γ-Fe4N composites with effective magnetic exchange coupling

γ-Fe4N composites with effective magnetic exchange coupling

Journal Pre-proof Magnetic properties and thermal stability of SrFe12O19/γ-Fe4N composites with effective magnetic exchange coupling Hao Zhang PII: S...

925KB Sizes 1 Downloads 24 Views

Journal Pre-proof Magnetic properties and thermal stability of SrFe12O19/γ-Fe4N composites with effective magnetic exchange coupling Hao Zhang PII:

S0272-8842(19)33722-8

DOI:

https://doi.org/10.1016/j.ceramint.2019.12.220

Reference:

CERI 23873

To appear in:

Ceramics International

Received Date: 30 September 2019 Revised Date:

12 December 2019

Accepted Date: 26 December 2019

Please cite this article as: H. Zhang, Magnetic properties and thermal stability of SrFe12O19/γ-Fe4N composites with effective magnetic exchange coupling, Ceramics International (2020), doi: https:// doi.org/10.1016/j.ceramint.2019.12.220. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Magnetic properties and thermal stability of SrFe12O19/γ-Fe4N composites with effective magnetic exchange coupling Hao Zhang1* 1

School of Civil Engineering and Architecture, Anhui University of Technology, Ma’anshan, Anhui,

243032, China *

Corresponding author: [email protected] (H. Zhang).

Abstract: The SrFe12O19/γ-Fe4N composites were fabricated through physical mixing and the mass of γ-Fe4N nanoparticles was controlled as 0, 5 wt.%, 10 wt.% and 15 wt.% in four batches of experiments. The magnetic properties of the composites were investigated. It was found that when γ-Fe4N nanoparticles were 5 wt.%, and 10 wt.%, effective exchange coupling between γ-Fe4N and SrFe12O19 was observed, and the maximum energy product was increased by 13.5%, and 21.2%, respectively, over pure SrFe12O19. The existence of magnetic exchange coupling between SrFe12O19 and γ-Fe4N was confirmed by both the shape of their hysteresis loops and Henkel plots. The thermal stability investigation indicated that the thermal treatment could slightly deteriorate the magnetic exchange coupling due to the sintering of γ-Fe4N nanoparticles, but the maximum energy product was little impacted. Keywords: SrFe12O19; γ-Fe4N; magnetic exchange coupling; thermal stability; composites; inert gas condensation.

1

1. Introduction M type hexagonal phased ferrite materials (SrFe12O19 and BaFe12O19) have been widely used nowadays due to its high chemical resistance, high thermal stability, and low cost. Besides using as permanent magnets, their applications could be further expanded by modifying their morphology. For example, porous and hollow BaFe12O19 particles were synthesized by Xu et al, which could be potentially used as catalyst supports [1, 2]. Porous SrFe12O19 nanoribbons were synthesized by Jing et al. for perpendicular recording media [3], and tunable microwave properties were achieved by Trukhanov et al. through Ga doping in BaFe12O19 [4, 5]. Compared with rare-earth-based permanent magnetic materials, such as Nd-Fe-B and Sm-Co, the biggest drawback of M type hexagonal phased ferrite materials is their relatively low (BH)max, which is the figure of merit for permanent magnets to evaluate their magnetic strength. According to Schomski’s theory, the (BH)max of a hard magnet could be further increased by magnetic exchange coupling, which requires hard/soft magnetic phases to be mixed at the nanoscale, and the size of the soft phase to be generally less than 20 nm [5-8]. Even though this brings great challenges to the synthesis of hard/soft composites with effective exchange coupling, successful results have been reported. For example, MnBi/FeCo composites were fabricated by ball milling, and a larger (BH)max was observed than pure MnBi phase [9]. SrFe12O19/FeCo core/shell structured composite was synthesized by magnetic self-assembly [10, 11]. Iron cobalt alloy (Fe-Co) nanoparticles were widely used as a soft magnetic material because of its high magnetization. Especially, Fe65Co35 has the highest magnetization in nature [8, 12]. Moreover, its magnetization could be tuned by changing Fe/Co molar ratio. Even though the Cobalt is a generally abundant element, its price is still more than 100 times higher than iron, which has limited the further application of Fe-Co alloys. Meanwhile, iron nitride (Fe-N) has been a great research interest due to its high saturation magnetization and abundance of the elements [13-15]. In Fe-N system, the widely investigated compositions include FeN, Fe2N, γ-Fe4N, and Fe16N2 [16-19]. Among them, γ-Fe4N has high chemical stability and magnetization, which make it a great candidate as soft magnetic material. In this paper, we synthesized γ-Fe4N nanoparticles as a soft phase and fabricated SrFe12O19/γ-Fe4N composites. The magnetic exchange coupling and thermal stability of SrFe12O19 /γ-Fe4N composites were investigated.

