Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside

doi:10.1007/s11706-019-0471-2

Front. Mater. Sci.

2019, Vol. 13

Issue (3) : 323-333 https://doi.org/10.1007/s11706-019-0471-2

RESEARCH ARTICLE

Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside

Wei LI¹, Lizhong ZHAO^1,², Zhongwu LIU¹(

)

¹. School of Materials Science and Engineering, South China University of Technology, Guangzhou 510640, China
². Innovative Center for Advanced Materials, Hangzhou Dianzi University, Hangzhou 310012, China

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Abstract

A simplified analysis method based on micromagnetic simulation is proposed to investigate effects of nonmagnetic particles on the demagnetizing field of a permanent magnet. By applying the additivity law of the demagnetizing field, the complicated demagnetizing field of the real magnet could be analyzed by only focusing on the stray field of the reserved magnet. For a magnet with nonmagnetic particles inside, the particle size has no significant effect on the maximum value of the demagnetization field, but the area of the affected region by the particle is proportional to the particle size. A large particle produces a large affected area overlapped with those influenced by other particles, which leads to the large demagnetization field. With increasing the length of the particle along the magnetization direction, the demagnetization field on the pole surface increases. The pole surface with a convex shape will increase the demagnetization field. The demagnetizing field near the nonmagnetic particle will be further increased by the large macroscopic demagnetizing field near the pole surface. This work suggests some practical approaches to optimize the microstructure of permanent magnets.

Keywords demagnetizing field additivity micromagnetic simulation nonmagnetic phase nucleation process

Corresponding Author(s): Zhongwu LIU

Online First Date: 14 August 2019 Issue Date: 29 September 2019

Cite this article:

Wei LI,Lizhong ZHAO,Zhongwu LIU. Micromagnetic investigation by a simplified approach on the demagnetization field of permanent magnets with nonmagnetic phase inside[J]. Front. Mater. Sci., 2019, 13(3): 323-333.

URL:

https://academic.hep.com.cn/foms/EN/10.1007/s11706-019-0471-2
https://academic.hep.com.cn/foms/EN/Y2019/V13/I3/323

Fig.1 The cuboid simulation region with the size of 600 nm × 600 nm × 1200 nm. The origin of the coordinate is in the center of the cuboid. The simulation results in the section with blue border (x = 1 nm, named “data section”) will be used to draw the 2D distribution diagram. The simulation results in the red line (x = 1 nm, y = 1 nm, named “data line”) will be used to draw a distribution curve.

Fig.2 The demagnetizing field of the simulation models to verify the additivity. Insets show the middle sections of the models. The magnetization in red regions is M_s and the magnetization in white regions is 0. The nonmagnetic particle model and the corresponding magnet model are shown above. The vertical axes represent the Z coordinate in magnets, and the horizontal axes represent the Z component of the demagnetizing field. The curves show the demagnetizing field in the dash-dotted lines (data line in Fig. 1).

Fig.3 The demagnetizing fields influenced by nonmagnetic phases. The middle sections of the models are shown in the insets. The magnetization in red regions is M_s, the magnetization in the white region is 0, and the magnetization in the blue region is −M_s. The vertical axes represent the Z coordinate in the magnets, and the horizontal axes represent the Z component of the demagnetizing field. The curves show the demagnetizing field in the dash-dotted lines (data line in Fig. 1).

Fig.4 (a) The cubic reversed magnets (−M_s) with different values of the side-length s. (b) The demagnetizing field curves in the data line. (c) The demagnetizing field curves with x-coordinate “z” divided by “s” correspondingly. (d) The sum of the demagnetizing field curves of the cubic reversed magnets with size s = 120 and 180 nm. The distance between them is 98 nm. The gray and light red regions represent the Z region of the demagnetizing fields with values larger than 30 kA/m (named influenced region), and the light blue region represents the overlapped region.

Fig.5 (a) The cuboid reversed magnets (−M_s) with the same side-length of 120 nm and different values of the height h. (b) The demagnetizing field curves in the data line. (c)(d) 2D distribution graphs of the demagnetizing fields for h = 40 and 360 nm, respectively. The demagnetizing field is along the −Z direction in the blue regions (+Z in the red regions). The dotted lines represent the demagnetizing field of 30 or −30 kA/m.

