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Frontiers of Physics

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ISSN 2095-0470(Online)

CN 11-5994/O4

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2018 Impact Factor: 2.483

Front. Phys.    2020, Vol. 15 Issue (6) : 63201    https://doi.org/10.1007/s11467-020-0974-4
TOPICAL REVIEW
Spin-1 pyrochlore antiferromagnets: Theory, model, and materials’ survey
Yong-Hao Gao1, Xu-Ping Yao2, Fei-Ye Li1, Gang Chen2()
1. State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China
2. Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics at Hong Kong, The University of Hong Kong, Hong Kong, China
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Abstract

Pyrochlore magnets can be a unique platform to demonstrate numerous important concepts and applications of frustrated magnetic physics in modern condensed matter physics. Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments, while much less works have studied the spin-1 systems. We here review the physics with interacting spin-1 local moments on the pyrochlore lattice to illustrate the potentially interesting physics associated with spin-1 magnets. The generic pyrochlore spin-1 model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii– Moriya interaction and the single-ion spin anisotropy. The global phase diagram of this generic spin model is reviewed, and the relation between different quantum phases in the phase diagram is clarified. The critical properties of the transition from the parent quantum paramagnet to the proximate orders are discussed. The presence of quantum order by disorder in the parts of the ordered phases is analyzed. The elementary excitations with respect to the ground states are further reviewed, and the topological natures of these excitations are carefully addressed. The materials’ relevance of the spin-1 pyrochlore magnets are finally reviewed. This review may provide insights about the interesting spin-1 local moments on frustrated systems.

Keywords topological magnon      quantum order by disorder      Dzyaloshinskii–Moriya interaction      flavor wave theory     
Corresponding Author(s): Gang Chen   
Issue Date: 21 July 2020
 Cite this article:   
Yong-Hao Gao,Xu-Ping Yao,Fei-Ye Li, et al. Spin-1 pyrochlore antiferromagnets: Theory, model, and materials’ survey[J]. Front. Phys. , 2020, 15(6): 63201.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-020-0974-4
https://academic.hep.com.cn/fop/EN/Y2020/V15/I6/63201
1 F. D. M. Haldane, Nonlinear field theory of large-spin Heisenberg antiferromagnets: Semiclassically quantized solitons of the one-dimensional easy-axis Néel state, Phys. Rev. Lett. 50(15), 1153 (1983)
https://doi.org/10.1103/PhysRevLett.50.1153
2 F. Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model, Phys. Lett. A 93(9), 464 (1983)
https://doi.org/10.1016/0375-9601(83)90631-X
3 I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Rigorous results on valence-bond ground states in antiferromagnets, Phys. Rev. Lett. 59(7), 799 (1987)
https://doi.org/10.1103/PhysRevLett.59.799
4 X. Chen, Z. C. Gu, and X. G. Wen, Classification of gapped symmetric phases in one-dimensional spin systems, Phys. Rev. B 83(3), 035107 (2011)
https://doi.org/10.1103/PhysRevB.83.035107
5 C. Wang, A. Nahum, and T. Senthil, Topological paramagnetism in frustrated spin-1 Mott insulators, Phys. Rev. B 91(19), 195131 (2015)
https://doi.org/10.1103/PhysRevB.91.195131
6 G. Chen, Quantum paramagnet and frustrated quantum criticality in a spin-one diamond lattice antiferromagnet, Phys. Rev. B 96(2), 020412 (2017)
https://doi.org/10.1103/PhysRevB.96.020412
7 L. Savary, Quantum loop states in spin–orbital models on the honeycomb lattice, arXiv: 1511.01505 (2015)
