Long range ordered, dimerized, large-D and Haldane phases in spin 1 chain compounds

References

• Bethe, H. Metal Theory. Z. Physik. 1931, 71, 205–226. doi:10.1007/BF01341708
   Google Scholar
• Yang, C. N.; Yang, C. P. One-Dimensional Chain of Anisotropic Spin-Spin Interactions. I. Proof of Bethe's Hypothesis for Ground State in a Finite System. Phys. Rev. 1966, 150, 321–327. doi:10.1103/PhysRev.150.321
   Web of Science ®Google Scholar
• Yang, C. N.; Yang, C. P. One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy per Lattice Site for an Infinite System. Phys. Rev. 1966, 150, 327–339. doi:10.1103/PhysRev.150.327
   Google Scholar
• Haldane, F.D.M. Continuum Dynamics of the 1-D Heisenberg Anti-Ferromagnet – Identification with the O(3) Non-Linear Sigma-Model. Phys. Lett. A 1983, 93, 464–468; Non-Linear Field-Theory of Large-Spin Heisenberg Anti-Ferromagnets – Semi-Classically Quantized Solitons of the One-Dimensional Easy-Axis Neel State. Phys. Rev. Lett. 1983, 50, 1153–1156. doi:10.1016/0375-9601(83)90631-X
   Web of Science ®Google Scholar
• Nightingale, M. P.; Blöte, H. W. Gap of the Linear Spin-1 Heisenberg Antiferromagnet: A Monte Carlo Calculation. Phys. Rev. B Condens. Matter 1986, 33, 659–661. doi:10.1103/physrevb.33.659
   PubMed Web of Science ®Google Scholar
• White, S. R.; Huse, D. A. Numerical Renormalization-Group Study of Low-Lying Eigenstates of the Antiferromagnetic S = 1 Heisenberg Chain. Phys. Rev. B Condens. Matter 1993, 48, 3844–3852. doi:10.1103/physrevb.48.3844
   PubMed Web of Science ®Google Scholar
• Yamashita, M.; Ishii, T.; Matsuzaka, H. Haldane Gap Systems. Coord. Chem. Rev. 2000, 198, 347–366. doi:10.1016/S0010-8545(99)00212-X
   Web of Science ®Google Scholar
• Renard, J. P.; Regnault, L. P.; Verdaguer, M. Haldane Quantum Spin Chains. In Magnetism: Molecules to Materials I: Models and Experiments; Miller, J. S., Drillon, M., Ed(s).; Wiley-VCH Verlag GmbH & Co., 2002; pp. 49–93.
   Google Scholar
• Buyers, W. J. L.; Morra, R. M.; Armstrong, R. L.; Hogan, M. J.; Gerlach, P.; Hirakawa, K. Gap Modes in the Spin-1 Quasi-One-Dimensional Antiferromagnet CsNiCl3 and the Haldane Conjecture. J. Magn. Magn. Mater. 1986, 54–57, 1277–1279. doi:10.1016/0304-8853(86)90817-6
   Web of Science ®Google Scholar
• Regnault, L. P.; Zaliznyak, I.; Renard, J. P.; Vettier, C. Inelastic-Neutron-Scattering Study of the Spin Dynamics in the Haldane-Gap System Ni(C2H8N2)2NO2ClO4. Phys. Rev. B Condens. Matter 1994, 50, 9174–9187. doi:10.1103/physrevb.50.9174
   PubMed Web of Science ®Google Scholar
• Darriet, J.; Regnault, L. P. The Compound Y2BaNiO5 – a New Example of a Haldane-Gap in a S = 1 Magnetic Chain. Solid St. Commun. 1993, 86, 409–412. doi:10.1016/0038-1098(93)90455-V
   Web of Science ®Google Scholar
• Achiwa, N. Linear Antiferromagnetic Chains in Hexagonal ABCl3-Type Compounds (A; Cs, or Rb, B; Cu, Ni, Co, or Fe. J. Phys. Soc. Jpn. 1969, 27, 561–574. doi:10.1143/JPSJ.27.561
   Google Scholar
• Morra, R. M.; Buyers, W. J. L.; Armstrong, R. L.; Hirakawa, K. Spin Dynamics and the Haldane Gap in the Spin-1 Quasi-One-Dimensional Antiferromagnet CsNiCl3. Phys. Rev. B Condens. Matter 1988, 38, 543–555. doi:10.1103/physrevb.38.543
   PubMed Web of Science ®Google Scholar
• Buyers, W. J.; Morra, R. M.; Armstrong, R. L.; Hogan, M. J.; Gerlach, P.; Hirakawa, aK. Experimental Evidence for the Haldane Gap in a Spin-1 Nearly Isotropic, Antiferromagnetic Chain. Phys. Rev. Lett. 1986, 56, 371–374. doi:10.1103/PhysRevLett.56.371
