カゴメ格子反強磁性体における新奇な異常量子現象の理論的・数値的研究

• Project Area: Novel States of Matter Induced by Frustration
• Project/Area Number: 22014012
• Research Category: Grant-in-Aid for Scientific Research on Priority Areas
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: University of Hyogo
• Principal Investigator: 坂井 徹 兵庫県立大学, 大学院・物質理学研究科, 教授 (60235116)
• Co-Investigator(Kenkyū-buntansha): 中野 博生 兵庫県立大学, 大学院・物質理学研究科, 助教 (00343418) ; 礒田 誠 香川大学, 教育学部, 教授 (10184590)
• Project Period (FY): 2010 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥1,800,000 (Direct Cost: ¥1,800,000); Fiscal Year 2011: ¥700,000 (Direct Cost: ¥700,000); Fiscal Year 2010: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: フラストレーション / カゴメ格子 / 量子スピン系 / 反強磁性 / 磁化プラトー / カゴメ格子反強磁性体 / スピンギャップ / 磁化過程 / 量子相転移

Research Abstract

カゴメ格子反強磁性体の磁化過程において、とくに飽和磁化の3分の1のところで現れる磁化曲線の異常として、これまでの研究により磁化ランプ現象を提唱した。本年度は、この磁化ランプ現象をより明確に定式化する目的で、従来から磁化プラトー現象が現れることで知られている三角格子反強磁性体との定量的な比較を試みた。まず飽和磁化の3分の1の点における磁化プラトー幅が存在するかどうかを、有限系の数値対角化と有限サイズスケーリングにより推定したところ、三角格子では予想通り明確なプラトーが存在するが、カゴメ格子では外挿による誤差の範囲でプラトー幅がゼロになり、プラトーを伴わない唯一の臨界磁場において量子相転移が起きる可能性が示唆された。さらに、この臨界磁場の両サイドにおける磁化曲線の臨界指数を、有限サイズスケーリングにより見積もったところ、三角格子においては二次元系の従来の磁化プラトーで理論的に求められている値と一致したが、カゴメ格子においては、これとは全く異なる値を示すとともに、低磁場側と高磁場側では違う値となり、これまでにない新しい量子相転移であることが判明した。このカゴメ格子と三角格子の違いをさらに明確にするために、空間的な非一様性を持つ三角格子で、相互作用パラメータを変化させることにより、一様な三角格子とカゴメ格子を連続的につなぐ理論模型を導入し、両者の間における量子相転移の有無を検討した。この非一様な三角格子に対して、有限サイズスケーリングを適用するため、相似形のクラスターのグループを作り、各グループで独立に求める外挿値が一致するという拘束条件のもとでサイズスケーリングを実行した。その結果、カゴメ格子に非常に近いパラメータ領域で、磁化3分の1における量子相転移が起きることが判明し、磁化ランプと磁化プラトーが全く違う現象であることが裏付けられた。

