. [J]. Frontiers of Physics, 2019, 14(2): 23302.
D. J. J. Farnell. Emergence of magnetic order in kagomé antiferromagnets. Front. Phys. , 2019, 14(2): 23302.
L. Balents, M. P. Fisher, and S. M. Girvin, Fractionalization in an easy-axis kagomé antiferromagnet, Phys. Rev. B 65(22), 224412 (2002) https://doi.org/10.1103/PhysRevB.65.224412
3
T. H. Han, J. S. Helton, S. Chu, D. G. Nocera, J. A. Rodriguez-Rivera, C. Broholm, and Y. S. Lee, Fractionalized excitations in the spin-liquid state of a kagomé- lattice antiferromagnet, Nature 492, 406 (2012) https://doi.org/10.1038/nature11659
4
J. Richter, J. Schulenburg, and A. Honecker, Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder, Lect. Notes Phys. 645, pp 85–153, Heidelberg Berlin: Springer, 2004 https://doi.org/10.1007/BFb0119592
5
D. J. J. Farnell, O. Götze, J. Richter, R. F. Bishop, and P. H. Y. Li, Quantum s= 1/2 antiferromagnets on Archimedean lattices: The route from semiclassical magnetic order to nonmagnetic quantum states, Phys. Rev. B 89(18), 184407 (2014) https://doi.org/10.1103/PhysRevB.89.184407
6
J. T. Chalker, P. C. W. Holdsworth, and E. F. Shender, Hidden order in a frustrated system: Properties of the Heisenberg kagomé antiferromagnet, Phys. Rev. Lett. 68(6), 855 (1992) https://doi.org/10.1103/PhysRevLett.68.855
7
J. T. Chalker and J. F. G. Eastmond, Ground-state disorder in the spin-1/2 kagomé Heisenberg antiferromagnet, Phys. Rev. B 46(21), 14201 (1992) https://doi.org/10.1103/PhysRevB.46.14201
8
I. Ritchey, P. Chandra, and P. Coleman, Spin folding in the two-dimensional Heisenberg kagomé antiferromagnet, Phys. Rev. B 47(22), 15342 (1993) https://doi.org/10.1103/PhysRevB.47.15342
P. Müller, A. Zander, and J. Richter, Thermodynamics of the kagomé-lattice Heisenberg antiferromagnet with arbitrary spin S, Phys. Rev. B 98(2), 024414 (2018) https://doi.org/10.1103/PhysRevB.98.024414
S. Sachdev, Kagomé- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons, Phys. Rev. B 45(21), 12377 (1992) https://doi.org/10.1103/PhysRevB.45.12377
13
C. L. Henley, Long-range order in the classical kagomé antiferromagnet: Effective Hamiltonian approach, Phys. Rev. B 80, 180401 (2009) https://doi.org/10.1103/PhysRevB.80.180401
14
S. Depenbrock, I. P. McCulloch, and U. Schollwöck, Nature of the spin-liquid ground state of the S= 1/2 Heisenberg model on the kagomé lattice, Phys. Rev. Lett. 109(6), 067201 (2012) https://doi.org/10.1103/PhysRevLett.109.067201
15
S. Yan, D. A. Huse, and S. R. White, Spin-liquid ground state of the S= 1/2 kagomé Heisenberg antiferromagnet, Science 332(6034), 1173 (2011) https://doi.org/10.1126/science.1201080
16
H. C. Jiang, Z. Y. Weng, and D. N. Sheng, Density matrix renormalization group numerical study of the kagomé antiferromagnet, Phys. Rev. Lett. 101(11), 117203 (2008) https://doi.org/10.1103/PhysRevLett.101.117203
17
G. Evenbly and G. Vidal, Frustrated antiferromagnets with entanglement renormalization: Ground state of the spin-1/2 Heisenberg model on a kagomé lattice, Phys. Rev. Lett. 104(18), 187203 (2010) https://doi.org/10.1103/PhysRevLett.104.187203