   PubMed Web of Science ®Google Scholar
• Renard, J. P.; Verdaguer, M.; Regnault, L. P.; Erkelens, W. A. C.; Rossat-Mignod, J.; Stirling, W. G. Presumption for a Quantum Energy Gap in the Quasi-One-Dimensional S = 1 Heisenberg Antiferromagnet Ni(C2H8N2)2NO2(ClO4). Europhys. Lett. 1987, 3, 945–951. doi:10.1209/0295-5075/3/8/013
   Google Scholar
• Xu, G.; DiTusa, J. F.; Ito, T.; Oka, K.; Takagi, H.; Broholm, C.; Aeppli, G. Y2BaNiO5: A Nearly Ideal Realization of the S = 1 Heisenberg Chain with Antiferromagnetic Interactions. Phys. Rev. B 1996, 54, R6827–R6830. doi:10.1103/PhysRevB.54.R6827
   Web of Science ®Google Scholar
• Zheludev, A.; Honda, Z.; Broholm, C. L.; Katsumata, K.; Shapiro, S. M.; Kolezhuk, A.; Park, S.; Qiu, Y. Massive Triplet Excitations in a Magnetized Anisotropic Haldane Spin Chain. Phys. Rev. B 2003, 68, 134438. doi:10.1103/PhysRevB.68.134438
   Web of Science ®Google Scholar
• Sakai, T.; Takahashi, M. Effect of the Haldane Gap on Quasi-One-Dimensional Systems. Phys. Rev. B Condens. Matter 1990, 42, 4537–4543. doi:10.1103/physrevb.42.4537
   PubMed Web of Science ®Google Scholar
• Affleck, I.; Kennedy, T.; Lieb, E. H.; Tasaki, H. Rigorous Results on Valence-Bond Ground States in Antiferromagnets. Phys. Rev. Lett. 1987, 59, 799–802. doi:10.1103/PhysRevLett.59.799
   PubMed Web of Science ®Google Scholar
• Fannes, M.; Nachtergaele, B.; Werner, R. F. Finitely Correlated States on Quantum Spin Liquids. Communmath. Phys. 1992, 144, 443–490. doi:10.1007/BF02099178
   Web of Science ®Google Scholar
• Klümper, A.; Schadschneider, A.; Zittartz, J. Ground State Properties of a Generalized VBS-Model. Z. Physik B – Condens. Matter 1992, 87, 281–287. doi:10.1007/BF01309281
   Google Scholar
• Affleck, I. Quantum Spin Gap and the Haldane Gap. J. Phys. Condens. Matter 1989, 1, 3047–3072. doi:10.1088/0953-8984/1/19/001
   Web of Science ®Google Scholar
• Golinelli, O.; Jolicoeur, T.; Lacaze, R. Finite-Lattice Extrapolations for a Haldane-Gap Antiferromagnet. Phys. Rev. B Condens. Matter 1994, 50, 3037–3044. doi:10.1103/physrevb.50.3037
   PubMed Web of Science ®Google Scholar
• Kim, Y.; Greven, M.; Wiese, U.; Birgeneau, R. Monte-Carlo Study of Correlations in Quantum Spin Chains at Non-Zerj Temperature. Eur. Phys. J. B. 1998, 4, 291–297. doi:10.1007/s100510050382
   Web of Science ®Google Scholar
• Jolicur, T.; Golinelli, O. Sigma -Model Study of Haldane-Gap Antiferromagnets. Phys. Rev. B Condens. Matter 1994, 50, 9265–9273. doi:10.1103/physrevb.50.9265
   PubMed Web of Science ®Google Scholar
• Kitazawa, A.; Nomura, K.; Okamoto, K. Phase Diagram of S = 1 Bond-Alternating XXZ Chains. Phys. Rev. Lett. 1996, 76, 4038–4041. doi:10.1103/PhysRevLett.76.4038
   PubMed Web of Science ®Google Scholar
• Hikihara, T.; Kaburagi, M.; Kawamura, H.; Tonegawa, T. Ground State Phase Diagram of Frustrated S = 1 XXZ Chains: Chiral Ordered Phases. J. Phys. Soc. Jpn. 2000, 69, 259–266. doi:10.1143/JPSJ.69.259
   Google Scholar
• Katanin, A. A.; Irkhin, V. Y. Magnetic Order and Spin Fluctuations in Low-Dimensional Insulating Systems. Phys. Usp. 2007, 177, 639–662. doi:10.1070/PU2007v050n06ABEH006313
   Google Scholar
• Johnson, P. B.; Rayne, J. A.; Friedberg, S. A. Magnetic Properties of CsNiCl3 and RbNiCl3. J. Appl. Phys. 1979, 50, 1853–1855. doi:10.1063/1.327143
