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Chin. Phys. B, 2022, Vol. 31(4): 040202    DOI: 10.1088/1674-1056/ac401e
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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:;

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
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