18
R. R. P. Singh and D. A. Huse, Ground state of the spin- 1/2 kagomé-lattice Heisenberg antiferromagnet, Phys. Rev. B 76(18), 180407 (2007) https://doi.org/10.1103/PhysRevB.76.180407
19
O. Götze, D. J. J. Farnell, R. F. Bishop, P. H. Y. Li, and J. Richter, Heisenberg antiferromagnet on the kagomé lattice with arbitrary spin: A higher-order coupled cluster treatment, Phys. Rev. B 84(22), 224428 (2011) https://doi.org/10.1103/PhysRevB.84.224428
20
H. J. Liao, Z. Y. Xie, J. Chen, Z. Y. Liu, H. D. Xie, R. Z. Huang, B. Normand, and T. Xiang, Gapless spin-liquid ground state in the S= 1/2 kagomé antiferromagnet, Phys. Rev. Lett. 118(13), 137202 (2017) https://doi.org/10.1103/PhysRevLett.118.137202
21
A. M. Läuchli, J. Sudan, and E. S. Sorensen, Groundstate energy and spin gap of spin-1/2 kagomé-Heisenberg antiferromagnetic clusters: Large-scale exact diagonalization results, Phys. Rev. B 83(21), 212401 (2011) https://doi.org/10.1103/PhysRevB.83.212401
22
H. Nakano and T. Sakai, Numerical-diagonalization study of spin gap issue of the kagomé lattice Heisenberg antiferromagnet, J. Phys. Soc. Jpn. 80(5), 053704 (2011) https://doi.org/10.1143/JPSJ.80.053704
M. Fu, T. Imai, T. H. Han, and Y. S. Lee, Evidence for a gapped spin-liquid ground state in a kagomé Heisenberg antiferromagnet, Science 350(6261), 655 (2015) https://doi.org/10.1126/science.aab2120
28
Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Gapless spin-liquid phase in the kagomé spin-1/2 Heisenberg antiferromagnet, Phys. Rev. B 87, 060405(R) (2013)
29
M. Hermele, Y. Ran, P. A. Lee, and X. G. Wen, Properties of an algebraic spin liquid on the kagomé lattice, Phys. Rev. B 77(22), 224413 (2008) https://doi.org/10.1103/PhysRevB.77.224413
30
J. B. Marston and C. Zeng, Spin-Peierls and spin-liquid phases of kagomé quantum antiferromagnets, J. Appl. Phys. 69(8), 5962 (1991) https://doi.org/10.1063/1.347830
31
P. Nikolic and T. Senthil, Physics of low-energy singlet states of the kagomé lattice quantum Heisenberg antiferromagnet, Phys. Rev. B 68(21), 214415 (2003) https://doi.org/10.1103/PhysRevB.68.214415
32
D. Schwandt, M. Mambrini, and D. Poilblanc, Generalized hard-core dimer model approach to low-energy Heisenberg frustrated antiferromagnets: General properties and application to the kagomé antiferromagnet, Phys. Rev. B 81(21), 214413 (2010) https://doi.org/10.1103/PhysRevB.81.214413
33
D. Poilblanc, M. Mambrini, and D. Schwandt, Effective quantum dimer model for the kagomé Heisenberg antiferromagnet: Nearby quantum critical point and hidden degeneracy, Phys. Rev. B 81(18), 180402 (2010) https://doi.org/10.1103/PhysRevB.81.180402
34
J. Oitmaa and R. R. P. Singh, Competing orders in spin- 1 and spin-3/2 XXZkagomé antiferromagnets: A series expansion study, Phys. Rev. B 93(1), 014424 (2016) https://doi.org/10.1103/PhysRevB.93.014424
35