   Google Scholar
• Plumer, M. L.; Hood, K.; Caille, A. Multicritical Point in the Magnetic Phase Diagram of CsNiCl3. Phys. Rev. Lett. 1988, 60, 45–48. doi:10.1103/PhysRevLett.60.1885.3
   PubMed Web of Science ®Google Scholar
• Tun, Z.; Buyers, W. J. L.; Harrison, A.; Rayne, J. A. Observation of the Haldane Gap in RbNiCl3. Phys. Rev. B Condens. Matter 1991, 43, 13331–13334. doi:10.1103/physrevb.43.13331
   PubMed Web of Science ®Google Scholar
• Zaliznyak, I. A.; Lee, S. H.; Petrov, S. V. Continuum in the Spin-Excitation Spectrum of a Haldane Chain Observed by Neutron Scattering in CsNiCl3. Phys. Rev. Lett. 2001, 87, 017202. doi:10.1103/PhysRevLett.87.017202
   PubMed Web of Science ®Google Scholar
• Hagiwara, M.; Katsumata, K.; Affleck, I.; Halperin, B. I.; Renard, J. P. Observation of S = 1/2 Degrees of Freedom in an S = 1 Linear-Chain Heisenberg Antiferromagnet. Phys. Rev. Lett. 1990, 65, 3181–3184. doi:10.1103/PhysRevLett.65.3181
   PubMed Web of Science ®Google Scholar
• Brambleby, J.; Manson, J. L.; Goddard, P. A.; Stone, M. B.; Johnson, R. D.; Manuel, P.; Villa, J. A.; Brown, C. M.; Lu, H.; Chikara, S.; et al. Combining Microscopic and Macroscopic Probes to Untangle the Single-Ion Anisotropy and Exchange Energies in an S = 1 Quantum Antiferromagnet. Phys. Rev. B. 2017, 95, 134435. doi:10.1103/PhysRevB.95.134435
   Web of Science ®Google Scholar
• Vasiliev, A. N.; Ignatchik, O. L.; Isobe, M.; Ueda, Y. Long Range Neel Order in Quasi-One-Dimensional Vanadium-Based (S = 1) Pyroxenes (Li,Na)V(Si,Ge)2O6. Phys. Rev. B. 2004, 70, 132415. doi:10.1103/PhysRevB.70.132415
   Web of Science ®Google Scholar
• Pedrini, B.; Wessel, S.; Gavilano, J. L.; Ott, H. R.; Kazakov, S. M.; Karpinski, J. Quenching of the Haldane Gap in LiVSi2O6 and Related Compounds. Eur. Phys. J. B. 2007, 55, 219–228. doi:10.1140/epjb/e2007-00056-0
   Web of Science ®Google Scholar
• Law, J. M.; Koo, H.-J.; Whangbo, M.-H.; Brücher, E.; Pomjakushin, V.; Kremer, R. K. Strongly Correlated One-Dimensional Magnetic Behavior of NiTa2O6. Phys. Rev. B. 2014, 89, 014423. doi:10.1103/PhysRevB.89.014423
   Web of Science ®Google Scholar
• Christian, A. B.; Hunt, C. D.; Neumeier, J. J. Local and Long-Range Order and the Influence of Applied Magnetic Field on Single-Crystalline NiSb2O6. Phys. Rev. B. 2017, 96, 024433. doi:10.1103/PhysRevB.96.024433
   Web of Science ®Google Scholar
• Doi, Y.; Suzuki, R.; Hinatsu, Y.; Kodama, K.; Igawa, N. Crystal Structures and Magnetic Properties of Nickel Chain Compounds PbM2Ni6Te3O18 (M = Mn, Cd). Inorg. Chem. 2015, 54, 10725–10731. doi:10.1021/acs.inorgchem.5b01619
   PubMed Web of Science ®Google Scholar
• Narumi, Y.; Sato, R.; Kindo, K.; Hagiwara, M. Magnetic Ptoperty of an S = 1 Antiferromagnetic Dimer Compound. J. Magn. Magn. Mater. 1998, 177-181, 685–686. doi:10.1016/S0304-8853(97)00549-0
   Web of Science ®Google Scholar
• Narumi, Y.; Kindo, K.; Hagiwara, M.; Nakano, H.; Kawaguchi, A.; Okunishi, K.; Kohno, M. High Field Magnetization of S = 1 Antiferromagnetic Bond-Alternating Chain Compounds. Phys. Rev. B. 2004, 69, 174405. doi:10.1103/PhysRevB.69.174405
   Web of Science ®Google Scholar
• Ohta, H.; Okubo, S.; Kimura, S.; Takeda, S.; Kikuchi, H.; Nagasawa, H. High-Field ESR Measurements of a Bond Alternating Heisenberg Chain System Ni2(µ-N3)3(Dpt)2ClO4. Phys. B 2001, 294–295, 55–59. doi:10.1016/S0921-4526(00)00607-4