2

2. Experimental 2.1. SrFe12O19 particle synthesis: SrFe12O19 particles were synthesized through spray pyrolysis [1]. Specifically, Sr(NO3)2 (2 mmol, VWR, 95%), and Fe(NO3)3 (24 mmol, VWR, 96%) were introduced in 200 mL distilled water to form a solution. The solution was then introduced into an ultrasonic nebulizer, and micro-sized solution droplets with Sr2+ and Fe3+ were generated. The solution droplets were then carried into a horizontal furnace (10 cm in diameter; 100 cm in length) at 1000 oC with an airflow rate of 1 L/min, and the particles were produced by pyrolysis in the furnace, cooled by a chiller, and gathered by a rare-earth magnet. 2.2. γ-Fe4N nanoparticle synthesis: γ-Fe4N nanoparticles were synthesized by inert gas condensation [20]. Fe metal vapors were generated by sputtering (300 W) of Fe target (99.99%), and N2/Ar gas mixture (5/10 sccm) gas was introduced into the sputtering chamber. γ-Fe4N nanoparticles were generated by condensing the vapors through liquid nitrogen. It is noted that the N percentage in Fe-N alloy could be regulated by the N2 ratio in N2/Ar mixed gas. Through our trials, we found that the gas of N2/Ar (5/10 sccm) generates high purity of γ-Fe4N nanoparticles. 2.3. SrFe12O19/ γ-Fe4N composites synthesis: Both SrFe12O19 and γ-Fe4N particles were introduced into isopropyl alcohol (IPA, 10 mL). The suspension was gently ground with mortar/pestle to evaporate the IPA. After the evaporation of IPA, the SrFe12O19/γ-Fe4N composites were obtained. In each experiment, the total mass of the composite was 0.1 g. In four experiments, the γ-Fe4N was 0 wt.%, 5 wt.%, 10 wt.%, and 15 wt.%, and the corresponding samples were named as SrFe12O19, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3. 2.4. Characterization: the particle morphology was determined by TEM (Hitachi, S4700), and the surface chemical conditions were studied by XPS (Thermal Scientific X201). The crystal structure of the particles was investigated by XRD (Shimadzu M5), and the magnetic characteristics were recorded by PPMS (Quantum Design, VersaLab) equipped with a VSM head.

3

3. Results and discussion The γ-Fe4N nanoparticles are characterized by TEM in Fig. 1a, which shows monodispersed nanoparticles. The HRTEM image in Fig. 2a indicates the fingerprint distance of 0.23 nm, corresponding to (111) plane of its crystal structure. TEM diffraction patterns show the dotted rings from (200) and (111) planes, indicating the polycrystal nature of the particles. The histogram regarding the particle size range is described in Fig. 1d. It can be seen that the size follows Gaussian distribution, and the average size is calculated as 9.23 nm by counting 112 nanoparticles. The XPS for both Fe and N elements are shown in Figs. 1e and f, respectively. In Fig. 1e, peaks are observed at 775.6 eV, and 720.3 eV, which come from Fe 2p3/2 and Fe 2p1/2, the characteristic peaks for Fe0. In Fig. 1f, one peak is detected at 397.5 eV, which is ascribed to N0. The magnetic hysteresis loop of γ-Fe4N in Fig. 1g shows the saturation magnetization of 150.2 emu/g and coercivity of 2.3 Oe, compared with 174 emu/g and 39 Oe [13], and 114.9 emu/g and 45 Oe [21], in previous reports. The XRD patterns show three feature peaks of (111), (200) and (220), which are consistent with JCPDS card (NO. 077-2006). As a reference, the molecule structure of γ-Fe4N is presented in Fig. 1i.