8 Z. Wang, A. E. Feiguin, W. Zhu, O. A. Starykh, A. V. Chubukov, and C. D. Batista, Chiral liquid phase of simple quantum magnets, Phys. Rev. B 96(18), 184409 (2017)
https://doi.org/10.1103/PhysRevB.96.184409
9 F. L. Buessen, M. Hering, J. Reuther, and S. Trebst, Quantum spin liquids in frustrated spin-1 diamond antiferromagnets, arXiv: 1706.06299 (2017)
https://doi.org/10.1103/PhysRevLett.120.057201
10 J. R. Chamorro, L. Ge, J. Flynn, M. A. Subramanian, M. Mourigal, and T. M. McQueen, Frustrated spin one on a diamond lattice in NiRh2O4, Phys. Rev. Mater. 2(3), 034404 (2018)
https://doi.org/10.1103/PhysRevMaterials.2.034404
11 J. G. Cheng, G. Li, L. Balicas, J. S. Zhou, J. B. Goodenough, C. Xu, and H. D. Zhou, High-pressure sequence of Ba3NiSb2O9 structural phases: New S= 1 quantum spin liquids based on Ni2+, Phys. Rev. Lett. 107(19), 197204 (2011)
https://doi.org/10.1103/PhysRevLett.107.197204
12 M. Serbyn, T. Senthil, and P. A. Lee, Exotic S= 1 spinliquid state with fermionic excitations on the triangular lattice, Phys. Rev. B 84(18), 180403 (2011)
https://doi.org/10.1103/PhysRevB.84.180403
13 S. Bieri, M. Serbyn, T. Senthil, and P. A. Lee, Paired chiral spin liquid with a Fermi surface in S= 1 model on the triangular lattice, Phys. Rev. B 86(22), 224409 (2012)
https://doi.org/10.1103/PhysRevB.86.224409
14 C. Xu, F. Wang, Y. Qi, L. Balents, and M. P. A. Fisher, Spin liquid phases for spin-1 systems on the triangular lattice, Phys. Rev. Lett. 108(8), 087204 (2012)
https://doi.org/10.1103/PhysRevLett.108.087204
15 G. Chen, M. Hermele, and L. Radzihovsky, Frustrated quantum critical theory of putative spin-liquid phenomenology in 6H-B-Ba3NiSb2O9, Phys. Rev. Lett. 109(1), 016402 (2012)
https://doi.org/10.1103/PhysRevLett.109.016402
16 K. Hwang, T. Dodds, S. Bhattacharjee, and Y. B. Kim, Three-dimensional nematic spin liquid in a stacked triangular lattice 6H-B structure, Phys. Rev. B 87(23), 235103 (2013)
https://doi.org/10.1103/PhysRevB.87.235103
17 J. A. Quilliam, F. Bert, A. Manseau, C. Darie, C. Guillot-Deudon, C. Payen, C. Baines, A. Amato, and P. Mendels, Gapless quantum spin liquid ground state in the spin-1 antiferromagnet 6HB-Ba3NiSb2O9, Phys. Rev. B 93(21), 214432 (2016)
https://doi.org/10.1103/PhysRevB.93.214432
18 J. S. Gardner, M. J. P. Gingras, and J. E. Greedan, Magnetic pyrochlore oxides, Rev. Mod. Phys. 82(1), 53 (2010)
https://doi.org/10.1103/RevModPhys.82.53
19 S. T. Bramwell and M. J. P. Gingras, Spin ice state in frustrated magnetic pyrochlore materials, Science 294(5546), 1495 (2001)
https://doi.org/10.1126/science.1064761
20 R. G. Melko, B. C. den Hertog, and M. J. P. Gingras, Long-range order at low temperatures in dipolar spin ice, Phys. Rev. Lett. 87(6), 067203 (2001)
https://doi.org/10.1103/PhysRevLett.87.067203
21 C. Castelnovo, R. Moessner, and S. L. Sondhi, Magnetic monopoles in spin ice, Nature 451(7174), 42 (2008)
https://doi.org/10.1038/nature06433
22 H. R. Molavian, M. J. P. Gingras, and B. Canals, Dynamically induced frustration as a route to a quantum spin ice state in Tb2Ti2O7 via virtual crystal field excitations and quantum many-body effects, Phys. Rev. Lett. 98(15), 157204 (2007)
https://doi.org/10.1103/PhysRevLett.98.157204
23 M. J. P. Gingras and P. A. McClarty, Quantum spin ice: A search for gapless quantum spin liquids in pyrochlore magnets, Rep. Prog. Phys. 77(5), 056501 (2014)
https://doi.org/10.1088/0034-4885/77/5/056501
24 L. Savary and L. Balents, Quantum spin liquids: A review, Rep. Prog. Phys. 80(1), 016502 (2017)
https://doi.org/10.1088/0034-4885/80/1/016502
25 S. Onoda and Y. Tanaka, Quantum melting of spin ice: Emergent cooperative quadrupole and chirality, Phys. Rev. Lett. 105(4), 047201 (2010)
https://doi.org/10.1103/PhysRevLett.105.047201
26 L. Savary and L. Balents, Coulombic quantum liquids in spin-1/2 pyrochlores, Phys. Rev. Lett. 108(3), 037202 (2012)