   Google Scholar
• Narumi, Y.; Hagiwara, M.; Sato, R.; Kindo, K.; Nakano, H.; Takahashi, M. High Field Magnetization in an S = 1 Antiferromagnetic Chain with Bond Alternation. Phys. B 1998, 246–247, 509–512. doi:10.1016/S0921-4526(97)00974-5
   Web of Science ®Google Scholar
• Hagiwara, M.; Narumi, Y.; Kindo, K.; Kohno, M.; Nakano, H.; Sato, R.; Takahashi, M. Experimental Verification of the Gapless Point in the S = 1 Antiferromagnetic Bond Alternating Chain. Phys. Rev. Lett. 1998, 80, 1312–1315. doi:10.1103/PhysRevLett.80.1312
   Web of Science ®Google Scholar
• Zheludev, A.; Masuda, T.; Sales, B.; Mandrus, D.; Papenbrock, T.; Barnes, T.; Park, S. Distribution of Exchange Energy in a Bond-Alternating S = 1 Quantum Spin Chains. Phys. Rev. B. 2004, 69, 144417. doi:10.1103/PhysRevB.69.144417
   Web of Science ®Google Scholar
• Narumi, Y.; Hagiwara, M.; Kohno, M.; Kindo, K. Evidence for the Singlet-Dimer Ground State in an S = 1 Antiferromagnetic Bond Alternating Chain. Phys. Rev. Lett. 2001, 86, 324–327. doi:10.1103/PhysRevLett.86.324
   PubMed Web of Science ®Google Scholar
• Kimura, S.; Hirai, S.; Narumi, Y.; Kindo, K.; Hagiwara, M. High Field ESR Measurements of an S = 1 Antiferromagnetic Dimer Compound. Phys. B 2001, 294–295, 47–50. doi:10.1016/S0921-4526(00)00605-0
   Google Scholar
• Rajendiran, T. M.; Kahn, O.; Golhen, S.; Ouahab, L.; Honda, Z.; Katsumata, K. Dimerized Nickel(2+) Chain Compounds with Nitro-Nitrito Bridges and Unprecedented [Ln(NO(3))(4)(CH(3)OH)(2)](-) Anions (Ln = Lanthanide). Crystal Structure and Magnetic Properties. Inorg. Chem. 1998, 37, 5693–5696. doi:10.1021/ic980458q
   PubMed Web of Science ®Google Scholar
• Massoud, S. S.; Mautner, F. A.; Vicente, R.; Gallo, A. A.; Ducasse, E. Dinuclear and Polynuclear Bridged Azido-Nickel(II) Complexes: Synthesis, Structure Determination, and Magnetic Properties. Eur. J. Inorg. Chem. 2007, 2007, 1091–1102. doi:10.1002/ejic.200600725
   Google Scholar
• Tsyrulin, N.; Batista, C. D.; Zapf, V. S.; Jaime, M.; Hansen, B. R.; Niedermayer, C.; Rule, K. C.; Habicht, K.; Prokes, K.; Kiefer, K.; et al. Neutron Study of the Magnetism in NiCl2-4SC(NH2)2. J. Phys. Condens. Matter 2013, 25, 216008. doi:10.1088/0953-8984/25/21/216008
   PubMed Web of Science ®Google Scholar
• Pajerowski, D. M.; Manson, J. L.; Herbrych, J.; Bendix, J.; Podlesnyak, A. A.; Cain, J. M.; Meisel, M. W. Inelastic Neutron Scattering Study of the Anisotropic S = 1 Spin Chain [Ni(HF2)(3-Clpyridine)4]BF4. Phys. Rev. B. 2020, 101, 094431. doi:10.1103/PhysRevB.101.094431
   Web of Science ®Google Scholar
• Orendác, M.; Orendáčová, A.; Černák, J.; Feher, A.; Signore, P. J. C.; Meisel, M. W.; Merah, S.; Verdaguer, M. Thermodynamic and Magnetic Properties of the S = 1 Heisenberg Chain Ni(C2H8N2)2Ni(CN)4: Experiments and Theory. Phys. Rev. B 1995, 52, 3435–3540. doi:10.1103/PhysRevB.52.3435
   Web of Science ®Google Scholar
• Batchelor, M. T.; Guan, X.-W.; Oelkers, N. Thermal and Magnetic Properties of Spin-1 Magnetic Chain Compounds with Large Single-Ion and in-Plane Anisotropies. Phys. Rev. B 2004, 70, 184408. doi:10.1103/PhysRevB.70.184408
   Web of Science ®Google Scholar
• Chattopadhyay, S.; Jain, D.; Ganesan, V.; Giri, S.; Majumdar, S. Observation of Large-D Magnetic Phase in Sr3NiPtO6. Phys. Rev. B 2010, 82, 094431. doi:10.1103/PhysRevB.82.094431
   Web of Science ®Google Scholar
