Please wait a minute...
Chin. Phys. B, 2019, Vol. 28(7): 077501    DOI: 10.1088/1674-1056/28/7/077501
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling

Jiayu Xie(谢家玉)1, Zhihao Deng(邓志豪)1, Xia Chang(昌霞)1, Bing Tang(唐炳)1,2
1 College of Physics, Mechanical and Electrical Engineering, Jishou University, Jishou 416000, China;
2 The Collaborative Innovation Center of Manganese-Zinc-Vanadium Industrial Technology, Jishou University, Jishou 416000, China
Abstract  

We report a theoretical work on the properties of modulational instability and bright type nonlinear localized modes in one-dimensional easy-axis weak ferromagnetic spin lattices involving next-nearest-neighbor couplings. With a linear stability analysis, we calculate the growth rates of the modulational instability, and plot the instability regions. When the strength of the next-nearest-neighbor coupling is large enough, two new asymmetric modulational instability regions appear near the boundary of the first Brillouin zone. Furthermore, analytical forms of the bright nonlinear localized modes are constructed by means of a quasi-discreteness approach. The influence of the next-nearest-neighbor coupling on the Brillouin zone center mode and boundary mode are discussed. In particular, we discover a reversal phenomenon of the propagation direction of the Brillouin zone boundary mode.

Keywords:  modulational instability analysis      intrinsic localized spin-wave modes      weak ferromagnets      next-nearest-neighbor couplings  
Received:  12 March 2019      Revised:  04 May 2019      Accepted manuscript online: 
PACS:  75.10.Jm (Quantized spin models, including quantum spin frustration)  
  75.30.Ds (Spin waves)  
  63.20.Pw (Localized modes)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 11604121 and 11875126), the Natural Science Fund Project of Hunan Province, China (Grant No. 2017JJ3255), the National College Students' Innovation Entrepreneurship Training Program, China (Grant No. 201810531014), and the Scientific Research Fund of Hunan Provincial Education Department, China (Grant No. 17B212).

Corresponding Authors:  Bing Tang     E-mail:  bingtangphy@jsu.edu.cn

Cite this article: 

Jiayu Xie(谢家玉), Zhihao Deng(邓志豪), Xia Chang(昌霞), Bing Tang(唐炳) Discrete modulational instability and bright localized spin wave modes in easy-axis weak ferromagnetic spin chains involving the next-nearest-neighbor coupling 2019 Chin. Phys. B 28 077501