D. J. J. Farnell, O. Götze, J. Richter, R. Zinke, R. F. Bishop, and P. H. Y. Li, The interplay between lattice topology, frustration, and spin quantum number in quantum antiferromagnets on Archimedean Lattices, Phys. Rev. B 98(22), 224402 (2018) https://doi.org/10.1103/PhysRevB.98.224402
36
T. Liu, W. Li, A. Weichselbaum, J. von Delft, and G. Su, Simplex valence-bond crystal in the spin-1 kagomé Heisenberg antiferromagnet. Phys. Rev. B 91, 060403(R) (2015)
37
H. Changlani and A. M. Läuchli. Trimerized ground state of the spin-1 Heisenberg antiferromagnet on the kagomé lattice, Phys. Rev. B 91, 100407(R) (2015)
38
S. Nishimoto and M. Nakamura, Non-symmetry-breaking ground state of the S= 1 Heisenberg model on the kagomé lattice, Phys. Rev. B 92, 140412(R) (2015)
39
T. Liu, W. Li, and G. Su, Spin-ordered ground state and thermodynamic behaviors of the spin-3/2 kagomé Heisenberg antiferromagnet, Phys. Rev. E 94(3), 032114 (2016) https://doi.org/10.1103/PhysRevE.94.032114
40
O. Cépas and A. Ralko, Resonating color state and emergent chromodynamics in the kagomé antiferromagnet, Phys. Rev. B 84(2), 020413 (2011) https://doi.org/10.1103/PhysRevB.84.020413
41
A. L. Chernyshev and M. E. Zhitomirsky, Quantum selection of order in an XXZantiferromagnet on a kagomé lattice, Phys. Rev. Lett. 113(23), 237202 (2014) https://doi.org/10.1103/PhysRevLett.113.237202
42
O. Götze and J. Richter, Ground-state phase diagram of the XXZ spin-skagomé antiferromagnet: A coupledcluster study, Phys. Rev. B 91(10), 104402 (2015) https://doi.org/10.1103/PhysRevB.91.104402
43
C. Xu and J. E. Moore, Geometric criticality for transitions between plaquette phases in integer-spin kagomé XXZantiferromagnets, Phys. Rev. B 72(6), 064455 (2005) https://doi.org/10.1103/PhysRevB.72.064455
44
Y. C. He and Y. Chen, Distinct spin liquids and their transitions in spin-1/2 XXZkagomé antiferromagnets, Phys. Rev. Lett. 114(3), 037201 (2015) https://doi.org/10.1103/PhysRevLett.114.037201
45
W. J. Hu, S. S. Gong, F. Becca, and D. N. Sheng, Variational Monte Carlo study of a gapless spin liquid in the spin-1/2 XXZantiferromagnetic model on the kagomé lattice, Phys. Rev. B 92(20), 201105 (2015) https://doi.org/10.1103/PhysRevB.92.201105
46
D. Schmalfuβ, J. Richter, and D. Ihle, Absence of longrange order in a spin-half Heisenberg antiferromagnet on the stacked kagomé lattice, Phys. Rev. B 70(18), 184412 (2004) https://doi.org/10.1103/PhysRevB.70.184412
47
D. Guterding, R. Valentí, and H. O. Jeschke, Reduction of magnetic interlayer coupling in barlowite through isoelectronic substitution, Phys. Rev. B 94(12), 125136 (2016) https://doi.org/10.1103/PhysRevB.94.125136
48
O. Götze and J. Richter, The route to magnetic order in the spin-1/2 kagomé Heisenberg antiferromagnet: The role of interlayer coupling, Europhys. Lett. 114(6), 67004 (2016) https://doi.org/10.1209/0295-5075/114/67004
49
T. Tay and O. I. Motrunich, Variational study of J1–J2 Heisenberg model on kagomé lattice using projected Schwinger-boson wave functions, Phys. Rev. B 84, 020404(R) (2011)
50