https://doi.org/10.1103/PhysRevLett.108.037202
27 S. Lee, S. Onoda, and L. Balents, Generic quantum spin ice, Phys. Rev. B 86(10), 104412 (2012)
https://doi.org/10.1103/PhysRevB.86.104412
28 L. Savary and L. Balents, Spin liquid regimes at nonzero temperature in quantum spin ice, Phys. Rev. B 87(20), 205130 (2013)
https://doi.org/10.1103/PhysRevB.87.205130
29 H. Fukazawa, R. G. Melko, R. Higashinaka, Y. Maeno, and M. J. P. Gingras, Magnetic anisotropy of the spin-ice compound Dy2Ti2O7, Phys. Rev. B 65(5), 054410 (2002)
https://doi.org/10.1103/PhysRevB.65.054410
30 S. T. Bramwell, M. J. Harris, B. C. den Hertog, M. J. P. Gingras, J. S. Gardner, D. F. McMorrow, A. R. Wildes, A. L. Cornelius, J. D. M. Champion, R. G. Melko, and T. Fennell, Spin correlations in Ho2Ti2O7: A dipolar spin ice system, Phys. Rev. Lett. 87(4), 047205 (2001)
https://doi.org/10.1103/PhysRevLett.87.047205
31 K. A. Ross, J. P. C. Ruff, C. P. Adams, J. S. Gardner, H. A. Dabkowska, Y. Qiu, J. R. D. Copley, and B. D. Gaulin, Two-dimensional Kagome correlations and field induced order in the ferromagnetic XY pyrochlore Yb2Ti2O7, Phys. Rev. Lett. 103(22), 227202 (2009)
https://doi.org/10.1103/PhysRevLett.103.227202
32 Y. P. Huang, G. Chen, and M. Hermele, Quantum spin ices and topological phases from dipolar–octupolar doublets on the pyrochlore lattice, Phys. Rev. Lett. 112(16), 167203 (2014)
https://doi.org/10.1103/PhysRevLett.112.167203
33 G. Chen, “Magnetic monopole” condensation of the pyrochlore ice U(1) quantum spin liquid: Application to Pr2Ir2O7 and Yb2Ti2O7, Phys. Rev. B 94(20), 205107 (2016)
https://doi.org/10.1103/PhysRevB.94.205107
34 Y. Wan and O. Tchernyshyov, Quantum strings in quantum spin ice, Phys. Rev. Lett. 108(24), 247210 (2012)
https://doi.org/10.1103/PhysRevLett.108.247210
35 Y. D. Li and G. Chen, Symmetry enriched U(1) topological orders for dipole–octupole doublets on a pyrochlore lattice, Phys. Rev. B 95(4), 041106 (2017)
https://doi.org/10.1103/PhysRevB.95.041106
36 H. Yan, O. Benton, L. Jaubert, and N. Shannon, Theory of multiple-phase competition in pyrochlore magnets with anisotropic exchange with application to Yb2Ti2O7, Er2Ti2O7, and Er2Sn2O7, Phys. Rev. B 95(9), 094422 (2017)
https://doi.org/10.1103/PhysRevB.95.094422
37 L. Savary, X. Wang, H. Y. Kee, Y. B. Kim, Y. Yu, and G. Chen, Quantum spin ice on the breathing pyrochlore lattice, Phys. Rev. B 94(7), 075146 (2016)
https://doi.org/10.1103/PhysRevB.94.075146
38 T. Fennell, M. Kenzelmann, B. Roessli, M. K. Haas, and R. J. Cava, Power-law spin correlations in the pyrochlore antiferromagnet Tb2Ti2O7, Phys. Rev. Lett. 109(1), 017201 (2012)
https://doi.org/10.1103/PhysRevLett.109.017201
39 Y. Yasui, M. Kanada, M. Ito, H. Harashina, M. Sato, H. Okumura, K. Kakurai, and H. Kadowaki, Static correlation and dynamical properties of Tb3+-moments in Tb2Ti2O7 – neutron scattering study, J. Phys. Soc. Jpn. 71(2), 599 (2002)
https://doi.org/10.1143/JPSJ.71.599
40 J. S. Gardner, B. D. Gaulin, A. J. Berlinsky, P. Waldron, S. R. Dunsiger, N. P. Raju, and J. E. Greedan, Neutron scattering studies of the cooperative paramagnet pyrochlore Tb2Ti2O7, Phys. Rev. B 64(22), 224416 (2001)
https://doi.org/10.1103/PhysRevB.64.224416
41 Z. Hao, A. G. R. Day, and M. J. P. Gingras, Bosonic many-body theory of quantum spin ice, Phys. Rev. B 90(21), 214430 (2014)
https://doi.org/10.1103/PhysRevB.90.214430
42 L. J. Chang, S. Onoda, Y. Su, Y. J. Kao, K. D. Tsuei, Y. Yasui, K. Kakurai, and M. R. Lees, Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb2Ti2O7, Nat. Commun. 3(1), 992 (2012)
https://doi.org/10.1038/ncomms1989
43 K. Kimura, K. Nakatsuji, J. J. Wen, C. Broholm, M. Stone, E. Nishibori, and H. Sawa, Quantum fluctuations in spin-ice-like Pr2Zr2O7, Nat. Commun. 4(1), 1934 (2013)