• Abdeldaim, A. H.; Badrtdinov, D. I.; Gibbs, A. S.; Manuel, P.; Walker, H. C.; Le, M. D.; Wu, C. H.; Wardecki, D.; Eriksson, S.-G.; Kvashnin, Y. O.; et al. Large Easy-Axis Anisotropy in the One-Dimensional Magnet BaMo(PO4)2. Phys. Rev. B 2019, 100, 214427. doi:10.1103/PhysRevB.100.214427
   Web of Science ®Google Scholar
• Masuda, T.; Sakaguchi, T.; Uchinokura, K. Magnetism of a New Spin-1 Material NaV(WO4)2. J. Phys. Soc. Jpn. 2002, 71, 2637–2639. doi:10.1143/JPSJ.71.2637
   Google Scholar
• Takeuchi, T.; Hori, H.; Yosida, T.; Yamagishi, A.; Katsumata, K.; Renard, J.-P.; Gadet, V.; Verdaguer, M.; Date, M. Magnetization Process of Haldane Materials TMNIN and NINAZ. J. Phys. Soc. Jpn. 1992, 61, 3262–3266. doi:10.1143/JPSJ.61.3262
   Google Scholar
• Goto, T.; Ishikawa, T.; Shimaoka, Y.; Fujii, Y. Quantum Spin Dynamics Studied by the Nuclear Magnetic Relaxation of Protons in the Haldane-Gap System (CH3)4NNi(NO2)3. Phys. Rev. B 2006, 73, 214406. doi:10.1103/PhysRevB.73.214406
   Google Scholar
• Landee, C. P.; Reza, K. A.; Bond, M. R.; Willett, R. D. Low-Temperature Crystal Structures of Two Haldane-Gap Nickel Chains, NENP and NENF. Phys. Rev. B 1997, 56, 147–153. doi:10.1103/PhysRevB.56.147
   Web of Science ®Google Scholar
• Koike, Y.; Metoki, N.; Morii, Y.; Kobayashi, T.; Ishii, T.; Yamashita, M. Neutron Scattering Studies in the Linear-Chain Haldane Materials, NDMAZ and NDMAP. J. Phys. Soc. Jpn. 2000, 69, 4034–4042. doi:10.1143/JPSJ.69.4034
   Google Scholar
• Honda, Z.; Asakawa, H.; Katsumata, K. Magnetic Field versus Temperature Phase Diagram of a Quasi-One-Dimensional S = 1 Heisenberg Antiferromagnet. Phys. Rev. Lett. 1998, 81, 2566–2569. doi:10.1103/PhysRevLett.81.2566
   Web of Science ®Google Scholar
• Takeuchi, T.; Ono, M.; Hori, H.; Yosida, T.; Yamagishi, A.; Date, M. Magnetization Measurement of NENP and NINO in High Magnetic Field. J. Phys. Soc. Jpn. 1992, 61, 3255–3261. doi:10.1143/JPSJ.61.3255
   Google Scholar
• Zheludev, A.; Nagler, S. E.; Shapiro, S. M.; Chou, L. K.; Talham, D. R.; Meisel, M. W. Spin Dynamics in the Linear-Chain S = 1 Antiferromagnet Ni(C3H10N2)2N3(ClO4). Phys. Rev. B Condens. Matter 1996, 53, 15004–15009. doi:10.1103/physrevb.53.15004
   PubMed Web of Science ®Google Scholar
• Tao, W.; Chen, L. M.; Wang, X. M.; Fan, C.; Ke, W. P.; Liu, X. G.; Zhao, Z. Y.; Li, Q. J.; Sun, X. F. Crystal Growth and Characterization of Haldane Chain Compound Ni(C3H10N2)2NO2ClO4. J. Cryst. Growth 2011, 327, 215–220. doi:10.1016/j.jcrysgro.2011.05.013
   Web of Science ®Google Scholar
• Meyer, A.; Gleizes, A.; Girerd, J. J.; Verdaguer, M.; Kahn, O. Crystal Structures, Magnetic Anisotropy Properties, and Orbital Interactions in Catena-(μ-Nitrito)-Bis(Ethylenediamine) Nickel (II) Perchlorate and Triiodide. Inorg. Chem. 1982, 21, 1729–1739. doi:10.1021/ic00135a006
   Web of Science ®Google Scholar
• Cizmar, E.; Ozerov, M.; Ignatchik, O.; Papageorgiou, T. P.; Wosnitza, J.; Zvyagin, S. A.; Krzystek, J.; Zhou, Z.; Landee, C. P.; Landry, B. R. Magnetic Properties of the Haldane-Gap Material [Ni(C2H8N2)2NO2](BF4). New J. Phys. 2008, 10, 033008. doi:10.1088/1367-2630/10/3/033008
   Web of Science ®Google Scholar
• Cernak, J.; Farkašová, N.; Tomás, M.; Kavečanský, V.; Čižmár E.; Orendáč, M. Ni(Bpy)(Ox)]: A Candidate in the Class of Haldane Gap Systems (Bpy = 2,2'-Bipyridine, Ox = Oxalate). J. Coord. Chem. 2015, 68, 2788–2797. doi:10.1080/00958972.2015.1058485.
