Spin waves and phase transition on a magnetically frustrated square lattice with long-range interactions

doi:10.1007/s11467-022-1238-2

Front. Phys.

2023, Vol. 18

Issue (3) : 33309 https://doi.org/10.1007/s11467-022-1238-2

RESEARCH ARTICLE

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

Download: PDF(5226 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

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.

Keywords spin wave phase transition frustration square lattice long-range interaction antiferromagnet

Corresponding Author(s): Dao-Xin Yao

Issue Date: 02 February 2023

Cite this article:

Yuting Tan,Dao-Xin Yao. Spin waves and phase transition on a magnetically frustrated square lattice with long-range interactions[J]. Front. Phys. , 2023, 18(3): 33309.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1238-2
https://academic.hep.com.cn/fop/EN/Y2023/V18/I3/33309

Fig.1 Magnetic ground states with long-range interactions: (a) Neel phase with wave vector (

π, π

) and (b) Stripe phase with wave vector (

π, 0

J (m, n)

represents the interactions between two spins with relative coordinates

(m, n)

Fig.2 Spin-wave dispersion band for the

(π, π)

Neel phase with

J 2 = 0.1

J 1 = 1

: (a)

α = 4

(long-range interactions) and (b)

α = 10

(short range interactions).

Fig.3 Spin-wave dispersions for the

(π, π)

Neel phase with

J 2 = 0.1

J 1 = 1

: (a)

α = 4

(long-range interactions) and (b)

α = 10

(short range interactions). The spin wave velocities

v x

and

v y

increase about

80 %

from

α = 10

to 4.

Fig.4 Spin-wave dispersion band for the

(π, 0)

stripe phase with

J 2 = 1

J 1 = 1

: (a)

α = 4

(long-range interactions) and (b)

α = 10

(short range interactions).

Fig.5 Spin-wave dispersions for the

(π, 0)

stripe phase with

J 2 = 1

J 1 = 1

: (a)

α = 4

(long-range interactions) and (b)

α = 10

(short range interactions). The spin wave velocity

v x

decreases about

13 %

and

v y

drops about

20 %

from

α = 10

4

Fig.6 Constant-energy slices (twinned) of the dynamic structure factor

S (k, ω)

for

J 2 = 0.1

J 1 = 1

λ = 1

: (a)

α = 4

(long-range interactions) and (b)

α = 10

(short range interactions). The x-axis and y-axis correspond to

k x

and

k y

respectively with the range

(0, 2 π)

Fig.7 Constant-energy slices (twinned) of the dynamic structure factor

S (k, ω)

for

J 2 = 1

J 1 = 1

λ = 1

: (a)

α = 4

(long-range interactions) and (b)

α = 10

(short range interactions). The x-axis and y-axis correspond to

k x

and

k y

respectively with the range

(0, 2 π)

Fig.8

| J 2 / J 1 |

dependence of

m

for

| J 1 | = 1

λ = 1

and

S = 1

. Blue is for

α = 10

(short-range interactions) and brown is for

α = 4

(long-range interactions).

Fig.9 Phase transition point vs.

α

with

J 1 = 1

and

λ = 1

1	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
5	Yosida K. . Magnetic properties of Cu−Mn alloys. Phys. Rev., 1957, 106(5): 893 https://doi.org/10.1103/PhysRev.106.893
6	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
7	W. Anderson P. , Hasegawa H. . Considerations on double exchange. Phys. Rev., 1955, 100(2): https://doi.org/10.1103/PhysRev.100.675
8	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
17	Aoki T. . Spin-wave theory of modified quantum Heisenberg model. J. Phys. Soc. Jpn., 1996, 65: 1430 https://doi.org/10.1143/JPSJ.65.1430
18	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
20	W. Sandvik A. . Ground states of a frustrated quantum spin chain with long-range interactions. Phys. Rev. Lett., 2010, 104(13): 137204 https://doi.org/10.1103/PhysRevLett.104.137204
21	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
25	W. Carlson E. , X. Yao D. , K. Campbell D. . Spin waves in striped phases. Phys. Rev. B, 2004, 70(6): 064505 https://doi.org/10.1103/PhysRevB.70.064505
26	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
27	X. Yao D. , W. Carlson E. . Magnetic excitations of undoped iron oxypnictides. Front. Phys. China, 2010, 5(2): 166 https://doi.org/10.1007/s11467-009-0075-x
28	Krüger F. , Scheidl S. . Spin dynamics of stripes. Phys. Rev. B, 2003, 67(13): 134512 https://doi.org/10.1103/PhysRevB.67.134512
29	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
30	Si Q. , Abrahams E. . Strong correlations and magnetic frustration in the high Tc iron pnictides. Phys. Rev. Lett., 2008, 101(7): 076401 https://doi.org/10.1103/PhysRevLett.101.076401
31	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

