). http://dx.doi.org/10.1142/s0217979221502234.

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We study the modification of low-temperature properties of quantum magnets such as magnetization, heat capacity, energy spectrum and densities of condensed and noncondensed quasiparticles (triplons) due to anisotropies in the framework of mean-field- based approach. We show that in contrast to exchange anisotropy (EA) interaction, Dzyaloshinsky–Moriya (DM) interaction modifies the physics dramatically. Particularly, it changes the sign of the anomalous density in the whole range of temperatures. Its critical behavior is slightly modified also by the EA. We have found that the shift of the critical temperature of phase transition (or crossover caused by DM interaction) is positive and significant. Using the experimental data on the magnetization of the compound TlCuCl3, we have found optimal values for the strengths of EA and DM interactions. The spectrum of the energy of low lying excitations has also been investigated and found to develop a linear dispersion similar to Goldstone mode with a negligibly small anisotropy gap.
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37

Fidrysiak, Maciej, and Józef Spałek. "Stable high-temperature paramagnons in a three-dimensional antiferromagnet near quantum criticality: Application to TlCuCl3." Physical Review B 95, no. 17 (May 25, 2017). http://dx.doi.org/10.1103/physrevb.95.174437.

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38

Jensen, Jens. "Self-consistent theory for the paramagnetic properties of TlCuCl3to first order in the high-density1/zexpansion." Physical Review B 83, no. 6 (February 25, 2011). http://dx.doi.org/10.1103/physrevb.83.064420.

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39

"The Origin of the Metal-insulator Transitions in Non-stoichiometric TlCu3-xS2 and α-BaCu2-xS2." Bulletin of the Korean Chemical Society 27, no. 3 (March 20, 2006): 363–67. http://dx.doi.org/10.5012/bkcs.2006.27.3.363.

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