[1] Baronio F, Chen S, Grelu P, Wabnitz S and Conforti M 2015 Phys. Rev. A 91 033804
[2] Wamba E, Mohamadou A, Ekogo T B, Atangana J and Kofane T C 2011 Phys. Lett. A 375 4288
[3] Stockhofe J and Schmelcher P 2016 Physica D 328-329 9
[4] Kibler B, Chabchoub A, Gelash A, Akhmediev N and Zakharov V E 2015 Phys. Rev. X 5 041026
[5] Zhang J H, Wang L and Liu C 2017 Proc. R. Soc. A 473 20160681
[6] Cai L Y, Wang X, Wang L, Li M, Liu Y and Shi Y Y 2017 Nonlin. Dynam. 90 2221
[7] Wang L, Zhang L L, Zhu Y J, Qi F H, Wang P, Guo R and Li M 2016 Commun. Nonlinear Sci. Numer. Simulat. 40 216
[8] Tabi C B, Mohamadou A and Kofane T C 2010 Eur. Phys. J. B 74 151
[9] Gori G, Macrí T and Trombettoni A 2013 Phys. Rev. E 87 032905
[10] Xie Y D 2018 Acta Phys. Sin. 67 197502 (in Chinese)
[11] Yang C Y, Wazwaz A M, Zhou Q and Liu W J 2019 Laser Phys. 29 035401
[12] Liu W J, Pang L H, Shen Z W, Lei M, Teng H and Wei Z Y 2016 Photon. Res. 4 111
[13] Liu W J, Pang L H, Han H N, Tian W L, Chen Hao, Lei M, Yan P G and Wei Z Y 2015 Opt. Exp. 23 26023
[14] Su W H, Xie J Y, Wu T L and Tang B 2018 Chin. Phys. B 27 097501
[15] Wang L, Zhu Y J, Wang Z Q, Xu T, Qi F H and Xue Y S 2016 J. Phys. Soc. Jpn. 85 024001
[16] Baronio F, Conforti M, Degasperis A, Lombardo S, Onorato M and Wabnitz S 2014 Phys. Rev. Lett. 113 034101
[17] Marklund M and Shukla P K 2006 Phys. Rev. E 73 057601
[18] Meier J, Stegeman G I, Christodoulides D N, Silberberg Y, Morandotti R, Yang H, Salamo G, Sorel M and Aitchison J S 2004 Phys. Rev. Lett. 92 163902
[19] Carr L D and Brand J 2004 Phys. Rev. Lett. 92 040401
[20] Kivshar Y S and Peyrard M 1992 Phys. Rev. A 46 3198
[21] Kivshar Y S 1993 Phys. Lett. A 173 172
[22] Abdullaev F K, Bouketir A, Messikh A and Umarov B A 2007 Physica D 232 54
[23] Daumont I, Dauxois T and Peyrard M 1997 Nonlinearity 10 617
[24] Yoshimura K 2004 Phys. Rev. E 70 016611
[25] Dauxois T, Khomeriki R and Ruffo S 2007 Eur. Phys. J. Spec. Top. 147 3
[26] Lai R and Sievers A J 1999 Phys. Rep. 314 147
[27] Lai R and Sievers A J 1998 Phys. Rev. B 57 3433
[28] Lai R, Kiselev S A and Sievers A J 1997 Phys. Rev. B 56 5345
[29] Huang G, Zhang S and Hu B 1998 Phys. Rev. B 58 9194
[30] Nguenang J P, Peyrard M, Kenfack A J and Kofané T C 2005 J. Phys.: Condens. Matter 17 3083
[31] Lakshmanan M, Subash B and Saxena A 2014 Phys. Lett. A 378 1119
[32] Kavitha L, Mohamadou A, Parasuraman E, Gopi D, Akila N and Prabhu A 2016 J. Magn. Magn. Mater. 404 91
[33] Tang B, Li G L and Fu M 2017 J. Magn. Magn. Mater. 426 429
[34] Kavitha L, Parasuraman E, Gopi D, Prabhu A and Vicencio R A 2016 J. Magn. Magn. Mater. 401 394
[35] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[36] Moriya T 1960 Phys. Rev. Lett. 4 228
[37] Tang B, Li D J and Tang Y 2014 Chaos 24 023113
[38] Di K, Zhang V L, Lim H S, Ng S C, Kuok M H, Yu J, Yoon J, Qiu X and Yang H 2015 Phys. Rev. Lett. 114 047201
