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Effect of magnetostatic interaction on magnetic properties of mixed powders: computer simulation and experimental results
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) e497–e498
Effect of magnetostatic interaction on magnetic properties of mixed powders: computer simulation and experimental results R. Sato Turtellia,*, P. Kerschlb, H. Fukunagac, Y. Kawazoec, a . A. Shintanid, R. Grossinger Inst. fur Technische Universitat . Festkorperphysik, . . Wien, Wiedner Hauptstrasse 8-10, Vienna A-1040, Austria Leibnitz Institute for Solid State and Materials Research Dresden, IFW, P.O. Box 270116, Dresden D-01171, Germany c Department of Electrical Engineering and Electronics, Nagasaki University, Nagasaki 852-8521, Japan d Research and Development Center, Kubota Co., 1-1 Hama 1-Chome, Amagasaki, Hyogo 661-8567, Japan a
b
Abstract Magnets were prepared by mixing powders of Ba-ferrite BaFe12 O19 and soft magnetic amorphous ðFe0:97 Cr0:03 Þ76 ðSi0:5 B0:5 Þ22 C2 : The shape of the hysteresis loops of these magnets is typical of a single phase material. The saturation magnetisation increases and the remanence decreases proportionally to the mass quantity of the amorphous phase. Computer simulation on magnetostatic interaction among the powders was made using magnetic charge and the fast Fourier transformation. Excellent agreement between the measured and calculated loop shapes was found. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50 Tt; 75.50.Ww; 75.60.Ej Keywords: Fine-particle system; Permanent magnet; Magnetisation curve; Hysteresis
Nanocomposite magnets composed of high coercivity hard magnetic phase and large magnetisation soft phase result in high-energy product if both phases are sufficiently exchange coupled [1]. The exchange coupling favours remanence enhancement [2]. Generally, the understanding of the magnetisation process in such heterogeneous systems is discussed neglecting magnetostatic interactions between soft and hard nanograins. For bulk nanocomposite magnets it is difficult to optimise the magnetic properties due to microstructural complexities. Mixed powder technique, however, can permit the preparation of artificial nano-disperse magnetic structures and facilitates to study fundamental magnetisation processes both experimentally and numerically. Therefore, in this work, magnets were prepared by mixing powders of hard and soft magnetic materials to study demagnetisation process in such *Corresponding author. Tel.: +43-1-58801-13150; fax: +431-58801-13199. E-mail address: [email protected] (R.S. Turtelli).
heterogeneous systems. Demagnetisation curves obtained from the computer simulation, based on the effect of magnetostatic interaction between the powders were compared with experimental results. Nanocrystalline hard magnetic Ba-ferrite BaFe12 O19 powder (grain size B30 nm; particle size = 80 mm; saturation polarisation Js ¼ m0 Ms ¼ 0:477 T and anisotropy constant Ku ¼ 70 kJ=m3 ) prepared by intensive milling technique [3] was mixed with ‘‘Kubota-powder’’ that is soft magnetic amorphous ðFe0:97 Cr0:03 Þ76 ðSi0:5 B0:5 Þ22 C2 powder (particle size o40 mm and Js ¼ 1:24 T) produced by spinning water atomisation process [4] by means of a high-energy ball mill for 10 min: The mixed powders were glued with a high-temperature glue in the cylinder form, obtaining a sample of 4.13 mm diameter and 5:93 mm length. Three compositions of the mixed powders ðBa ferriteÞx ðKubota powderÞ1x were prepared with a Ba-ferrite volume fraction of x ¼ 0:8; 0:5 and 0.2. Fig. 1 shows the hysteresis loops evolution with x at 300 K measured with SQUID magnetometer with a
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.1422
ARTICLE IN PRESS R.S. Turtelli et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e497–e498
e498 1.2 0.8
800 nm
0.8
(a)
(b) x=
0.8
400 nm
800 nm
hard powder
0.4
x=
1
0.0
0.0
x = 0.5
x=
-1.2
0.5
x = 0. x= 2 0
x = 0.2 x=0
-2
0
2
-0.2
H (MA/m)
-0.8 0.0
0.2
0.08
0.8 µ 0Mr µ 0Ms
0.04
0.00
0.0 0.0
0.2
0.4
0.6
0.8
Coercive field (MA/m)
µ0Ms; µ0Mr (T)
0.12
Hc = 0.0039exp(x/0.2922)
0.4
Fig. 3. Model magnet composed of powders with low- and high-anisotropy fields.