https://doi.org/10.1038/ncomms2914
44 E. Lhotel, S. R. Giblin, M. R. Lees, G. Balakrishnan, L. J. Chang, and Y. Yasui, First-order magnetic transition in Yb2Ti2O7, Phys. Rev. B 89(22), 224419 (2014)
https://doi.org/10.1103/PhysRevB.89.224419
45 L.J. Chang, M. R. Lees, I. Watanabe, A. D. Hillier, Y. Yasui, and S. Onoda, Static magnetic moments revealed by muon spin relaxation and thermodynamic measurements in the quantum spin ice Yb2Ti2O7, Phys. Rev. B 89(18), 184416 (2014)
https://doi.org/10.1103/PhysRevB.89.184416
46 Y. Yasui, M. Soda, S. Iikubo, M. Ito, M. Sato, N. Hamaguchi, T. Matsushita, N. Wada, T. Takeuchi, N. Aso, and K. Kakurai, Ferromagnetic transition of pyrochlore compound Yb2Ti2O7, J. Phys. Soc. Jpn. 72(11), 3014 (2003)
https://doi.org/10.1143/JPSJ.72.3014
47 K. Ross, L. Savary, B. Gaulin, and L. Balents, Quantum excitations in quantum spin ice, Phys. Rev. X 1(2), 021002 (2011)
https://doi.org/10.1103/PhysRevX.1.021002
48 N. Shannon, O. Sikora, F. Pollmann, K. Penc, and P. Fulde, Quantum ice: A quantum Monte Carlo study, Phys. Rev. Lett. 108(6), 067204 (2012)
https://doi.org/10.1103/PhysRevLett.108.067204
49 P. Goswami, B. Roy, and S. Das Sarma, Itinerant spin ice order, Weyl metal, and anomalous Hall effect in Pr2Ir2O7, arXiv: 1603.02273 (2016)
50 K. E. Arpino, B. A. Trump, A. O. Scheie, T. M. Mc-Queen, and S. M. Koohpayeh, Impact of stoichiometry of Yb2Ti2O7 on its physical properties, Phys. Rev. B 95(9), 094407 (2017)
https://doi.org/10.1103/PhysRevB.95.094407
51 J. J. Wen, S. M. Koohpayeh, K. A. Ross, B. A. Trump, T. M. McQueen, K. Kimura, S. Nakatsuji, Y. Qiu, D. M. Pajerowski, J. R. D. Copley, and C. L. Broholm, Disordered route to the Coulomb quantum spin liquid: Random transverse fields on spin ice in Pr2Zr2O7, Phys. Rev. Lett. 118(10), 107206 (2017)
https://doi.org/10.1103/PhysRevLett.118.107206
52 D. E. MacLaughlin, O. O. Bernal, L. Shu, J. Ishikawa, Y. Matsumoto, J. J. Wen, M. Mourigal, C. Stock, G. Ehlers, C. L. Broholm, Y. Machida, K. Kimura, S. Nakatsuji, Y. Shimura, and T. Sakakibara, Unstable spin-ice order in the stuffed metallic pyrochlore Pr2+xIr2−xO7−δ, Phys. Rev. B 92(5), 054432 (2015)
https://doi.org/10.1103/PhysRevB.92.054432
53 G. Chen, H. Y. Kee, and Y. B. Kim, Fractionalized charge excitations in a spin liquid on partially filled pyrochlore lattices, Phys. Rev. Lett. 113(19), 197202 (2014)
https://doi.org/10.1103/PhysRevLett.113.197202
54 J. Fu, J. G. Rau, M. J. Gingras, and N. B. Perkins, Fingerprints of quantum spin ice in Raman scattering, arXiv: 1703.03836 (2017)
55 O. Benton, O. Sikora, and N. Shannon, Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice, Phys. Rev. B 86(7), 075154 (2012)
https://doi.org/10.1103/PhysRevB.86.075154
56 L. D. C. Jaubert, O. Benton, J. G. Rau, J. Oitmaa, R. R. P. Singh, N. Shannon, and M. J. P. Gingras, Are multiphase competition and order by disorder the keys to understanding Yb2Ti2O7? Phys. Rev. Lett. 115(26), 267208 (2015)
https://doi.org/10.1103/PhysRevLett.115.267208
57 R. Applegate, N. R. Hayre, R. R. P. Singh, T. Lin, A. G. R. Day, and M. J. P. Gingras, Vindication of Yb2Ti2O7 as a model exchange quantum spin ice, Phys. Rev. Lett. 109(9), 097205 (2012)
https://doi.org/10.1103/PhysRevLett.109.097205
58 S. R. Dunsiger, A. A. Aczel, C. Arguello, H. Dabkowska, A. Dabkowski, M. H. Du, T. Goko, B. Javanparast, T. Lin, F. L. Ning, H. M. L. Noad, D. J. Singh, T. J. Williams, Y. J. Uemura, M. J. P. Gingras, and G. M. Luke, Spin ice: Magnetic excitations without monopole signatures using muon spin rotation, Phys. Rev. Lett. 107(20), 207207 (2011)
https://doi.org/10.1103/PhysRevLett.107.207207
59 R. Sibille, E. Lhotel, V. Pomjakushin, C. Baines, T. Fennell, and M. Kenzelmann, Candidate quantum spin liquid in the Ce3+ pyrochlore stannate Ce2Sn2O7, Phys. Rev. Lett. 115(9), 097202 (2015)