[39] Moon J H, Seo S M, Lee K J, Kim K W, Ryu J, Lee H W, McMichael R D and Stiles M D 2013 Phys. Rev. B 88 184404
[40] Djoufack Z I, Kenfack Jiotsa A and Nguenang J P 2012 Eur. Phys. J. B 85 96
[41] Brächer T, Boulle O, Gaudin G and Pirro P 2017 Phys. Rev. B 95 064429
[42] Je S G, Kim D H, Yoo S C, Min B C, Lee K J and Choe S B 2013 Phys. Rev. B 88 214401
[43] Ding J, Wu T, Chang X and Tang B 2018 Commun. Nonlinear Sci. Numer. Simulat. 59 349
[44] Tang B and Deng K 2017 Nonlin. Dynam. 88 2417
[45] Dyson F J 1956 Phys. Rev. 102 1217
[46] Dyson F J 1956 Phys. Rev. 102 1230
[47] Glauber R J 1963 Phys. Rev. 131 2766
[48] Smith H 1991 Introduction to Quantum Mechanics (Singapore: World Scientific)
[49] Li P, Wang L, Kong L Q, Wang X and Xie Z Y 2018 Appl. Math. Lett. 85 110
[50] Huang G, Shi Z P and Xu Z 1993 Phys. Rev. B 47 14561
[51] Ablowitz M and Segur H 1985 Solitons and the Inverse Scattering Transform (Philadelphia: SIAM)
[52] Liu W, Yu W, Yang C, Liu M, Zhang Y and Ming L 2017 Nonlin. Dynam. 89 2933
[53] Liu W, Yang C, Liu M, Yu W, Zhang Y and Lei M 2017 Phys. Rev. E 96 042201
[54] Lü X and Lin F 2016 Commun. Nonlinear Sci. Numer. Simulat. 32 241
[55] Li Z D, Li Q Y, Li L and Liu W M 2007 Phys. Rev. E 76 026605
[56] Huang G, Xu Z and Xu W 1993 J. Phys. Soc. Jpn. 62 3231
[57] Li D C, Li X M, Li H, Tao R, Yang M and Cao Z L 2015 Chin. Phys. Lett. 32 50302
[58] Liao H J, Xie H D, Liu Z Y, Xie Z Y, Li W, Normand B and Xiang T 2016 Chin. Phys. Lett. 33 77503
[59] Liu W J, Liu M L, Liu B, Quhe R G, Lei M, Fang S B, Teng H and Wei Z Y 2019 Opt. Exp. 27 6689
[60] Dai J, Wang P S, Sun S S, Pang F, Zhang J S, Dong X L, Yue G, Jin K, Cong J Z and Sun Y 2015 Chin. Phys. Lett. 32 127503
[61] Faizi E and Eftekhari H 2015 Chin. Phys. Lett. 32 100303
[62] Fang J, Han D M, Liu H, Liu H D and Zheng T Y 2017 Acta Phys. Sin. 66 160302 (in Chinese)
[63] Wang C J, Chen A H and Gao X L 2012 Acta Phys. Sin. 61 127501 (in Chinese)
[64] Liu M L, Ouyang Y Y, Hou H R, Liu W J and Hou H R 2019 Chin. Opt. Lett. 17 020006
[65] Bai Y H, Zhou W P, Yun G H and Bai N 2011 Acta Phys. Sin. 60 056805 (in Chinese)
[66] Liu L, Sandvik A W and Guo W A 2018 Chin. Phys. B 27 087501
[67] Zhu S B, Qian J and Wang Y Z 2017 Chin. Phys. B 26 046702
[68] Yang D N, Huang Y L, Ni S L, Zhou H X, Mao Y Y, Hu W, Yuang J, Jin K, Zhang G M and Dong X L 2016 Chin. Phys. B 25 077404
[69] Li D C, Wang X P, Li H, Li X M, Yang M and Cao Z L 2016 Chin. Phys. Lett. 33 50301
[70] Li Y F, Shen Y Y, Kong X M 2012 Acta Phys. Sin. 61 107501 (in Chinese)
[1] Green's function Monte Carlo method combined with restricted Boltzmann machine approach to the frustrated J1-J2 Heisenberg model
He-Yu Lin(林赫羽), Rong-Qiang He(贺荣强), and Zhong-Yi Lu(卢仲毅). Chin. Phys. B, 2022, 31(8): 080203.
