Spin waves and phase transition on a magnetically frustrated square lattice with long-range interactions
Yuting Tan, Dao-Xin Yao()
State Key Laboratory of Optoelectronic Materials and Technologies, Center for Neutron Science and Technology, Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University, Guangzhou 510275, China
We investigate the effects of long-range interactions on the spin wave spectra and the competition between magnetic phases on a frustrated square lattice with large spin S. Applying the spin wave theory and assisted with symmetry analysis, we obtain analytical expressions for spin wave spectra of competing Neel and (π, 0) stripe states of systems containing any-order long-range interactions. In the specific case of long-range interactions with power-law decay, we find surprisingly that the staggered long-range interaction suppresses quantum fluctuation and enlarges the ordered moment, especially in the Neel state, and thus extends its phase boundary to the stripe state. Our findings illustrate the rich possibilities of the roles of long-range interactions, and advocate future investigations in other magnetic systems with different structures of interactions.
Dietl T. , Ohno H. , Matsukura F. , Cibert J. , Ferrand D. . Zener model description of ferromagnetism in zinc-blende magnetic semiconductors. Science, 2000, 287(5455): 1019 https://doi.org/10.1126/science.287.5455.1019
2
F. Jalbout A. , Chen H. , L. Whittenburg S. . Monte Carlo simulation on the indirect exchange interactions of Co-doped ZnO film. Appl. Phys. Lett., 2002, 81(12): 2217 https://doi.org/10.1063/1.1508168
3
A. Ruderman M. , Kittel C. . Indirect exchange coupling of nuclear magnetic moments by conduction electrons. Phys. Rev., 1954, 96(1): 99 https://doi.org/10.1103/PhysRev.96.99
4
Kasuya T. . A theory of metallic ferro- and antiferromagnetism on Zener’s model. Prog. Theor. Phys., 1956, 16(1): 45 https://doi.org/10.1143/PTP.16.45
Zener C. . Interaction between the d-shells in the transition metals (II): Ferromagnetic compounds of manganese with perovskite structure. Phys. Rev., 1951, 82(3): 403 https://doi.org/10.1103/PhysRev.82.403
Chen J. , J. Qin H. , Yang F. , Liu J. , Guan T. , M. Qu F. , H. Zhang G. , R. Shi J. , C. Xie X. , L. Yang C. , H. Wu K. , Q. Li Y. , Lu L. . Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3. Phys. Rev. Lett., 2010, 105(17): 176602 https://doi.org/10.1103/PhysRevLett.105.176602
9
J. Kim H. , S. Kim K. , F. Wang J. , A. Kulbachinskii V. , Ogawa K. , Sasaki M. , Ohnishi A. , Kitaura M. , Y. Wu Y. , Li L. , Yamamoto I. , Azuma J. , Kamada M. , Dobrosavljević V. . Topological phase transitions driven by magnetic phase transitions in FexBi2Te3 (0 ≤ x ≤ 0.1) single crystals. Phys. Rev. Lett., 2013, 110(13): 136601 https://doi.org/10.1103/PhysRevLett.110.136601
10
Li B. , Fan Q. , Ji F. , Liu Z. , Pan H. , Qiao S. . Carrier dependent ferromagnetism in chromium doped topological insulator Cry(BixSb1−x)2−yTe3. Phys. Lett. A, 2013, 377(31-33): 1925 https://doi.org/10.1016/j.physleta.2013.05.020
11
J. Zhu J. , X. Yao D. , C. Zhang S. , Chang K. . Electrically controllable surface magnetism on the surface of topological insulators. Phys. Rev. Lett., 2011, 106(9): 097201 https://doi.org/10.1103/PhysRevLett.106.097201
12
M. Zhang G. , H. Su Y. , Y. Lu Z. , Y. Weng Z. , H. Lee D. , Xiang T. . Universal linear-temperature dependence of static magnetic susceptibility in iron pnictides. Europhys. Lett., 2009, 86(3): 37006 https://doi.org/10.1209/0295-5075/86/37006
13
Lv W. , Kruger F. , Phillips P. . Orbital ordering and unfrustrated (π, 0) magnetism from degenerate double exchange in the iron pnictides. Phys. Rev. B, 2010, 82(4): 045125 https://doi.org/10.1103/PhysRevB.82.045125
14
X. Yao D. . Iron-based superconductors: A new family to find the origin of high Tc superconductivity. Front. Phys., 2011, 6(4): 344 https://doi.org/10.1007/s11467-011-0218-8
15
Jiang Q. , T. Kang Y. , X. Yao D. . Spin, charge, and orbital orderings in iron-based superconductors. Chin. Phys. B, 2013, 22(8): 087402 https://doi.org/10.1088/1674-1056/22/8/087402
16
T. Tam Y. , X. Yao D. , Ku W. . Itinerancy-enhanced quantum fluctuation of magnetic moments in iron-based superconductors. Phys. Rev. Lett., 2015, 115(11): 117001 https://doi.org/10.1103/PhysRevLett.115.117001
Yusuf E. , Joshi A. , Yang K. . Spin waves in antiferromagnetic spin chains with long-range interactions. Phys. Rev. B, 2004, 69(14): 144412 https://doi.org/10.1103/PhysRevB.69.144412