R. Suttner, C. Platt, J. Reuther, and R. Thomale, Renormalization group analysis of competing quantum phases in the J1–J2 Heisenberg model on the kagomé lattice, Phys. Rev. B 89(2), 020408 (2014) https://doi.org/10.1103/PhysRevB.89.020408
51
F. Kolley, S. Depenbrock, I. P. McCulloch, U. Schollwöck, and V. Alba, Phase diagram of the J1–J2 Heisenberg model on the kagomé lattice, Phys. Rev. B 91(10), 104418 (2015) https://doi.org/10.1103/PhysRevB.91.104418
52
J. Richter and O. Götze, unpublished
53
A. B. Harris, C. Kallin, and A. J. Berlinsky, Possible Néel orderings of the Kagomé antiferromagnet, Phys. Rev. B 45(6), 2899 (1992) https://doi.org/10.1103/PhysRevB.45.2899
54
B. Bernu, C. Lhuillier, E. Kermarrec, F. Bert, P. Mendels, R. H. Colman, and A. S. Wills, Exchange energies of kapellasite from high-temperature series analysis of the kagomé lattice J1–J2–JdHeisenberg model, Phys. Rev. B 87(15), 155107 (2013) https://doi.org/10.1103/PhysRevB.87.155107
55
Y. Iqbal, H. O. Jeschke, J. Reuther, R. Valenti, I. I. Mazin, M. Greiter, and R. Thomale, Paramagnetism in the kagomé compounds (Zn,Mg,Cd)Cu3(OH)6Cl2, Phys. Rev. B 92(22), 220404 (2015) https://doi.org/10.1103/PhysRevB.92.220404
56
S. Bieri, L. Messio, B. Bernu, and C. Lhuillier, Gapless chiral spin liquid in a kagomé Heisenberg model, Phys. Rev. B 92(6), 060407 (2015) https://doi.org/10.1103/PhysRevB.92.060407
57
A. Wietek, A. Sterdyniak, and A. M. Läuchli, Nature of chiral spin liquids on the kagomé lattice, Phys. Rev. B 92(12), 125122 (2015) https://doi.org/10.1103/PhysRevB.92.125122
58
Z. Hiroi, H. Yoshida, Y. Okamoto, and M. Takigawa, Spin-1/2 kagomé compounds: Volborthite vs. herbertsmithite, J. Phys. Conf. Ser. 145(1), 012002 (2009) https://doi.org/10.1088/1742-6596/145/1/012002
59
O. Janson, J. Richter, and H. Rosner, Modified kagomé physics in the natural spin-1/2 kagomé lattice systems: Kapellasite Cu3Zn(OH)6Cl2 and haydeeite Cu3Mg(OH)6Cl2, Phys. Rev. Lett. 101(10), 106403 (2008) https://doi.org/10.1103/PhysRevLett.101.106403
60
Y. Okamoto, H. Yoshida, and Z. Hiroi, Vesignieite BaCu3V2OV8(OH)2 as a candidate spin-1/2 kagomé antiferromagnet, J. Phys. Soc. Jpn. 78(3), 033701 (2009) https://doi.org/10.1143/JPSJ.78.033701
61
B. Fåk, E. Kermarrec, L. Messio, B. Bernu, C. Lhuillier, F. Bert, P. Mendels, B. Koteswararao, F. Bouquet, J. Ollivier, A. D. Hillier, A. Amato, R. H. Colman, and A. S. Wills, Kapellasite: A kagomé quantum spin liquid with competing interactions, Phys. Rev. Lett. 109(3), 037208 (2012) https://doi.org/10.1103/PhysRevLett.109.037208
62
O. Janson, J. Richter, P. Sindzingre, and H. Rosner, Coupled frustrated quantum spin-1/2 chains with orbital order in volborthite Cu3V2O7(OH)2··2H2O, Phys. Rev. B 82(10), 104434 (2010) https://doi.org/10.1103/PhysRevB.82.104434
63
I. Rousochatzakis, J. Richter, R. Zinke, and A. A. Tsirlin, Frustration and Dzyaloshinsky-Moriya anisotropy in the kagomé francisites Cu3Bi(SeO3)2O2X (X= Br, Cl), Phys. Rev. B 91(2), 024416 (2015) https://doi.org/10.1103/PhysRevB.91.024416