   Web of Science ®Google Scholar
• Sanjeewa, L. D.; McGuire, M. A.; Garlea, V. O.; Hu, L.; Chumanov, G.; McMillen, C. D.; Kolis, J. W. Hydrothermal Synthesis and Characterization of Novel Brackebuschite-Type Transition Metal Vanadates: Ba2M(VO4)2(OH), M = V(3+), Mn(3+), and Fe(3+), with Interesting Jahn-Teller and Spin-Liquid Behavior. Inorg. Chem. 2015, 54, 7014–7020. doi:10.1021/acs.inorgchem.5b01037
   PubMed Web of Science ®Google Scholar
• Zheludev, A.; Masuda, T.; Tsukada, I.; Uchiyama, Y.; Uchinokura, K.; Böni, P.; Lee, S.-H. Magnetic Excitations in Coupled Haldane Spin Chains near the quantum critical point. Phys. Rev. B 2000, 62, 8921–8930. doi:10.1103/PhysRevB.62.8921
   Web of Science ®Google Scholar
• Bera, A. K.; Lake, B.; Islam, A. T. M. N.; Klemke, B.; Faulhaber, E.; Law, J. M. Field-Induced Magnetic Ordering and Single-Ion Anisotropy in the Quasi-One-Dimensional Haldane Chain Compound SrNi2V2O8: A Single-Crystal Investigation. Phys. Rev. B 2013, 87, 224423. doi:10.1103/PhysRevB.87.224423
   Web of Science ®Google Scholar
• Uchiyama, Y.; Sasago, Y.; Tsukada, I.; Uchinokura, K.; Zheludev, A.; Hayashi, T.; Miura, N.; Böni, P. Spin-Vacancy-Induced Long-Range Order in a New Haldane-Gap Antiferromagnet. Phys. Rev. Lett. 1999, 83, 632–635. doi:10.1103/PhysRevLett.83.632
   Web of Science ®Google Scholar
• Sakaguchi, T.; Kakurai, K.; Yokoo, T.; Akimitsu, J. Neutron Scattering Study of Magnetic Excitations in the Spin S = 1 One-Dimensional Heisenberg Antiferromagnet Y2BaNiO5. J. Phys. Soc. Jpn. 1996, 65, 3025–3031. doi:10.1143/JPSJ.65.3025
   Google Scholar
• DiTusa, J. F.; Cheong, S. W.; Park, J.; Aeppli, G.; Broholm, C.; Chen, C. T. Magnetic and Charge Dynamics in a Doped One-Dimensional Transition Metal Oxide. Phys. Rev. Lett. 1994, 73, 1857–1860. doi:10.1103/PhysRevLett.73.1857
   PubMed Web of Science ®Google Scholar
• Mutka, H.; Soubeyroux, J. L.; Bourleaux, G.; Colombet, P. Support for the Haldane Conjecture: Gap for Magnetic Excitations in the Quasi-One-Dimensional S = 1 Heisenberg Antiferromagnet AgVP2S6. Phys. Rev. B Condens. Matter 1989, 39, 4820–4823. doi:10.1103/physrevb.39.4820
   PubMed Web of Science ®Google Scholar
• Takigawa, M.; Asano, T.; Ajiro, Y.; Mekata, M.; Uemura, Y. J. Dynamics in the S = 1 One-Dimensional Antiferromagnet AgVP2S6 via 31P and 51V NMR. Phys. Rev. Lett. 1996, 76, 2173–2176. doi:10.1103/PhysRevLett.76.2173
   PubMed Web of Science ®Google Scholar
• Wierschem, K.; Sengupta, P. Characterizing the Haldane Phase in Quasi-One-Dimensional Spin-1 Antiferromagnets. Mod. Phys. Lett. B 2014, 28, 1430017. doi:10.1142/S0217984914300178
   Web of Science ®Google Scholar
• Pchelkina, Z. V.; Mazurenko, V. V.; Volkova, O. S.; Deeva, E. B.; Morozov, I. V.; Shutov, V. V.; Troyanov, S. I.; Werner, J.; Koo, C.; Klingeler, R.; Vasiliev, A. N. Electronic Structure and Magnetic Properties of the Strong-Rung Spin-1 Ladder Compound Rb3Ni2(NO3)7. Phys. Rev. B 2018, 97, 144420. doi:10.1103/PhysRevB.97.144420
   Google Scholar
• Kirsanova, M. A.; Aksyonov, D. A.; Maximova, O. V.; Shvanskaya, L. V.; Vasiliev, A. N.; Tsirlin, A. A.; Abakumov, A. M. Crystal Structures and Low-Dimensional Ferromagnetism of Sodium Nickel Phosphates Na5Ni2(PO4)3·H2O and Na6Ni2(PO4)3OH. Inorg. Chem. 2019, 58, 610–621. doi:10.1021/acs.inorgchem.8b02791
   PubMed Web of Science ®Google Scholar
• de Jongh, L. J.; Miedema, A. R. Experiments on Simple Magnetic Model Systems. Adv. Phys. 2001, 50, 947–1170. doi:10.1080/00018730110101412