Fig. 1. γ-Fe4N characterization: (a). TEM; (b). HRTEM; (c). TEM diffraction; (d). Particle size distribution; (e). Fe XPS spectrum; (f). N XPS spectrum; (g). Magnetic hysteresis loop; (h). XRD patterns; (i). Molecular structure. 4

Fig. 2. SrFe12O19 characterization: (a). TEM; (b). HRTEM; (c). TEM diffraction patterns; SrFe12O19/Fe4N2: (d). TEM; (e). HRTEM; (f). EDX line scan spectrum. The TEM image of the SrFe12O19 particle is presented in Fig. 2a, and spherical-shaped particles are observed, with the size ~100 nm. It is noted that the product particle size can be tuned through the precursor ion concentration [22]. The HRTEM image in Fig. 2b presents the fingerprint distance of 0.225 nm, referring to (114) plane of hexagonal phased M type ferrite. The TEM diffraction patterns show the diffraction rings of (110), (107), (217) and (2011) planes, and the dotted nature of the ring indicates the polycrystalline of the particles. The TEM image of SrFe12O19/Fe4N-2 is presented in Fig. 2d. It shows that the γ-Fe4N nanoparticles are decorated on the SrFe12O19 particle surface, which could be ascribed to the magnetic attraction between SrFe12O19 and γ-Fe4N, due to the remanent magnetization from SrFe12O19 [10]. The HRTEM image regarding the interface between SrFe12O19 and γ-Fe4N is presented in Fig. 2e, and an EDX line scan spectrum regarding Sr (representing SrFe12O19) and N (representing γ-Fe4N) are presented in Fig. 1f. The XRD patterns of SrFe12O19, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3 are presented in Fig. 3. For pure SrFe12O19, the XRD diffraction patterns follow the standard peaks in the JCPDS card (NO. 33-1340) for M-typed hexagonal ferrite. There is no secondary phase or impurity observed. When γFe4N is introduced into SrFe12O19, ranging from 5 to 15% in mass percentage, the corresponding diffraction peaks are not observed. The reason could be that, the largest XRD peak height (111) in γ-Fe4N is only 135.82, while the largest XRD peak height (114) in SrFe12O19 is 2865.64. Because the 5

crystallization in γ-Fe4N is much lower than that in SrFe12O19 (featured by much lower XRD peak intensity), plus the mass percentage is relatively low, the XRD peaks from γ-Fe4N were not observed in SrFe12O19/Fe4N composites. This could be attributed to that the crystallization level of γ-Fe4N is low, and/or the mass percentage of Fe4N is too low to be detected by the diffraction tool. The existence of γFe4N in the composites is already confirmed by the TEM images in Figs. 2d and e.

Fig. 3. XRD patterns of SrFe12O19, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3.

Fig. 4. The characterization of SrFe12O19, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3: (a). Magnetic hysteresis loops; (b). Magnetization and coercivity changes with γ-Fe4N mass percentage; (c). (BH)max changes with γ-Fe4N mass percentage; (d). Henkel plots.

6

Tab. 1 The magnetization (in emu/g) of SrFe12O19, γ-Fe4N, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3 from experiment and calculation. Sample