[1]	San-Dong Guo, Yu-Ling Tao, Wen-Qi Mu, Bang-Gui Liu. Correlation-driven threefold topological phase transition in monolayer OsBr₂[J]. Front. Phys. , 2023, 18(3): 33304-.
[2]	Jing-Kai Fang, Jun-Han Huang, Han-Qing Wu, Dao-Xin Yao. Dynamical properties of the Haldane chain with bond disorder[J]. Front. Phys. , 2022, 17(3): 33503-.
[3]	Na Kang, Wenhui Wan, Yanfeng Ge, Yong Liu. Diverse magnetism in stable and metastable structures of CrTe[J]. Front. Phys. , 2021, 16(6): 63506-.
[4]	Jorge A. López, Claudio O. Dorso, Guillermo Frank. Properties of nuclear pastas[J]. Front. Phys. , 2021, 16(2): 24301-.
[5]	Zhen-Ming Xu (许震明). Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space[J]. Front. Phys. , 2021, 16(2): 24502-.
[6]	Lu Qi, Guo-Li Wang, Shutian Liu, Shou Zhang, Hong-Fu Wang. Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice[J]. Front. Phys. , 2021, 16(1): 12503-.
[7]	Shuang Zhou, Lu You, Hailin Zhou, Yong Pu, Zhigang Gui, Junling Wang. Van der Waals layered ferroelectric CuInP₂S₆: Physical properties and device applications[J]. Front. Phys. , 2021, 16(1): 13301-.
[8]	Jin-Bo Wang, Rao Huang, Yu-Hua Wen. Thermally activated phase transitions in Fe-Ni core-shell nanoparticles[J]. Front. Phys. , 2019, 14(6): 63604-.
[9]	Ai-Yuan Hu, Lin Wen, Guo-Pin Qin, Zhi-Min Wu, Peng Yu, Yu-Ting Cui. Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature[J]. Front. Phys. , 2019, 14(5): 53601-.
[10]	Yan-Rong Zhang, Ze-Zheng Zhang, Jia-Qi Yuan, Ming Kang, Jing Chen. High-order exceptional points in non-Hermitian Moiré lattices[J]. Front. Phys. , 2019, 14(5): 53603-.
[11]	Gui-Lei Zhu, Xin-You Lü, Shang-Wu Bin, Cai You, Ying Wu. Entanglement and excited-state quantum phase transition in an extended Dicke model[J]. Front. Phys. , 2019, 14(5): 52602-.
[12]	Ai-Yuan Hu, Huai-Yu Wang. Phase transition of the frustrated antiferromagntic J₁-J₂-J₃ spin-1/2 Heisenberg model on a simple cubic lattice[J]. Front. Phys. , 2019, 14(1): 13605-.
[13]	Jian Lv, Xin Yang, Dan Xu, Yu-Xin Huang, Hong-Bo Wang, Hui Wang. High-pressure polymorphs of LiPN₂: A first-principles study[J]. Front. Phys. , 2018, 13(5): 136104-.
[14]	Xia Huang, Jin Dong, Wen-Jing Jia, Zhi-Gang Zheng, Can Xu. Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling[J]. Front. Phys. , 2018, 13(5): 130506-.
[15]	Zhi Lin, Wanli Liu. Analytic calculation of high-order corrections to quantum phase transitions of ultracold Bose gases in bipartite superlattices[J]. Front. Phys. , 2018, 13(5): 136402-.

Viewed

Full text

Abstract

Cited

Shared

Discussed