https://doi.org/10.1103/PhysRevLett.115.097202
60 M. Taillefumier, O. Benton, H. Yan, L. D. C. Jaubert, and N. Shannon, Competing spin liquids and hidden spinnematic order in spin ice with frustrated transverse exchange, Phys. Rev. X 7(4), 041057 (2017)
https://doi.org/10.1103/PhysRevX.7.041057
61 G. Chen, Spectral periodicity of the spinon continuum in quantum spin ice, Phys. Rev. B 96(8), 085136 (2017)
https://doi.org/10.1103/PhysRevB.96.085136
62 L. Savary and L. Balents, Disorder-induced quantum spin liquid in spin ice pyrochlores, Phys. Rev. Lett. 118(8), 087203 (2017)
https://doi.org/10.1103/PhysRevLett.118.087203
63 G. Chen, Dirac’s “magnetic monopoles” in pyrochlore ice U(1) spin liquids: Spectrum and classification, Phys. Rev. B 96(19), 195127 (2017)
https://doi.org/10.1103/PhysRevB.96.195127
64 S. H. Curnoe, Structural distortion and the spin liquid state in Tb2Ti2O7, Phys. Rev. B 78(9), 094418 (2008)
https://doi.org/10.1103/PhysRevB.78.094418
65 S. Onoda, Effective quantum pseudospin-1/2 model for Yb pyrochlore oxides, J. Phys.: Conf. Ser. 320, 012065 (2011)
https://doi.org/10.1088/1742-6596/320/1/012065
66 J. W. Krizan and R. J. Cava, NaCaNi2F7: A single-crystal high-temperature pyrochlore antiferromagnet with S= 1 Ni2+, Phys. Rev. B 92, 014406 (2015)
https://doi.org/10.1103/PhysRevB.92.014406
67 J. W. Krizan and R. J. Cava, NaCaCo2F7: A singlecrystal high-temperature pyrochlore antiferromagnet, Phys. Rev. B 89(21), 214401 (2014)
https://doi.org/10.1103/PhysRevB.89.214401
68 K. A. Ross, J. M. Brown, R. J. Cava, J. W. Krizan, S. E. Nagler, J. A. Rodriguez-Rivera, and M. B. Stone, Singleion properties of the Seff= 1/2 XY antiferromagnetic pyrochlores NaA′Co2F7 (A′= Ca2+,Sr2+), Phys. Rev. B 95(14), 144414 (2017)
https://doi.org/10.1103/PhysRevB.95.144414
69 M. B. Sanders, J. W. Krizan, K. W. Plumb, T. M. Mc-Queen, and R. J. Cava, NaSrMn2F7, NaCaFe2F7, and NaSrFe2F7: Novel single crystal pyrochlore antiferromagnets, J. Phys.: Condens. Matter 29(4), 045801 (2017)
https://doi.org/10.1088/1361-648X/29/4/045801
70 W. Witczak-Krempa, G. Chen, Y. B. Kim, and L. Balents, Correlated quantum phenomena in the strong spin–orbit regime, Annu. Rev. Condens. Matter Phys. 5(1), 57 (2014)
https://doi.org/10.1146/annurev-conmatphys-020911-125138
71 F. Y. Li and G. Chen, Competing phases and topological excitations of spin-1 pyrochlore antiferromagnets, Phys. Rev. B 98(4), 045109 (2018)
https://doi.org/10.1103/PhysRevB.98.045109
72 M. Elhajal, B. Canals, R. Sunyer, and C. Lacroix, Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky–Moriya interactions, Phys. Rev. B 71(9), 094420 (2005)
https://doi.org/10.1103/PhysRevB.71.094420
73 S. Maekawa, T. Tohyama, S. Barnes, S. Ishihara, W. Koshibae, and G. Khaliullin, Physics of Transition Metal Oxides, Springer, 2004
https://doi.org/10.1007/978-3-662-09298-9
74 A. Joshi, M. Ma, F. Mila, D. N. Shi, and F. C. Zhang, Elementary excitations in magnetically ordered systems with orbital degeneracy, Phys. Rev. B 60(9), 6584 (1999)
https://doi.org/10.1103/PhysRevB.60.6584
75 Y. Q. Li, M. Ma, D. N. Shi, and F. C. Zhang, SU(4) theory for spin systems with orbital degeneracy, Phys. Rev. Lett. 81(16), 3527 (1998)
https://doi.org/10.1103/PhysRevLett.81.3527
76 S. E. Palmer and J. T. Chalker, Order induced by dipolar interactions in a geometrically frustrated antiferromagnet, Phys. Rev. B 62(1), 488 (2000)
https://doi.org/10.1103/PhysRevB.62.488
77 A. Poole, A. S. Wills, and E. Lelièvre-Berna, Magnetic ordering in the XY pyrochlore antiferromagnet Er2Ti2O7: A spherical neutron polarimetry study, J. Phys.: Condens. Matter 19(45), 452201 (2007)
https://doi.org/10.1088/0953-8984/19/45/452201
78 L. Savary, K. A. Ross, B. D. Gaulin, J. P. C. Ruff, and L. Balents, Order by quantum disorder in Er2Ti2O7, Phys. Rev. Lett. 109(16), 167201 (2012)