[2] Gauss quadrature based finite temperature Lanczos method
Jian Li(李健) and Hai-Qing Lin(林海青). Chin. Phys. B, 2022, 31(5): 050203.
[3] Structure and frustrated magnetism of the two-dimensional triangular lattice antiferromagnet Na2BaNi(PO4)2
Fei Ding(丁飞), Yongxiang Ma(马雍翔), Xiangnan Gong(公祥南), Die Hu(胡蝶), Jun Zhao(赵俊), Lingli Li(李玲丽), Hui Zheng(郑慧), Yao Zhang(张耀), Yongjiang Yu(于永江), Lichun Zhang(张立春), Fengzhou Zhao(赵风周), and Bingying Pan(泮丙营). Chin. Phys. B, 2021, 30(11): 117505.
[4] LnCu3(OH)6Cl3 (Ln = Gd, Tb, Dy): Heavy lanthanides on spin-1/2 kagome magnets
Ying Fu(付盈), Lianglong Huang(黄良龙), Xuefeng Zhou(周雪峰), Jian Chen(陈见), Xinyuan Zhang(张馨元), Pengyun Chen(陈鹏允), Shanmin Wang(王善民), Cai Liu(刘才), Dapeng Yu(俞大鹏), Hai-Feng Li(李海峰), Le Wang(王乐), and Jia-Wei Mei(梅佳伟). Chin. Phys. B, 2021, 30(10): 100601.
[5] Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder
Cong Fu(傅聪), Hui Zhao(赵晖), Yu-Guang Chen(陈宇光), and Yong-Hong Yan(鄢永红). Chin. Phys. B, 2021, 30(8): 087501.
[6] Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
Guangyu Sun(孙光宇), Nvsen Ma(马女森), Bowen Zhao(赵博文), Anders W. Sandvik, and Zi Yang Meng(孟子杨). Chin. Phys. B, 2021, 30(6): 067505.
[7] Exact solution of the Gaudin model with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions
Fa-Kai Wen(温发楷) and Xin Zhang(张鑫). Chin. Phys. B, 2021, 30(5): 050201.
[8] Origin of itinerant ferromagnetism in two-dimensional Fe3GeTe2
Xi Chen(陈熙), Zheng-Zhe Lin(林正喆), and Li-Rong Cheng(程丽蓉). Chin. Phys. B, 2021, 30(4): 047502.
[9] Some experimental schemes to identify quantum spin liquids
Yonghao Gao(高永豪), Gang Chen(陈钢). Chin. Phys. B, 2020, 29(9): 097501.
[10] Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
Bowen Zhao(赵博文), Jun Takahashi, Anders W. Sandvik. Chin. Phys. B, 2020, 29(5): 057506.
[11] High pressure synthesis and characterization of the pyrochlore Dy2Pt2O7: A new spin ice material
Qi Cui(崔琦), Yun-Qi Cai(蔡云麒), Xiang Li(李翔), Zhi-Ling Dun(顿志凌), Pei-Jie Sun(孙培杰), Jian-Shi Zhou(周建十), Hai-Dong Zhou(周海东), Jin-Guang Cheng(程金光). Chin. Phys. B, 2020, 29(4): 047502.
[12] Quantum coherence and correlation dynamics of two-qubit system in spin bath environment
Hao Yang(杨豪), Li-Guo Qin(秦立国), Li-Jun Tian(田立君), Hong-Yang Ma(马鸿洋). Chin. Phys. B, 2020, 29(4): 040303.
[13] Quantum steering in Heisenberg models with Dzyaloshinskii-Moriya interactions
Hui-Zhen Li(李慧贞), Rong-Sheng Han(韩榕生), Ye-Qi Zhang(张业奇), Liang Chen(陈亮). Chin. Phys. B, 2018, 27(12): 120304.
[14] Modulational instability, quantum breathers and two-breathers in a frustrated ferromagnetic spin lattice under an external magnetic field
Wanhan Su(苏琬涵), Jiayu Xie(谢家玉), Tianle Wu(吴天乐), Bing Tang(唐炳). Chin. Phys. B, 2018, 27(9): 097501.
[15] Typicality at quantum-critical points
Lu Liu(刘录), Anders W Sandvik, Wenan Guo(郭文安). Chin. Phys. B, 2018, 27(8): 087501.
No Suggested Reading articles found!