   Web of Science ®Google Scholar
• Streltsov, S. V.; Khomskii, D. I. Electronic Structure and Magnetic Properties of Pyroxenes (Li,Na)TM(Si,Ge)2O6: Low-Dimensional Magnets with 90 Bonds. Phys. Rev. B. 2008, 77, 064405. doi:10.1103/PhysRevB.77.064405
   Google Scholar
• Singh, R. R. P.; Gelfand, M. P. Ordering and Criticality in Spin-1 Chains. Phys. Rev. Lett. 1988, 61, 2133–2136. doi:10.1103/PhysRevLett.61.2133
   PubMed Web of Science ®Google Scholar
• Totsuka, K.; Nishiyama, Y.; Hatano, N.; Suzuki, M. Isotropic Spin-1 with Bond Alternation – Analytical and Numerical Studies. J. Phys.: Condens. Matter 1995, 7, 4895–4920. doi:10.1088/0953-8984/7/25/014
   Web of Science ®Google Scholar
• Yamamoto, S. Phase Transitions in Antiferromagnetic Quantum Chains with Bond Alternation. Phys. Rev. B. 1997, 55, 3603–3612. doi:10.1103/PhysRevB.55.3603
   Web of Science ®Google Scholar
• Oshikawa, M.; Yamanaka, M.; Affleck, I. Magnetization Plateaus in Spin Chains: “Haldane Gap” for Half-Integer Spins. Phys. Rev. Lett. 1997, 78, 1984–1987. doi:10.1103/PhysRevLett.78.1984
   Web of Science ®Google Scholar
• Tonegawa, T.; Nakao, T.; Kaburagi, M. Ground-State Phase Diagram and Magnetization Curves of the Spin-1 Antiferromagnetic Heisenberg Chain with Bond Alternation and Uniaxial Single-Ion-Type Anisotropy. J. Phys. Soc. Jpn. 1996, 65, 3317–3330. doi:10.1143/JPSJ.65.3317
   Google Scholar
• Totsuka, K. Magnetization Processes in Bond-Alternating Quantum Spin Chains. Phys. Lett. A 1997, 228, 103–110. doi:10.1016/S0375-9601(97)00087-X
   Web of Science ®Google Scholar
• Zheludev, A.; Chen, Y.; Broholm, C. L.; Honda, Z.; Katsumata, K. Haldane-Gap Excitations in the Low-Hc One-Dimensional Quantum Antiferromagnet Ni(C5D14N2)2N3(PF6). Phys. Rev. B 2001, 63, 104410. doi:10.1103/PhysRevB.63.104410
   Web of Science ®Google Scholar
• Yan, X.; Li, W.; Zhao, Y.; Ran, S.-J.; Su, G. Phase Diagrams, Distinct Conformal Anomalies, and Thermodynamics of Spin-1 Bond-Alternating Heisenberg Antiferromagnetic Chain in Magnetic Fields. Phys. Rev. B 2012, 85, 134425. doi:10.1103/PhysRevB.85.134425
   Web of Science ®Google Scholar
• Hagiwara, M.; Tsujii, H.; Rotundu, C. R.; Andraka, B.; Takano, Y.; Tateiwa, N.; Kobayashi, T. C.; Suzuki, T.; Suga, S. Tomonaga-Luttinger Liquid in a Quasi-One-Dimensional S = 1 Antiferromagnet Observed by Specific Heat Measurements. Phys. Rev. Lett. 2006, 96, 147205. doi:10.1103/PhysRevLett.96.147203
   PubMed Web of Science ®Google Scholar
• Chen, W.; Hida, K.; Sanctuary, B. C. Ground-State Phase Diagram of S = 1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy. Phys. Rev. B 2003, 67, 104401. doi:10.1103/PhysRevB.67.104401
   Web of Science ®Google Scholar
• Albuquerque, A. F.; Hamer, C. J.; Oitmaa, J. Quantum Phase Diagram and Excitations for the One-Dimensional S = 1 Heisenberg Antiferromagnet with Single-Ion Anisotropy. Phys. Rev. B 2009, 79, 054412. doi:10.1103/PhysRevB.79.054412
   Web of Science ®Google Scholar
• Rao, W. J.; Zhu, G. Y.; Zhang, G. M. SU (3) Quantum Critical Model Emerging from a Spin-1 Topological Phase. Phys. Rev. B 2016, 93, 165135. doi:10.1103/PhysRevB.93.165135
   Web of Science ®Google Scholar
• Huang, J. H.; Zhang, G. M.; Yao, D. X. Dynamical Spin Excitations of Topological Haldane Gapped Phase in the S = 1 Heisenberg Antiferromagnetic Chain with Single-Ion Anisotropy. arXiv Preprint arXiv:2003 2020, 07857.