https://doi.org/10.1103/PhysRevLett.109.167201
79 M. E. Zhitomirsky, M. V. Gvozdikova, P. C. W. Holdsworth, and R. Moessner, Quantum order by disorder and accidental soft mode in Er2Ti2O7, Phys. Rev. Lett. 109(7), 077204 (2012)
https://doi.org/10.1103/PhysRevLett.109.077204
80 M. E. Zhitomirsky, P. C. W. Holdsworth, and R. Moessner, Nature of finite-temperature transition in anisotropic pyrochlore Er2Ti2O7, Phys. Rev. B 89(14), 140403 (2014)
https://doi.org/10.1103/PhysRevB.89.140403
81 F. Y. Li, Y. D. Li, Y. B. Kim, L. Balents, Y. Yu, and G. Chen, Weyl magnons in breathing pyrochlore antiferromagnets, Nat. Commun. 7(1), 12691 (2016)
https://doi.org/10.1038/ncomms12691
82 A. Mook, J. Henk, and I. Mertig, Tunable magnon Weyl points in ferromagnetic pyrochlores, Phys. Rev. Lett. 117(15), 157204 (2016)
https://doi.org/10.1103/PhysRevLett.117.157204
83 F. Y. Li, Y. D. Li, Y. Yu, A. Paramekanti, and G. Chen, Kitaev materials beyond iridates: Order by quantum disorder and Weyl magnons in rare-earth double perovskites, Phys. Rev. B 95(8), 085132 (2017)
https://doi.org/10.1103/PhysRevB.95.085132
84 S. A. Owerre, Magnonic analogs of topological Dirac semimetals, J. Phys. Commun. 1(2), 025007 (2017)
https://doi.org/10.1088/2399-6528/aa86d1
85 S. A. Owerre, Topological magnetic excitations on the distorted Kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite, EPL 117(3), 37006 (2017)
https://doi.org/10.1209/0295-5075/117/37006
86 J. Fransson, A. M. Black-Schaffer, and A. V. Balatsky, Magnon Dirac materials, Phys. Rev. B 94(7), 075401 (2016)
https://doi.org/10.1103/PhysRevB.94.075401
87 K. Li, C. Li, J. Hu, Y. Li, and C. Fang, Dirac and nodal line magnons in three-dimensional antiferromagnets, Phys. Rev. Lett. 119(24), 247202 (2017)
https://doi.org/10.1103/PhysRevLett.119.247202
88 X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)
https://doi.org/10.1103/PhysRevB.83.205101
89 A. A. Burkov, M. D. Hook, and L. Balents, Topological nodal semimetals, Phys. Rev. B 84(23), 235126 (2011)
https://doi.org/10.1103/PhysRevB.84.235126
90 R. Moessner and J. T. Chalker, Low-temperature properties of classical geometrically frustrated antiferromagnets, Phys. Rev. B 58(18), 12049 (1998)
https://doi.org/10.1103/PhysRevB.58.12049
91 R. Moessner and J. T. Chalker, Properties of a classical spin liquid: The Heisenberg pyrochlore antiferromagnet, Phys. Rev. Lett. 80(13), 2929 (1998)
https://doi.org/10.1103/PhysRevLett.80.2929
92 R. Kmieć, Z. Świątkowska, J. Gurgul, M. Rams, A. Zarzycki, and K. Tomala, Investigation of the magnetic properties of Y2Ru2O7 by 99Ru Mössbauer spectroscopy, Phys. Rev. B 74(10), 104425 (2006)
https://doi.org/10.1103/PhysRevB.74.104425
93 S. Lee, J. G. Park, D. T. Adroja, D. Khomskii, S. Streltsov, K. A. McEwen, H. Sakai, K. Yoshimura, V. I. Anisimov, D. Mori, R. Kanno, and R. Ibberson, Spin gap in Tl2Ru2O7 and the possible formation of Haldane chains in three-dimensional crystals,Nat. Mater. 5(6), 471 (2006)
https://doi.org/10.1038/nmat1605
94 S. M. Perez1, R. Cobas, J. M. Cadogan, J. A. Aguiar, C. Frontera, T. Puig, G. Long, M. DeMarco, D. Coffey, and X. Obradors, Anomalous electronic and magnetic properties of the Eu2Ru2O7 pyrochlore, J. Appl. Phys. 113, 17E102 (2013)
https://doi.org/10.1063/1.4793517
95 M. Tachibanaa, Heat capacity of pyrochlore Pr2Ru2O7, J. Appl. Phys. 101, 09D502 (2007)
https://doi.org/10.1063/1.2667992
96 S. Zouari, R. Ballou, A. Cheikhrouhou, and P. Strobel, Structural and magnetic properties of the (Bi2−xPrx)Ru2O7 pyrochlore solid solution (0≤x≤2), J. Alloys Compd. 476(1–2), 43 (2009)
https://doi.org/10.1016/j.jallcom.2008.09.106