Research Products

• [Journal Article] Spin-chirality separation and S3-symmetry breakings in the magnetization plateau of the quantum spin tube (2012)
  • Author(s): Kouichi Okunishi, Masahiro Sato, Toru Sakai, Kiyomi Okamoto, and Chigak. Itoi
  • Journal Title: Phys. Rev. B Volume: 85 Issue: 5 Pages: 54416-54416
  • DOI: 10.1103/physrevb.85.054416
  • Peer Reviewed
• [Journal Article] Frustration Induced Ferrimagnetism in S=1/2 Heisenberg Spin Chain (2011)
  • Author(s): T.Shimokawa
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 4 Pages: 043703-043703
  • DOI: 10.1143/jpsj.80.043703
  • Peer Reviewed
• [Journal Article] Numerical-Diagonalization Study of Spin Gap Issue of the Kagome Lattice Heisenberg Antiferromagnet (2011)
  • Author(s): H.Nakano
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 5 Pages: 053704-053704
  • DOI: 10.1143/jpsj.80.053704
  • NAID: 40018798403
  • Peer Reviewed
• [Journal Article] Thermodynamic Properties of Spin-1/2 Ising-like Heisenberg Model on Triangle-based Lattices (2011)
  • Author(s): M.Isoda
  • Journal Title: Modern Physics Letters B Volume: 25 Issue: 12n13 Pages: 909-915
  • DOI: 10.1142/s0217984911026619
  • Peer Reviewed
• [Journal Article] Ferrimagnetism of the Heisenberg model on the Kagome strip lattice (2011)
  • Author(s): T.Shimokawa
  • Journal Title: Journal of Physics : Conference Series Volume: 320 Pages: 012007-012007
  • DOI: 10.1088/1742-6596/320/1/012007
  • Peer Reviewed
• [Journal Article] Quantum critical phenomena in magnetization process of the Kagome and triangular lattice antiferromagnets (2011)
  • Author(s): T.Sakai
  • Journal Title: Journal of Physics : Conference Series Volume: 320 Pages: 012016-012016
  • DOI: 10.1088/1742-6596/320/1/012016
  • Peer Reviewed
• [Journal Article] Numerical exact diagonalization study of triangulated kagome Heisenberg spin system (2011)
  • Author(s): M.Isoda
  • Journal Title: Journal of Physics : Conference Series Volume: 320 Pages: 012010-012010
  • DOI: 10.1088/1742-6596/320/1/012010
  • Peer Reviewed
• [Journal Article] Magnetization ramp of the kagome lattice antiferromagnet (2011)
  • Author(s): H.Nakano
  • Journal Title: Journal of Physics : Conference Series Volume: 320 Pages: 012017-012017
  • DOI: 10.1088/1742-6596/320/1/012017
  • Peer Reviewed
• [Journal Article] Ground-state phase diagram of S=2 quantum spin chain with the XXZ and on-site anisotropies (2011)
  • Author(s): K.Okamoto
  • Journal Title: Journal of Physics : Conference Series Volume: 302 Pages: 012014-012014
  • DOI: 10.1088/1742-6596/302/1/012014
  • Peer Reviewed
• [Journal Article] Specific Heat and Magnetic Susceptibility of Ising-like Anisotropic Heisenberg Model on Kagome Lattice (2011)
  • Author(s): M.Isoda
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 8 Pages: 084704-084704
  • DOI: 10.1143/jpsj.80.084704
  • NAID: 40018947234
  • Peer Reviewed
• [Journal Article] Hyperbolic Deformation Applied to S=1 Spin Chains-Scaling Relation in Excitation Energy- (2011)
  • Author(s): Hiroshi Ueda
  • Journal Title: Journal of the Physical Society of Japan Volume: 80 Issue: 9 Pages: 094001-094001
  • DOI: 10.1143/jpsj.80.094001
  • Peer Reviewed
• [Journal Article] Quantum Magnetization Plateau in Spin-1 Triangular-Lattice Antiferromagnet Ba3NiSb2O9 (2011)
  • Author(s): Y.Shirata
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 9 Pages: 093702-093702
  • DOI: 10.1143/jpsj.80.093702
  • Peer Reviewed
• [Journal Article] Magnetic-Field Induced Quantum Phase Transitions in Triangular-Lattice Antiferromagnets (2011)
  • Author(s): T.Ono
  • Journal Title: Journal of Physics : Conference Series Volume: 302 Pages: 012003-012003
  • DOI: 10.1088/1742-6596/302/1/012003
  • Peer Reviewed
• [Journal Article] How to distinguish the Haldane/Large-D state and the intermediate-D state in an S=2 quantum spin chain with the XXZ and on-site anisotropies (2011)
  • Author(s): K.Okamoto
  • Journal Title: Journal of Physics : Conference Series Volume: 320 Pages: 012018-012018
  • DOI: 10.1088/1742-6596/320/1/012018
  • Peer Reviewed
• [Journal Article] Frustration Induced Ferrimagnetism in Heisenberg Spin Chains (2011)
  • Author(s): T.Shimokawa
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 12 Pages: 125003-125003
  • DOI: 10.1143/jpsj.80.125003
  • Peer Reviewed
• [Journal Article] Numerical Study on the Spin Gap of the Kagome Lattice Antiferromagnet (2011)
  • Author(s): T.Sakai
  • Journal Title: Journal of Physical Society of Japan, Supplement B Volume: 80
  • Peer Reviewed
• [Journal Article] Magnetization Plateau of the Quantum Spin Nanotube (2011)
  • Author(s): K.Okamoto
  • Journal Title: Physica E Volume: 43 Issue: 3 Pages: 769-772
  • DOI: 10.1016/j.physe.2010.07.047