Fig.6 (a) The models used to simulate concavity and convexity of reversed magnets. (b) The 2D demagnetizing field distribution in the data section of magnets (M_s) with different concavity and convexity (different h_p). (c) The 2D demagnetizing field distribution in the data section of corresponding inset models with concavity and convexity in different dimensions (h_p = 40 or −40 nm). The demagnetizing field is along the −Z direction in the blue regions (+Z in the red regions). The dotted lines represent the demagnetizing field of 30 or −30 kA/m.

Fig.7 The demagnetizing fields along the dash-dotted lines (data line in Fig. 1) of cuboid magnets (red region, M_s) with nonmagnetic particles (white cuboid region) in different positions. The inset is the middle sections (data section in Fig. 1) of the models. The red region represents the magnets with the size of 600 nm × 600 nm × 1200 nm and the magnetization M_s along the+Z direction. The white cuboid region represents nonmagnetic particles with the size of 40 nm × 40 nm × 80 nm in different positions inside the magnet.

1	T G Woodcock, Y Zhang, G Hrkac, et al.. Understanding the microstructure and coercivity of high performance NdFeB-based magnets. Scripta Materialia, 2012, 67(6): 536–541 https://doi.org/10.1016/j.scriptamat.2012.05.038
2	H Sepehri-Amin, T Ohkubo, T Shima, et al.. Grain boundary and interface chemistry of an Nd–Fe–B-based sintered magnet. Acta Materialia, 2012, 60(3): 819–830 https://doi.org/10.1016/j.actamat.2011.10.043
3	R K Mishra, J K Chen, G Thomas. Effect of annealing on the microstructure of sintered Nd–Fe–B magnets. Journal of Applied Physics, 1986, 59(6): 2244–2246 https://doi.org/10.1063/1.336366
4	H J Engelmann, A S Kim, G Thomas. Microstructure and magnetic effects of small Cu additions to (Nd, Dy)FeB magnets. Scripta Materialia, 1997, 36(1): 55–62 https://doi.org/10.1016/S1359-6462(96)00312-0
5	M Xia, A B Abrahamsen, C R H Bahl, et al.. The influence of carbon and oxygen on the magnetic characteristics of press-less sintered NdFeB magnets. Journal of Magnetism and Magnetic Materials, 2017, 422: 232–236 https://doi.org/10.1016/j.jmmm.2016.09.014
6	Y H Hou, Y L Wang, Y L Huang, et al.. Effects of Nd-rich phase on the improved properties and recoil loops for hot deformed Nd–Fe–B magnets. Acta Materialia, 2016, 115: 385–391 https://doi.org/10.1016/j.actamat.2016.06.015
7	Q Zhou, W Li, Y Hong, et al.. Microstructure improvement related coercivity enhancement for sintered NdFeB magnets after optimized additional heat treatment. Journal of Rare Earths, 2018, 36(4): 379–384 https://doi.org/10.1016/j.jre.2017.11.007
8	K Hono, H Sepehri-Amin. Strategy for high-coercivity Nd–Fe–B magnets. Scripta Materialia, 2012, 67(6): 530–535 https://doi.org/10.1016/j.scriptamat.2012.06.038
9	J Fidler, T Schrefl. Micromagnetic modelling –– the current state of the art. Journal of Physics D: Applied Physics, 2000, 33(15): R135–R156 https://doi.org/10.1088/0022-3727/33/15/201
10	R I Joseph. Ballistic demagnetizing factor in uniformly magnetized rectangular prisms. Journal of Applied Physics, 1967, 38(5): 2405–2406 https://doi.org/10.1063/1.1709907
11	W Si, G P Zhao, N Ran, et al.. Deterioration of the coercivity due to the diffusion induced interface layer in hard/soft multilayers. Scientific Reports, 2015, 5(1): 16212 (9 pages) https://doi.org/10.1038/srep16212 pmid: 26586226
12	X J Weng, L C Shen, H Tang, et al.. Change of coercivity mechanism with the soft film thickness in hard-soft trilayers. Journal of Magnetism and Magnetic Materials, 2019, 475: 352–358 https://doi.org/10.1016/j.jmmm.2018.10.118