97 M. W. Gaultois, P. T. Barton, C. S. Birkel, L. M. Misch, E. E. Rodriguez, G. D. Stucky, and R. Seshadri, Structural disorder, magnetism, and electrical and thermoelectric properties of pyrochlore Nd2Ru2O7, J. Phys.: Condens. Matter 25(18), 186004 (2013)
https://doi.org/10.1088/0953-8984/25/18/186004
98 J. Gurgul, M. Rams, Z. Świątkowska, R. Kmieć, and K. Tomala, Bulk magnetic measurements and 99Ru and 155Gd Mössbauer spectroscopies of Gd2Ru2O7, Phys. Rev. B 75(6), 064426 (2007)
https://doi.org/10.1103/PhysRevB.75.064426
99 L. J. Chang, M. Prager, J. Perβon, J. Walter, E. Jansen, Y. Y. Chen, and J. S. Gardner, Magnetic order in the double pyrochlore Tb2Ru2O7, J. Phys.: Condens. Matter 22(7), 076003 (2010)
https://doi.org/10.1088/0953-8984/22/7/076003
100 Z. C. Xu, M. F. Liu, L. Lin, H. Liu, Z. B. Yan, and J. M. Liu, Experimental observations of ferroelectricity in double pyrochlore Dy2Ru2O7, Front. Phys. 9(1), 82 (2014)
https://doi.org/10.1007/s11467-013-0395-8
101 C. R. Wiebe, J. S. Gardner, S. J. Kim, G. M. Luke, A. S. Wills, B. D. Gaulin, J. E. Greedan, I. Swainson, Y. Qiu, and C. Y. Jones, Magnetic ordering in the spinice candidate Ho2Ru2O7, Phys. Rev. Lett. 93(7), 076403 (2004)
https://doi.org/10.1103/PhysRevLett.93.076403
102 N. Taira, M. Wakeshima, and Y. Hinatsu, Magnetic susceptibility and specific heat studies on heavy rare earth ruthenate pyrochlores R2Ru2O7 (R= Gd–Yb), J. Mater. Chem. 12(5), 1475 (2002)
https://doi.org/10.1039/b110596p
103 J. S. Gardner and G. Ehlers, Magnetic order and crystal field excitations in Er2Ru2O7: A neutron scattering study, J. Phys.: Condens. Matter 21(43), 436004 (2009)
https://doi.org/10.1088/0953-8984/21/43/436004
104 N. Taira, M. Wakeshima, Y. Hinatsu, A. Tobo, and K. Ohoyama, Magnetic structure of pyrochlore-type Er2Ru2O7, J. Solid State Chem. 176(1), 165 (2003)
https://doi.org/10.1016/S0022-4596(03)00384-0
105 A. Keren and J. S. Gardner, Frustration driven lattice distortion: An NMR investigation of Y2Mo2O7, Phys. Rev. Lett. 87(17), 177201 (2001)
https://doi.org/10.1103/PhysRevLett.87.177201
106 P. M. M. Thygesen, J. A. M. Paddison, R. Zhang, K. A. Beyer, K. W. Chapman, H. Y. Playford, M. G. Tucker, D. A. Keen, M. A. Hayward, and A. L. Goodwin, Orbital dimer model for the spin-glass state in Y2Mo2O7, Phys. Rev. Lett. 118(6), 067201 (2017)
https://doi.org/10.1103/PhysRevLett.118.067201
107 H. J. Silverstein, K. Fritsch, F. Flicker, A. M. Hallas, J. S. Gardner, Y. Qiu, G. Ehlers, A. T. Savici, Z. Yamani, K. A. Ross, B. D. Gaulin, M. J. P. Gingras, J. A. M. Paddison, K. Foyevtsova, R. Valenti, F. Hawthorne, C. R. Wiebe, and H. D. Zhou, Liquidlike correlations in single-crystalline Y2Mo2O7: An unconventional spin glass,Phys. Rev. B 89(5), 054433 (2014)
https://doi.org/10.1103/PhysRevB.89.054433
108 S. R. Dunsiger, R. F. Kiefl, K. H. Chow, B. D. Gaulin, M. J. P. Gingras, J. E. Greedan, A. Keren, K. Kojima, G. M. Luke, W. A. MacFarlane, N. P. Raju, J. E. Sonier, Y. J. Uemura, and W. D. Wu, Muon spin relaxation investigation of the spin dynamics of geometrically frustrated antiferromagnets Y2Mo2O7 and Tb2Mo2O7, Phys. Rev. B 54(13), 9019 (1996)
https://doi.org/10.1103/PhysRevB.54.9019
109 L. Clark, G. J. Nilsen, E. Kermarrec, G. Ehlers, K. S. Knight, A. Harrison, J. P. Attfield, and B. D. Gaulin, From spin glass to quantum spin liquid ground states in molybdate pyrochlores, Phys. Rev. Lett. 113(11), 117201 (2014)
https://doi.org/10.1103/PhysRevLett.113.117201
110 Y. Jiang, A. Huq, C. H. Booth, G. Ehlers, J. E. Greedan, and J. S. Gardner, Order and disorder in the local and long-range structure of the spin-glass pyrochlore, Tb2Mo2O7, J. Phys.: Condens. Matter 23(16), 164214 (2011)
https://doi.org/10.1088/0953-8984/23/16/164214
111 G. Ehlers, J. E. Greedan, J. R. Stewart, K. C. Rule, P. Fouquet, A. L. Cornelius, C. Adriano, P. G. Pagliuso, Y. Qiu, and J. S. Gardner, High-resolution neutron scattering study of Tb2Mo2O7: A geometrically frustrated spin glass, Phys. Rev. B 81(22), 224405 (2010)