  • Peer Reviewed
• [Journal Article] Haldane, Large-D and Intermediate-D States in an S=2 Quantum Spin Chain with On-Site and XXZ Anisotropies (2011)
  • Author(s): T.Tonegawa
  • Journal Title: Journal of Physical Society of Japan Volume: 80 Issue: 4 Pages: 043001-043001
  • DOI: 10.1143/jpsj.80.043001
  • Peer Reviewed
• [Journal Article] Exotic Quantum Critical Phenomena of the Spin Nanotubes (2011)
  • Author(s): T.Sakai
  • Journal Title: Journal of Physics : Conference Series Volume: 302 Pages: 012013-012013
  • DOI: 10.1088/1742-6596/302/1/012013
  • Peer Reviewed
• [Journal Article] Exotic quantum phase transitions in the spin nanotube (2011)
  • Author(s): T.Sakai
  • Journal Title: Journal of Physics : Conference Series Volume: 320 Pages: 012022-012022
  • DOI: 10.1088/1742-6596/320/1/012022
  • Peer Reviewed
• [Journal Article] 籠目格子反強磁性体の磁化過程--「磁化ランプ」という異常臨界現象-- (2011)
  • Author(s): 中野博生
  • Journal Title: 日本物理学会誌 Volume: 66 Pages: 832-836
  • Peer Reviewed
• [Journal Article] Collapse of Ferrimagnetism in Two-Dimensional Heisenberg Antiferromagnet due to Frustration (2011)
  • Author(s): H.Nakano
  • Journal Title: Journal of Physical Society of Japan Volume: 80
  • NAID: 40018753705
  • Peer Reviewed
• [Journal Article] Critical magnetization behavior of the triangular- and kagome-lattice quantum antiferromagnets (2011)
  • Author(s): T.Sakai
  • Journal Title: Physical Review B Volume: 83
  • Peer Reviewed
• [Journal Article] Magnetization Process of the Kagome Lattice Antiferromagnet (2010)
  • Author(s): H.Nakano
  • Journal Title: Journal of Physical Society of Japan Volume: 79
  • Peer Reviewed
• [Journal Article] Field Induced Exotic Phenomena of the S=1/2 Three-Leg Quantum Spin Nanotube (2010)
  • Author(s): T.Sakai
  • Journal Title: Journal of Low Temperature Physics Volume: 159 Pages: 55-58
  • Peer Reviewed
• [Journal Article] Magnetization Process of the S=1/2 Distorted Diamond Spin Chain with the Dzyaloshinsky-Moriya interaction (2010)
  • Author(s): T.Sakai
  • Journal Title: Journal of Physics : Conference Series Volume: 200
  • Peer Reviewed
• [Journal Article] Field-Induced Nematic Phase in the Spin Ladder System with Easy-Axis Anisotropy (2010)
  • Author(s): T.Sakai
  • Journal Title: Physica Status Solidi B Volume: 247 Pages: 583-585
  • Peer Reviewed
• [Journal Article] Numerical Exact Diagonalization Study on a Phonon-Assisted Hole Paring in the High-Tc Cuprates (2010)
  • Author(s): T.Sakai
  • Journal Title: Physica C Volume: 470
  • Peer Reviewed
• [Journal Article] Quantum Spin Nanotubes---frustration, competing orders and Criticalities (2010)
  • Author(s): T.Sakai
  • Journal Title: Journal of Physics : Condensed Matter Volume: 22
  • Peer Reviewed
• [Presentation] 数値対角化法による2次元フラストレート系の研究-カゴメ格子反強磁性体と三角格子反強磁性体- (2012)
  • Author(s): 中野博生
  • Organizer: 東大物性研短期研究会、物性研究所共同利用スパコン成果報告会「計算科学の課題と展望」
  • Place of Presentation: 東京大学物性研究所(千葉県)(招待講演)
  • Year and Date: 2012-02-21
• [Presentation] カゴメ格子反強磁性体の新しい量子現象'磁化ランプ'とスピンギャップ問題 (2011)
  • Author(s): 中野博生
  • Organizer: 日本物理学会2011年秋季大会
  • Place of Presentation: 富山大学五福キャンパス(富山県)(招待講演)
  • Year and Date: 2011-09-23
• [Presentation] Quantum Critical Magnetization Behaviors of the Kagome and Triangular Lattice Antiferromagnets (2011)
  • Author(s): T.Sakai
  • Organizer: Workshop on Development of Functionalized Mole cular-Based Magnetic Materials
  • Place of Presentation: IMR, Tohoku University, Sendai(宮城県)(Invited)
  • Year and Date: 2011-09-12
• [Presentation] 量子スピン系の大規模並列数値対角化計算---カゴメ格子反強磁性体の物性解明--- (2011)
  • Author(s): 中野博生
  • Organizer: 異分野交流研究会「量子系の固有値問題と大規模計算」
  • Place of Presentation: 筑波大学計算科学研究センター(茨城県)(招待講演)
  • Year and Date: 2011-07-26
• [Presentation] スピンナノチューブの量子現象 (2010)
  • Author(s): 坂井徹
  • Organizer: 東北大学理学部GCOE研究会「金属錯体の固体物性科学最前線-錯体化学と固体物性物理と生物物性の連携新領域創成をめざして-」
  • Place of Presentation: 東北大学理学研究科(宮城県)(招待講演)
  • Year and Date: 2010-12-05
• [Presentation] Topological Aspects of the Quantum Spin Nanotube (2010)
  • Author(s): T.Sakai
  • Organizer: International and Interdisciplinary Workshop on Novel Phenomena in Integrated Complex Sciences
  • Place of Presentation: 京都コープイン(京都府)(招待講演)
  • Year and Date: 2010-10-14
• [Presentation] Magnetization Ramp of Kagome Lattice Antiferromagnet (2010)
  • Author(s): T.Sakai
  • Organizer: International Workshop on Statistical Physics of Quantum Systems
  • Place of Presentation: 東京大学生産技術研究所(東京都)(招待講演)
  • Year and Date: 2010-08-02
• [Presentation] Magnetization Process of Kagome Lattice Antifferomagnet (2010)
  • Author(s): T.Sakai
  • Organizer: magnetism and superconductivity meeting
  • Place of Presentation: Institut Laue Langevinグルノーブル(フランス)(招待講演)
  • Year and Date: 2010-05-27
• [Remarks]
  • URL: http://cmt.spring8.or.jp/index.shtml