Experimental magnetization

Calculated magnetization

SrFe12O19

54.32 emu/g

--

γ-Fe4N

150.20 emu/g

--

SrFe12O19/Fe4N-1

59.03 emu/g

59.11 emu/g

SrFe12O19/Fe4N-2

63.02 emu/g

63.91 emu/g

SrFe12O19/Fe4N-3

67.98 emu/g

68.70 emu/g

The hysteresis loops of SrFe12O19, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3 are presented in Fig. 4a, and changes of magnetization and coercivity over a different mass percentage of γFe4N are presented in Fig. 4b. It is observed that, with the increase of the γ-Fe4N mass percentage, the magnetization is improved, and the coercivity is decreased, which follows the general magnetization and coercivity changes in magnetically hard/soft composites [23]. Besides the magnetization characterized by VSM, the composite magnetization could also be calculated based on the mass ratio and magnetization of SrFe12O19 and γ-Fe4N. The magnetization from both experimental characterization and calculation is presented in Tab. 1. It is observed that the experimental characterization results are pretty consistent with those from the calculation. Furthermore, it is also observed that, in Fig. 4a, when the γ-Fe4N mass percentage is 5% and 10%, the hysteresis loops are smooth. Generally, when the hysteresis loop of a magnetically hard/soft composite is smooth, it shows single-phase magnetic behavior, indicating that magnetic exchange coupling is occurring between hard and soft phases. However, when the mass percentage is 15%, the hysteresis loop is not smooth anymore, indicating a destroyed magnetic exchange coupling. The efficient magnetic exchange coupling requires all the soft phase to be magnetically exchange coupled with the hard phase. When γ-Fe4N mass percentage increases to 15%, it is possible that γ-Fe4N is exessive, and not all γ-Fe4N nanoparticles could be magnetically exchange coupled with SrFe12O19, showing two-phase magnetic behaviors. Therefore, a kink is presented in the hysteresis loop of SrFe12O19/Fe4N-3. The (BH)max changes over the mass percentage of γ-Fe4N for SrFe12O19, SrFe12O19/Fe4N-1, SrFe12O19/Fe4N-2, and SrFe12O19/Fe4N-3 are presented in Fig. 4c. When the γ-Fe4N increases from 0 to 5 wt.% and 10 wt.%, (BH)max in SrFe12O19/Fe4N composites increases, due to the observed magnetic exchange coupling verified in Fig. 4a. However, when the γ-Fe4N increases to 15 wt.%, the (BH)max is decreased over pure SrFe12O19, which could be ascribed to the excessive γ-Fe4N nanoparticles that can not 7

be effectively exchange coupled with SrFe12O19. The trend for (BH)max changes is in a great agreement with the smoothness change of the hysteresis loops presented in Fig. 4a. The exchange coupling could be further studied by Henkel plots, which could be described as: ∆M = md(H) – [1 – 2mr(H)],

(1)

where md(H) and mr(H) refer to external magnetic field dependent DC demagnetization remanence and isothermal remanence, respectively [24]. md(H) and mr(H) could be obtained directly by choosing Henkle Plot mode on VSM control software. Generally, the positive peaks in the hard/soft composites indicate the magnetic exchange coupling, while negative peaks indicate magnetostatic interaction among the particles [25]. In Fig. 4d, for pure SrFe12O19, there is only one negative peak, indicating zero magnetic exchange coupling. When the mass percentage of γ-Fe4N is 5% and 10%, their Henkel plots are dominated by a major positive peak, together with a minor negative peak, indicating that the existence of magnetic exchange coupling in the SrFe12O19/γ-Fe4N composites [17]. However, when γ-Fe4N is 15 wt.%, increased intensity of a negative peak and decreased intensity of a positive peak are observed, indicating dipole interactions from incoherent domain rotation, resulting in deterioration of magnetic exchange coupling [17]. The thermal stability of SrFe12O19/Fe4N-2 is studied by heating the composite in N2 environment at 200 o

C for 72 hours. The morphology change is observed by TEM, as presented in Fig. 5a. It shows that, after

annealing, the γ-Fe4N nanoparticles are slightly sintered, resulting in increased cluster size, while there is little change with SrFe12O19 morphology. The XRD patterns before and after annealing are compared in Fig. 5b. It is noted that there are negligible changes over annealing. Similar to the results in Fig. 3, γ-Fe4N phase is still not observed after annealing. The magnetic hysteresis loops of SrFe12O19, γ-Fe4N, and SrFe12O19/Fe4N-2 before and after annealing are presented in Figs. 5c, d, and e. For pure SrFe12O19, there is no noticeable change. For γ-Fe4N, the magnetization is slightly increased by 7.2 emu/g, possibly due to the sintering, as observed in Fig. 5a, which decreases the particle surface area, and decreases the surface canting effect [7]. For SrFe12O19/Fe4N-2, the magnetization is also slightly increased, which could be attributed to the increased magnetization of γ-Fe4N. However, the coercivity is slightly decreased. The Henkel plots of SrFe12O19/Fe4N-2 before and after annealing are shown in Fig. 5f. A slightly decreased positive peak and increased negative peak are presented, indicating a slightly decreased magnetic exchange coupling, possibly due to the sintering of γ-Fe4N nanoparticles. Due to the strict requirements on the size of the soft phase, the increased size of the soft phase is not beneficial to the exchange coupling [7]. The (BH)max for SrFe12O19/Fe4N-2 before and after annealing is calculated as 1.31 and 1.26 MGOe, respectively, indicating that exposing the composite under 200 oC for a long time could deteriorate its magnetic properties. 8