   Google Scholar
• Hu, S.; Normand, B.; Wang, X.; Yu, L. Accurate Determination of the Gaussian Transition in Spin-1 Chains with Single-Ion Anisotropy. Phys. Rev. B 2011, 84, 220402. doi:10.1103/PhysRevB.84.220402
   Web of Science ®Google Scholar
• Zapf, V. S.; Zocco, D.; Hansen, B. R.; Jaime, M.; Harrison, N.; Batista, C. D.; Kenzelmann, M.; Niedermayer, C.; Lacerda, A.; Paduan-Filho, A. Bose-Einstein Condensation of S= 1 Nickel Spin Degrees of Freedom in NiCl2 − 4SC(NH2)2. Phys. Rev. Lett. 2006, 96, 077204. doi:10.1103/PhysRevLett.96.077204
   PubMed Web of Science ®Google Scholar
• Soldatov, T. A.; Smirnov, A. I.; Povarov, K. Y.; Paduan-Filho, A.; Zheludev, A. Microwave Dynamics of the Stoichiometric and Bond-Disordered Anisotropic S= 1 Chain Antiferromagnet NiCl2 − 4SC(NH2)2. Phys. Rev. B 2020, 101, 104410. doi:10.1103/PhysRevB.101.104410
   Web of Science ®Google Scholar
• Tzeng, Y. C.; Onishi, H.; Okubo, T.; Kao, Y. J. Quantum Phase Transitions Driven by Rhombic-Type Single-Ion Anisotropy in the S = 1 Haldane Chain. Phys. Rev. B 2017, 96, 060404. doi:10.1103/PhysRevB.96.060404
   Web of Science ®Google Scholar
• Wierschem, K.; Sengupta, P. Quenching the Haldane Gap in Spin-1 Heisenberg Antiferromagnets. Phys. Rev. Lett. 2014, 112, 247203. doi:10.1103/PhysRevLett.112.247203
   PubMed Web of Science ®Google Scholar
• Lee, S.; Park, J.-G.; Adroja, D. T.; Khomskii, D.; Streltsov, S.; McEwen, K. A.; Sakai, H.; Yoshimura, K.; Anisimov, V. I.; Mori, D.; et al. Spin Gap in Tl2Ru2O7 and the Possible Formation of Haldane Chains in Three-Dimensional Crystals. Nat. Mater. 2006, 5, 471–476. doi:10.1038/nmat1605
   PubMed Web of Science ®Google Scholar
• Renard, J. P.; Regnault, L. P.; Verdaguer, M. Experimental Evidences for An Haldane Gap in Quasi One-Dimensional Antiferromagnets. J. Phys. (Paris) 1988, 49, 1425–1429. doi:10.1051/jphyscol:19888655
   Google Scholar
• Eggert, S.; Affleck, I.; Horton, M. D. P. Néel Order in Doped Quasi-One-Dimensional Antiferromagnets. Phys. Rev. Lett. 2002, 89, 047202. doi:10.1103/PhysRevLett.89.047202
   PubMed Web of Science ®Google Scholar
• Jolicoeur, T.; Golinelli, O. Physics of Integer-Spin Antiferromagnetic Chains: Haldane Gaps and Edge States. CR Chim. 2019, 22, 445–451. doi:10.1016/j.crci.2019.05.005
   Web of Science ®Google Scholar
• Vasiliev, A.; Volkova, O.; Zvereva, E.; Markina, M. Milestones of low-D Quantum Magnetism. Npj Quant. Mater. 2018, 3, 18. doi:10.1038/s41535-018-0090-7
   Web of Science ®Google Scholar
• Streltsov, S. V.; Khomskii, D. I. Orbital Physics in Transition Metal Compounds: New Trends. Phys.-Usp. 2017, 60, 1121–1146. doi:10.3367/UFNe.2017.08.038196
   Web of Science ®Google Scholar
• Bartlett, S. D.; Brennen, G. K.; Miyake, A.; Renes, J. M. Quantum Computational Renormalization in the Haldane Phase. Phys. Rev. Lett. 2010, 105, 110502. doi:10.1103/PhysRevLett.105.110502
   PubMed Web of Science ®Google Scholar
• Else, D. V.; Schwarz, I.; Bartlett, S. D.; Doherty, A. C. Symmetry-Protected Phases for Measurement-Based Quantum Computation. Phys. Rev. Lett. 2012, 108, 240505. doi:10.1103/PhysRevLett.108.240505
   PubMed Web of Science ®Google Scholar
• Lajkó, M.; Wamer, K.; Mila, F.; Affleck, I. Generalization of the Haldane Conjecture to SU(3) Chains. Nucl. Phys. B 2017, 924, 508–577. doi:10.1016/j.nuclphysb.2017.09.015
   Web of Science ®Google Scholar
• Gozel, S.; Nataf, P.; Mila, F. Haldane Gap of the Three-Box Symmetric SU(3) Chain. Phys. Rev. Lett. 2020, 125, 057202. doi:10.1103/PhysRevLett.125.057202
   PubMed Web of Science ®Google Scholar
• Haldane, F. D. M. Nobel Lecture: Topological Quantum Matter. Rev. Mod. Phys. 2017, 89, 040502. doi:10.1103/RevModPhys.89.040502
   Web of Science ®Google Scholar