19
Laflorencie N. , Affleck I. , Berciu M. . Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains. J. Stat. Mech:Theory & Exp., 2005, 12: 12001 https://doi.org/10.1088/1742-5468/2005/12/P12001
Yang S.X. Yao D.W. Sandvik A., Deconfined quantum criticality in spin-1/2 chains with long-range interactions, arXiv: 2001.02821 (2020)
22
de la Cruz C. , Huang Q. , W. Lynn J. , Li J. , R. Ii W. , L. Zarestky J. , A. Mook H. , F. Chen G. , L. Luo J. , L. Wang N. , Dai P. . Magnetic order close to superconductivity in the iron-based layered LaO1−xFxFeAs systems. Nature, 2008, 453(7197): 899 https://doi.org/10.1038/nature07057
23
Zhao J. , T. Adroja D. , X. Yao D. , Bewley R. , Li S. , F. Wang X. , Wu G. , H. Chen X. , P. Hu J. , Dai P. . Spin waves and magnetic exchange interactions in CaFe2As2. Nat. Phys., 2009, 5(8): 555 https://doi.org/10.1038/nphys1336
24
Ma F. , Ji W. , Hu J. , Y. Lu Z. , Xiang T. . First-principles calculations of the electronic structure of tetragonal α-FeTe and α-FeSe crystals: Evidence for a bicollinear antiferromagnetic order. Phys. Rev. Lett., 2009, 102(17): 177003 https://doi.org/10.1103/PhysRevLett.102.177003
A. Ewings R. , G. Perring T. , I. Bewley R. , Guidi T. , J. Pitcher M. , R. Parker D. , J. Clarke S. , T. Boothroyd A. . High-energy spin excitations in BaFe2As2 observed by inelastic neutron scattering. Phys. Rev. B, 2008, 78: 220501(R) https://doi.org/10.1103/PhysRevB.78.220501
X. Yao D. , W. Carlson E. , K. Campbell D. . Magnetic excitations of stripes near a quantum critical point. Phys. Rev. Lett., 2006, 97(1): 017003 https://doi.org/10.1103/PhysRevLett.97.017003
Fang C. , Yao H. , F. Tsai W. , P. Hu J. , A. Kivelson S. . Theory of electron nematic order in LaFeAsO. Phys. Rev. B, 2008, 77(22): 224509 https://doi.org/10.1103/PhysRevB.77.224509
32
Shao H. , Q. Qin Y. , Capponi S. , Chesi S. , Y. Meng Z. , W. Sandvik A. . Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet. Phys. Rev. X, 2017, 7(4): 041072 https://doi.org/10.1103/PhysRevX.7.041072
33
Xu Y. , Xiong Z. , Q. Wu H. , X. Yao D. . Spin excitation spectra of the two-dimensional S = 1/2 Heisenberg model with a checkerboard structure. Phys. Rev. B, 2019, 99(8): 085112 https://doi.org/10.1103/PhysRevB.99.085112
34
Yan T. , Jin S. , Xiong Z. , Li J. , X. Yao D. . Magnetic excitations of diagonally coupled checkerboards. Chin. Phys. B, 2021, 30: 107505 https://doi.org/10.1088/1674-1056/ac1b94
35
Huang J. , Liu Z. , Q. Wu H. , X. Yao D. . Ground states and dynamical properties of the S > 1/2 quantum Heisenberg model on the 1/5-depleted square lattice. Phys. Rev. B, 2022, 106(8): 085101 https://doi.org/10.1103/PhysRevB.106.085101
36
K. Fang J. , H. Huang J. , Q. Wu H. , X. Yao D. . Dynamical properties of the Haldane chain with bond disorder. Front. Phys., 2022, 17(3): 33503 https://doi.org/10.1007/s11467-021-1124-3
37
Q. Cheng J. , Li J. , Xiong Z. , Q. Wu H. , W. Sandvik A. , X. Yao D. . Fractional and composite excitations of antiferromagnetic quantum spin trimer chains. npj Quantum Mater., 2022, 7: 3 https://doi.org/10.1038/s41535-021-00416-4
38
X. Yao D. , W. Carlson E. , K. Campbell D. . Magnetic excitations of stripes near a quantum critical point. Phys. Rev. Lett., 2006, 97(1): 017003 https://doi.org/10.1103/PhysRevLett.97.017003
39
X. Yao D. , W. Carlson E. . Incompatibility of modulated checkerboard patterns with the neutron scattering resonance peak in cuprate superconductors. Phys. Rev. B, 2008, 77(2): 024503 https://doi.org/10.1103/PhysRevB.77.024503
40
G. Freeman P. , Enderle M. , M. Hayden S. , D. Frost C. , X. Yao D. , W. Carlson E. , Prabhakaran D. , T. Boothroyd A. . Inward dispersion of the spin excitation spectrum of stripe-ordered La2NiO4+δ. Phys. Rev. B, 2009, 80(14): 144523 https://doi.org/10.1103/PhysRevB.80.144523
41
D. Christianson A. , A. Goremychkin E. , Osborn R. , Rosenkranz S. , D. Lumsden M. , D. Malliakas C. , S. Todorov I. , Claus H. , Y. Chung D. , G. Kanatzidis M. , I. Bewley R. , Guidi T. . Unconventional superconductivity in Ba0.6K0.4Fe2As2 from inelastic neutron scattering. Nature, 2008, 456(7224): 930 https://doi.org/10.1038/nature07625
42
F. Li H. , Broholm C. , Vaknin D. , M. Fernandes R. , L. Abernathy D. , B. Stone M. , K. Pratt D. , Tian W. , Qiu Y. , Ni N. , O. Diallo S. , L. Zarestky J. , L. Bud'ko S. , C. Canfield P. , J. McQueeney R. . Anisotropic and quasipropagating spin excitations in superconducting Ba(Fe0.926Co0.074)2As2. Phys. Rev. B, 2010, 82: 140503(R) https://doi.org/10.1103/PhysRevB.82.140503