13	H Kronmüller. General micromagnetic theory. In: Kronmüller H, Parkin S, eds. Handbook of Magnetism and Advanced Magnetic Materials. John Wiley & Sons, Ltd., 2007, doi: 10.1002/9780470022184.hmm201
14	X Tan, J S Baras, P S Krishnaprasad. Fast evaluation of demagnetizing field in three-dimensional micromagnetics using multipole approximation. In: Proceedings of SPIE — The International Society for Optical Engineering, 2001, 3984: 195–201
15	M J Donahue. Parallelizing a micromagnetic program for use on multiprocessor shared memory computers. IEEE Transactions on Magnetics, 2009, 45(10): 3923–3925 https://doi.org/10.1109/TMAG.2009.2023866
16	W F Brown. Magnetoelastic Interactions. New York: Springer, 1966
17	M Donahue, D Porter. Object oriented micro-magnetic framework. Interagency Report No. NISTIR, 2006, 6376: 13
18	E Della Torre. Problems in physical modeling of magnetic materials. Physica B: Condensed Matter, 2004, 343(1–4): 1–9 https://doi.org/10.1016/j.physb.2003.08.052
19	T Schrefl, J Fidler. Finite element modeling of nanocomposite magnets. IEEE Transactions on Magnetics, 1999, 35(5): 3223–3228 https://doi.org/10.1109/20.800483
20	B B Straumal, Y O Kucheev, I L Yatskovskaya, et al.. Grain boundary wetting in the NdFeB-based hard magnetic alloys. Journal of Materials Science, 2012, 47(24): 8352–8359 https://doi.org/10.1007/s10853-012-6618-5
21	Q Zhou, Z W Liu, X C Zhong, et al.. Properties improvement and structural optimization of sintered NdFeB magnets by non-rare earth compound grain boundary diffusion. Materials & Design, 2015, 86: 114–120 https://doi.org/10.1016/j.matdes.2015.07.067
22	K Hono, H Sepehri-Amin. Strategy for high-coercivity Nd–Fe–B magnets. Scripta Materialia, 2012, 67(6): 530–535 https://doi.org/10.1016/j.scriptamat.2012.06.038
23	J Fischbacher, A Kovacs, L Exl, et al.. Searching the weakest link: Demagnetizing fields and magnetization reversal in permanent magnets. Scripta Materialia, 2018, 154: 253–258 https://doi.org/10.1016/j.scriptamat.2017.11.020
24	Q Zhou, Z W Liu, X C Zhong, et al.. Properties improvement and structural optimization of sintered NdFeB magnets by non-rare earth compound grain boundary diffusion. Materials & Design, 2015, 86: 114–120 https://doi.org/10.1016/j.matdes.2015.07.067
25	K Hirota, H Nakamura, T Minowa, et al.. Coercivity enhancement by the grain boundary diffusion process to Nd–Fe–B sintered magnets. IEEE Transactions on Magnetics, 2006, 42(10): 2909–2911 https://doi.org/10.1109/TMAG.2006.879906
26	H Sepehri-Amin, T Ohkubo, K Hono. The mechanism of coercivity enhancement by the grain boundary diffusion process of Nd–Fe–B sintered magnets. Acta Materialia, 2013, 61(6): 1982–1990 https://doi.org/10.1016/j.actamat.2012.12.018
27	T Akiya, J Liu, H Sepehri-Amin, et al.. Low temperature diffusion process using rare earth–Cu eutectic alloys for hot-deformed Nd–Fe–B bulk magnets. Journal of Applied Physics, 2014, 115(17): 17A766 https://doi.org/10.1063/1.4869062
28	F Vial, F Joly, E Nevalainen, et al.. Improvement of coercivity of sintered NdFeB permanent magnets by heat treatment. Journal of Magnetism and Magnetic Materials, 2002, 242–245: 1329–1334 https://doi.org/10.1016/S0304-8853(01)00967-2
29	F Chen, T Zhang, J Wang, et al.. Coercivity enhancement of a NdFeB sintered magnet by diffusion of Nd70Cu30 alloy under pressure. Scripta Materialia, 2015, 107: 38–41 https://doi.org/10.1016/j.scriptamat.2015.05.015
30	W Li, Q Zhou, L Z Zhao, et al.. Micromagnetic simulation of anisotropic grain boundary diffusion for sintered Nd–Fe–B magnets. Journal of Magnetism and Magnetic Materials, 2018, 451: 704–709 https://doi.org/10.1016/j.jmmm.2017.12.002

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