Fig. 5. (a). TEM of SrFe12O19/Fe4N-2 after annealing; (b). XRD patterns of SrFe12O19/Fe4N-2 before and after annealing; (c). Magnetic hysteresis loops of SrFe12O19 before and after annealing; (d). Magnetic hysteresis loops of γ-Fe4N before and after annealing; (e). Magnetic hysteresis loops of SrFe12O19/Fe4N-2 before and after annealing; (f). Henkel plots of SrFe12O19/Fe4N-2 before and after annealing. 4. Conclusions The SrFe12O19/Fe4N composites were fabricated through physical mixing and the mass percentage of γFe4N was controlled as 5%, 10%, and 15%. TEM images showed that the γ-Fe4N nanoparticles were magnetically decorated on the SrFe12O19 surface, which was ascribed to the remanent magnetization of SrFe12O19. The exchange coupling was studied by both magnetic hysteresis loops and Henkel plots. The results indicated that when the γ-Fe4N was 5 wt.% and 10 wt.%, exchange coupling was observed between SrFe12O19 and γ-Fe4N, indicated by smooth hysteresis loops and dominated positive peaks in the Henkel plots. The thermal stability investigation showed that, after annealing at 200 oC for 72 hours, and the exchange coupling was slightly decreased, possibly due to the sintering of the γ-Fe4N nanoparticles. Acknowledgment The work was supported by the China Postdoctoral Science Foundation (No. 2017M612051), University Outstanding Young Talents Overseas Visit Study Project (No. gxgwfx2018021). Declaration of Interest Statement We confirm that there are no known conflicts of interest associated with this publication and there has 9