https://doi.org/10.1103/PhysRevB.81.224405
112 D. K. Singh, J. S. Helton, S. Chu, T. H. Han, C. J. Bonnoit, S. Chang, H. J. Kang, J. W. Lynn, and Y. S. Lee, Spin correlations in the geometrically frustrated pyrochlore Tb2Mo2O7, Phys. Rev. B78(22), 220405 (2008)
https://doi.org/10.1103/PhysRevB.78.220405
113 K. W. Plumb, H. J. Changlani, A. Scheie, S. Zhang, J. W. Krizan, J. A. Rodriguez-Rivera, Y. Qiu, B. Winn, R. J. Cava, and C. L. Broholm, Continuum of quantum fluctuations in a three-dimensional s= 1 heisenberg magnet, arXiv: 1711.07509 (2017)
https://doi.org/10.1038/s41567-018-0317-3
114 T. Moriya, Anisotropic superexchange interaction and weak ferromagnetism, Phys. Rev. 120(1), 91 (1960)
https://doi.org/10.1103/PhysRev.120.91
115 D. L. Bergman, R. Shindou, G. A. Fiete, and L. Balents, Models of degeneracy breaking in pyrochlore antiferromagnets, Phys. Rev. B 74(13), 134409 (2006)
https://doi.org/10.1103/PhysRevB.74.134409
116 K. Penc, N. Shannon, and H. Shiba, Half-magnetization plateau stabilized by structural distortion in the antiferromagnetic Heisenberg model on a pyrochlore lattice, Phys. Rev. Lett. 93(19), 197203 (2004)
https://doi.org/10.1103/PhysRevLett.93.197203
117 G. Chen and L. Balents, Spin–orbit coupling in d2 ordered double perovskites, Phys. Rev. B 84(9), 094420 (2011)
https://doi.org/10.1103/PhysRevB.84.094420
118 Z. Y. Zhao, S. Calder, A. A. Aczel, M. A. McGuire, B. C. Sales, D. G. Mandrus, G. Chen, N. Trivedi, H. D. Zhou, and J. Q. Yan, Fragile singlet ground-state magnetism in the pyrochlore osmates R2Os2O7 (R= Y and Ho), Phys. Rev. B 93(13), 134426 (2016)
https://doi.org/10.1103/PhysRevB.93.134426
119 G. Khaliullin, Excitonic magnetism in Van Vleck–type d4 Mott insulators, Phys. Rev. Lett. 111(19), 197201 (2013)
https://doi.org/10.1103/PhysRevLett.111.197201
120 A. Georges, L. Medici, and J. Mravlje, Strong correlations from Hund’s coupling, Annu. Rev. Condens. Matter Phys. 4(1), 137 (2013)
https://doi.org/10.1146/annurev-conmatphys-020911-125045
121 K. I. Kugel and D. I. Khomskii, The Jahn–Teller effect and magnetism: Transition metal compounds, Sov. Phys. Usp. 25(4), 231 (1982)
https://doi.org/10.1070/PU1982v025n04ABEH004537
122 S. H. Lee, D. Louca, H. Ueda, S. Park, T. J. Sato, M. Isobe, Y. Ueda, S. Rosenkranz, P. Zschack, J. Íñiguez, Y. Qiu, and R. Osborn, Orbital and spin chains in ZnV2O4, Phys. Rev. Lett. 93(15), 156407 (2004)
https://doi.org/10.1103/PhysRevLett.93.156407
123 T. Maitra and R. Valentí, Orbital order in ZnV2O4, Phys. Rev. Lett. 99(12), 126401 (2007)
https://doi.org/10.1103/PhysRevLett.99.126401
124 G. Giovannetti, A. Stroppa, S. Picozzi, D. Baldomir, V. Pardo, S. Blanco-Canosa, F. Rivadulla, S. Jodlauk, D. Niermann, J. Rohrkamp, T. Lorenz, S. Streltsov, D. I. Khomskii, and J. Hemberger, Dielectric properties and magnetostriction of the collinear multiferroic spinel CdV2O4, Phys. Rev. B 83(6), 060402 (2011)
https://doi.org/10.1103/PhysRevB.83.060402
125 D. I. Khomskii and T. Mizokawa, Orbitally induced peierls state in spinels, Phys. Rev. Lett. 94(15), 156402 (2005)
https://doi.org/10.1103/PhysRevLett.94.156402
126 S. Niitaka, H. Ohsumi, K. Sugimoto, S. Lee, Y. Oshima, K. Kato, D. Hashizume, T. Arima, M. Takata, and H. Takagi, A-type antiferro-orbital ordering with I41/asymmetry and geometrical frustration in the spinel vanadate MgV2O4, Phys. Rev. Lett. 111(26), 267201 (2013)
https://doi.org/10.1103/PhysRevLett.111.267201
127 E. M. Wheeler, B. Lake, A. T. M. N. Islam, M. Reehuis, P. Steffens, T. Guidi, and A. H. Hill, Spin and orbital order in the vanadium spinel MgV2O4, Phys. Rev. B 82(14), 140406 (2010)
https://doi.org/10.1103/PhysRevB.82.140406
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