Please wait a minute...
 Chin. Phys. B, 2022, Vol. 31(4): 040202    DOI: 10.1088/1674-1056/ac401e
 GENERAL Prev   Next

# Anti-function solution of uniaxial anisotropic Stoner-Wohlfarth model

Kun Zheng(郑坤)1, Yu Miao(缪宇)1, Tong Li(李通)1, Shuang-Long Yang(杨双龙)1, Li Xi(席力)1, Yang Yang(杨洋)1, Dun Zhao(赵敦)2,†, and De-Sheng Xue(薛德胜)1,‡
1 Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China;
2 School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Abstract  The anti-trigonometric function is used to strictly solve the uniaxial anisotropic Stoner-Wohlfarth (SW) model, which can obtain the relation of the angle α (θ) between the magnetization (the anisotropy field) and the applied magnetic field. Using this analytic solution, the hysteresis loops of uniaxial anisotropic SW particles magnetized in typical directions could be numerically calculated. Then, the hysteresis loops are obtained in randomly distributed SW particle ensembles while ignoring the dipole interaction among them with the analytic solution. Finally, the correctness of the analytic solution is verified by the exact solutions of remanence, switching field, and coercivity from the SW model. The analytic solution provides an important reference for understanding the magnetizing and magnetization reversal processes of magnetic materials.
Keywords:  Stoner-Wohlfarth model      anti-trigonometric function      hysteresis loop
Received:  29 July 2021      Revised:  16 November 2021      Accepted manuscript online:  05 December 2021
 PACS: 02.60.Cb (Numerical simulation; solution of equations) 75.30.Gw (Magnetic anisotropy) 75.40.Cx (Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.)) 75.60.Ej (Magnetization curves, hysteresis, Barkhausen and related effects)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 91963201, 12174163, and 12075102), PCSIRT (Grant No. IRT-16R35), and the 111 Project (Grant No. B20063).
Corresponding Authors:  Dun Zhao, De-Sheng Xue     E-mail:  zhaod@lzu.edu.cn;xueds@lzu.edu.cn

#### Cite this article:

Kun Zheng(郑坤), Yu Miao(缪宇), Tong Li(李通), Shuang-Long Yang(杨双龙), Li Xi(席力), Yang Yang(杨洋), Dun Zhao(赵敦), and De-Sheng Xue(薛德胜) Anti-function solution of uniaxial anisotropic Stoner-Wohlfarth model 2022 Chin. Phys. B 31 040202