been no significant financial support for this work that could have influenced its outcome. References [1] X. Xu, J. Park, Y.K. Hong, A.M. Lane, Synthesis and characterization of hollow mesoporous BaFe12O19 spheres, J Solid State Chem, 222 (2015) 84-89. [2] X. Qiao, C. Zhao, Q. Shao, M. Hassan, Structural Characterization of Corn Stover Lignin after Hydrogen Peroxide Presoaking Prior to Ammonia Fiber Expansion Pretreatment, Energy & Fuels, 32 (2018) 6022-6030. [3] P. Jing, J. Du, J. Wang, J. Wei, L. Pan, J. Li, Q. Liu, Width-controlled M-type hexagonal strontium ferrite (SrFe12O19) nanoribbons with high saturation magnetization and superior coercivity synthesized by electrospinning, Sci Rep-Uk, 5 (2015) 15089-15089. [4] A.V. Trukhanov, S.V. Trukhanov, V.G. Kostishyn, L.V. Panina, I.S. Kazakevich, A.V. Trukhanov, V.O. Natarov, D.N. Chitanov, V.A. Turchenko, V.V. Oleynik, E.S. Yakovenko, L.Y. Macuy, E.L. Trukhanova, Microwave properties of the Ga-substituted BaFe12O19 hexaferrites, Materials Research Express, 4 (2017) 076106. [5] C. Zhao, X. Qiao, Y. Cao, Q. Shao, Application of hydrogen peroxide presoaking prior to ammonia fiber expansion pretreatment of energy crops, Fuel, 205 (2017) 184-191. [6] R. Skomski, J.M.D. Coey, Exchange Coupling and Energy Product in Random 2-Phase Aligned Magnets, Ieee T Magn, 30 (1994) 607-609. [7] R. Skomski, Aligned 2-Phase Magnets - Permanent Magnetism of the Future (Invited), J Appl Phys, 76 (1994) 7059-7064. [8] C. Zhao, Q. Shao, Z. Ma, B. Li, X. Zhao, Physical and chemical characterizations of corn stalk resulting from hydrogen peroxide presoaking prior to ammonia fiber expansion pretreatment, Industrial Crops and Products, 83 (2016) 86-93. [9] Y. Cheng, H. Wang, Z. Li, W. Liu, I. Bao, The thermal stability of magnetically exchange coupled MnBi/FeCo composites at electric motor working temperature, Materials Research Express, 5 (2018) 046103. [10] X. Xu, Y.-K. Hong, J. Park, W. Lee, A.M. Lane, Exchange coupled SrFe12O19/Fe-Co core/shell particles with different shell thickness, Electronic Materials Letters, 11 (2015) 1021-1027. [11] C. Zhao, Y. Cao, Z. Ma, Q. Shao, Optimization of liquid ammonia pretreatment conditions for maximizing sugar release from giant reed (Arundo donax L.), Biomass and Bioenergy, 98 (2017) 61-69. [12] A. Goldman, Soft Cobalt-Iron Alloys, in: A. Goldman (Ed.) Handbook of Modern Ferromagnetic Materials, Springer US, Boston, MA, 1999, pp. 137-144. [13] C. Zhang, X. Liu, M. Li, C. Liu, H. Li, X. Meng, K.M.U. Rehman, Preparation and soft magnetic properties of γ′-Fe4N particles, Journal of Materials Science: Materials in Electronics, 29 (2018) 1254-1257. [14] C. Zhao, Z. Ma, Q. Shao, B. Li, J. Ye, H. Peng, Enzymatic Hydrolysis and Physiochemical Characterization of Corn Leaf after H-AFEX Pretreatment, Energy & Fuels, 30 (2016) 1154-1161. [15] M. Hassan, M. Umar, W. Ding, E. Mehryar, C. Zhao, Methane enhancement through co-digestion of chicken manure and oxidative cleaved wheat straw: Stability performance and kinetic modeling perspectives, Energy, 141 (2017) 2314-2320. [16] M.-S. Balogun, M. Yu, Y. Huang, C. Li, P. Fang, Y. Liu, X. Lu, Y. Tong, Binder-free Fe2N nanoparticles on carbon textile with high power density as novel anode for high-performance flexible lithium ion batteries, Nano Energy, 11 (2015) 348-355. [17] Y. Jiang, M.A. Mehedi, E. Fu, Y. Wang, L.F. Allard, J.-P. Wang, Synthesis of Fe16N2 compound Free-Standing Foils with 20 MGOe Magnetic Energy Product by Nitrogen Ion-Implantation, Sci Rep-Uk, 6 (2016) 25436. [18] D. Laniel, A. Dewaele, S. Anzellini, N. Guignot, Study of the iron nitride FeN into the megabar regime, J Alloy Compd, 733 (2018) 53-58.

10

[19] C. Zhao, Q. Shao, B. Li, W. Ding, Comparison of Hydrogen Peroxide and Ammonia Pretreatment of Corn Stover: Solid Recovery, Composition Changes, and Enzymatic Hydrolysis, Energy & Fuels, 28 (2014) 6392-6397. [20] T. Wang, C. Zhou, Z. Zhang, M. Liao, C. Sun, The impacts of operating pressure on the structural and magnetic properties of HfCo7 nanoparticles synthesized by inert gas condensation, Chem Phys Lett, 721 (2019) 18-21. [21] R. Vinod. K, S. Padmanapan, S. Mohan, B. Subramanian, Insights into the nitridation of zero-valent iron nanoparticles for the facile synthesis of iron nitride nanoparticles, RSC Adv., 6 (2016). [22] G.L. Messing, S.C. Zhang, G.V. Jayanthi, Ceramic Powder Synthesis by Spray-Pyrolysis, J Am Ceram Soc, 76 (1993) 2707-2726. [23] J. Park, Y.-K. Hong, W. Lee, S.-G. Kim, C. Rong, N. Poudyal, J.P. Liu, C.-J. Choi, A Simple Analytical Model for Magnetization and Coercivity of Hard/Soft Nanocomposite Magnets, Sci Rep-Uk, 7 (2017) 4960. [24] X. Liu, G. Ishida, A. Morisako, Magnetization reversal mechanism of Nd-Fe-B films with perpendicular magnetic anisotropy, J Appl Phys, 109 (2011) 07A725. [25] V. Christoph, K. Elk, Magnetostatic interaction in fine particle magnets, J Magn Magn Mater, 74 (1988) 143148.

11