 [1] Stoner E C and Wohlfarth E P 1948 Phil. Trans. Roy. Soc. A 240 599[2] Jiles D C and Atherton D L 1986 J. Magn. Magn. Mater. 61 48[3] Kronmuller H and Durst K D 1988 J. Magn. Magn. Mater. 74 291[4] Stoner E C and Wohlfarth E P 1991 IEEE Trans. Magn. 27 3475[5] Slonczewski J C 2009 IEEE Trans. Magn. 45 8[6] Coffey K R, Thomson T and Thiele J U 2003 J. Appl. Phys. 93 8471[7] Spratt G W D, Bissel P R and Chantrell R W 1987 IEEE Trans. Magn. 23 186[8] Spratt G W D, Fearon M, Bissel P R, Chantrell R W, Lyberatos A and Wohlfarth E P 1988 IEEE Trans. Magn. 24 1895[9] Campos M F de, Romero S A, Landgraf F J G and Missell F P 2011 J. Phys. Conf. Ser. 303 012049[10] Girt E, Krishnan K M, Thomas G, Girt E and Altounian Z 2001 J. Magn. Magn. Mater. 231 219[11] Chai G Z, Xue D S, Fan X L, Li X L and Guo D W 2008 Appl. Phys. Lett. 93 152516[12] Wang C L, Zhang S H, Li S D, Du H L, Zhao G X and Cao D R 2020 Chin. Phys. B 29 046202[13] Fan X L, Xue D S, Lin M, Zhang Z M, Guo D W, Jiang C J and Wei J Q 2008 Appl. Phys. Lett. 92 222505[14] Li C Z, Jiang C J and Chai G Z 2021 Chin. Phys. B 30 037502[15] Cao X Q, Li S D, Cai Z Y, Du H L, Xue Q, Gao X Y and Xie S M 2014 Chin. Phys. B 23 086201[16] Ye J, He W, Wu Q, Liu H L, Zhang X Q, Chen Z Y and Cheng Z H 2013 Sci. Rep. 3 2148[17] Zhan Q F, Vandezande S, Haesendonck C V and Temst K 2007 Appl. Phys. Lett. 91 122510[18] Lee A J, Brangham J T, Cheng Y, White S P, Ruane W T, Esser B D, McComb D W, Hammel P C and Yang F Y 2017 Nat. Commun. 8 234[19] Li S and Zhu T 2020 Jpn. J. Appl. Phys. 59 040906[20] Shi G Y, Wan C H, Chang Y S, Li F, Zhou X J, Zhang P X, Cai J W, Han X F, Pan F and Song C 2017 Phys. Rev. B 95 104435[21] Zhong W D 1987 Ferromagnetism, 2nd edn. (Beijing:Science Press) pp. 329-333[22] Slonczewski J C 1956 "Research Memorandum RM" 003.111.224, IBM Research Center Poughkeepsie, unpublished[23] Thiaville A 1998 J. Magn. Magn. Mater. 182 5[24] Pfeiffer H 1990 Phys. Stat. Sol. 118 295[25] Szabo Z and Ivanyi A 2000 J. Magn. Magn. Mater. 215-216 33[26] Henry Y, Mangin S, Cucchiara J, Katine J A and Fullerton E E 2009 Phys. Rev. B 79 214422[27] Campos M F de, Silva F A S da, Perigo E A and Castro J A de 2013 J. Magn. Magn. Mater. 345 147[28] Wood R 2009 IEEE Trans. Magn. 45 100[29] Fal T J, Mercer J I, Leblanc M D, Whitehead J P, Plumer M L and van Ek J 2013 Phys. Rev. B 87 064405[30] He S Q 1998 Mathematical Dictionary (Taiyuan:Shanxi Education Press) p. 204[31] Delgado-Garcia R, Rodriguez-Rodriguez G and Colino J M 2021 AIP Adv. 11 015137[32] Lavín R, Denardin J C, Escrig J, Altbir D, Cortés A and Gómez H 2009 J. Appl. Phys. 106 103903[33] Xue D S and Miao Y 2019 College Physics 38 7
 [1] Prediction of flexoelectricity in BaTiO3 using molecular dynamics simulations Long Zhou(周龙), Xu-Long Zhang(张旭龙), Yu-Ying Cao(曹玉莹), Fu Zheng(郑富), Hua Gao(高华), Hong-Fei Liu(刘红飞), and Zhi Ma(马治). Chin. Phys. B, 2023, 32(1): 017701. [2] Magnetic properties of a mixed spin-3/2 and spin-2 Ising octahedral chain Xiao-Chen Na(那小晨), Nan Si(司楠), Feng-Ge Zhang(张凤阁), and Wei Jiang(姜伟). Chin. Phys. B, 2022, 31(8): 087502. [3] Magnetic properties of La2CuMnO6 double perovskite ceramic investigated by Monte Carlo simulations S Mtougui, I EL Housni, N EL Mekkaoui, S Ziti, S Idrissi, H Labrim, R Khalladi, L Bahmad. Chin. Phys. B, 2020, 29(5): 056101. [4] Interfacial effect on the reverse of magnetization and ultrafast demagnetization in Co/Ni bilayers with perpendicular magnetic anisotropy Zi-Zhao Gong(弓子召), Wei Zhang(张伟), Wei He(何为), Xiang-Qun Zhang(张向群), Yong Liu(刘永), Zhao-Hua Cheng(成昭华). Chin. Phys. B, 2018, 27(5): 057501. [5] Random crystal field effect on hysteresis loops and compensation behavior of mixed spin-(1,3/2) Ising system K Htoutou, Y Benhouria, A Oubelkacem, R Ahl laamara, L B Drissi. Chin. Phys. B, 2017, 26(12): 127501. [6] Effect of exchange coupling on magnetic property in Sm-Co/α-Fe layered system C X Sang(桑成祥), G P Zhao(赵国平), W X Xia(夏卫星), X L Wan(万秀琳), F J Morvan, X C Zhang(张溪超), L H Xie(谢林华), J Zhang(张健), J Du(杜娟), A R Yan(闫阿儒), P Liu(刘平). Chin. Phys. B, 2016, 25(3): 037501. [7] Generic meminductive characteristics ofswitched reluctance machines Liang Yan (梁燕), Chen Hao (陈昊), Liu Hua-Jian (刘华建), Shi Jiao-Tong (石交通). Chin. Phys. B, 2015, 24(6): 068401. [8] Theoretical study of mutual control mechanism between magnetization and polarization in multiferroic materials Liu Yu (刘宇), Zhai Liang-Jun (翟良君), Wang Huai-Yu (王怀玉). Chin. Phys. B, 2015, 24(3): 037510. [9] Hysteresis loop behaviors of ferroelectric thin films: A Monte Carlo simulation study C. M. Bedoya-Hincapié, H. H. Ortiz-Álvarez, E. Restrepo-Parra, J. J. Olaya-Flórez, J. E. Alfonso. Chin. Phys. B, 2015, 24(11): 117701. [10] Micromagnetic simulation of Sm-Co/α-Fe/Sm-Co trilayers with various angles between easy axes and the film plane Zhang Xi-Chao (张溪超), Zhao Guo-Ping (赵国平), Xia Jing (夏静), Yue Ming (岳明), Yuan Xin-Hong (袁新红), Xie Lin-Hua (谢林华). Chin. Phys. B, 2014, 23(9): 097504. [11] Energy dissipation of a ring-like metal rubber isolator Yan Hui (闫辉), Zhang Wen-Jing (张文静), Jiang Hong-Yuan (姜洪源), Chen Liang (陈亮). Chin. Phys. B, 2014, 23(4): 040702. [12] Computation of the locus crossing point location of MC circuit Liu Hai-Jun (刘海军), Li Zhi-Wei (李智炜), Bu Kai (步凯), Sun Zhao-Lin (孙兆林), Nie Hong-Shan (聂洪山). Chin. Phys. B, 2014, 23(4): 048401. [13] The hysteresis loops of a ferroelectric bilayer film with surface transition layers Cui Lian(崔莲), Lü Tian-Quan(吕天全), Sun Pu-Nan(孙普男), and Xue Hui-Jie(薛惠杰). Chin. Phys. B, 2010, 19(7): 077701. [14] Preisach analysis of (La0.2Nd0.8)0.67Pb0.33MnO3 Cao Xian-Sheng (曹先胜), Xiao Chun-Tao (肖春涛), Gywn Williams, Roy Roshko. Chin. Phys. B, 2005, 14(5): 1051-1054. [15] Zero-field-cooled and field-cooled magnetizations and magnetic susceptibility of itinerant ferromagnet SrRuO3 Hou Deng-Lu (侯登录), Jiang En-Yong (姜恩永), Bai Hai-Li (白海力). Chin. Phys. B, 2002, 11(8): 827-833.
 No Suggested Reading articles found!