H (MA/m)
Fig. 1. (a) Hysteresis loops of different compositions. (b) Enlarged scale in the vicinity of coercive field.
1.2
soft powder
-0.4
1.0
Ba-ferrite volume fraction x
Magnetisation [T]
-0.8
800 nm
Averaged Static Field [kA/m]
-0.4
x=1 x = 0.8
µ 0 M (T)
µ0M (T)
0.4
1.0
100
Applied Field [kA/m] -300 -150
0
150
300 -300
-150
total magnet
hard powder 0
150
300
Applied Field [kA/m] -100 Field on Hard Powder Field on Soft Powder
(a)
soft powder
-1.0
(b)
Fig. 4. Averaged static magnetic field (a) and demagnetisation curves (b) for model magnet, e.g., with x ¼ 0:5:
Fig. 2. Coercive field, remanence and saturation magnetisation as function of composition.
maximum applied field H of 6:5 T: The magnetisation M as function of H in the vicinity of HB0 is smooth like that of a single phase material, but the remanence decreases linearly with decreasing x as shows Fig. 2. Ms decreases linearly with x; however, the coercive field decreases exponentially by adding the amorphous phase (see Fig. 2). These results suggest that in these compositions the exchange interaction has not been achieved and the smooth curves in the vicinity of remanence can have been caused by the magnetostatic interaction among powders. In order to investigate the origin of the these experimental results, computer simulations considering the effect of magnetostatic interaction on the demagnetisation curves were performed. Cubic model magnets composed of, in total, 512 isotropic Ba-ferrite and amorphous cubic-powders were assumed and the periodic boundary condition was used for the three directions. Each powder was subdivided into 64 grains. The powder and grain sizes considered in this model are shown in Fig. 3. M in a grain was assumed to interact with M in other grains by the exchange and magnetostatic interactions. The energy of magnetic anisotropy, magnetostatic interaction and H were taken into account, but an exchange interaction with grains in different powders was not assumed. The direction of M in each grain was determined by minimising the total energy for a given applied field.
Magnetostatic field created by div. M were calculated using magnetic charge and the fast Fourier transform. Details of the calculation method are reported elsewhere [5]. As can be seen in Fig. 4(a), the static field averaged for all the grains is zero. Thus, M of the soft powder couples with that of hard powder, and is prevented from M reversal when a negative field is applied. An opposite tendency was observed for the hard powder, and M in the hard powder was reversed easily when a negative field was applied. The demagnetisation curve for a model magnet is smooth despite of the existence of magnetically soft and hard powders (see Fig. 4(b)). As there exists no exchange interactions between powders, this smoothing can be attributed to the magnetostatic interaction between the powders.
References [1] T. Schrefl, H. Kronmuller, . J. Fidler, Phys. Rev. B 49 (1994) 6100. [2] E.F. Kneller, R. Hawig, IEEE Trans. Magn. 27 (1991) 3588. [3] P. Kerschl, Diplomarbeit, Institute for Solid State Physics, TU Vienna, 2000. [4] I. Endo, I. Otsuka, R. Okuno, A. Shintani, M. Yoshino, M. Yagi, IEEE Trans. Magn. 35 (1999) 3385. [5] H. Fukunaga, J. Kuma, Y. Kanai, IEEE Trans. Magn. 35 (1999) 3235.
Journal of Magnetism and Magnetic Materials 272–276 (2004) e497–e498
Effect of magnetostatic interaction on magnetic properties of mixed powders: computer simulation and experimental results R. Sato Turtellia,*, P. Kerschlb, H. Fukunagac, Y. Kawazoec, a . A. Shintanid, R. Grossinger Inst. fur Technische Universitat . Festkorperphysik, . . Wien, Wiedner Hauptstrasse 8-10, Vienna A-1040, Austria Leibnitz Institute for Solid State and Materials Research Dresden, IFW, P.O. Box 270116, Dresden D-01171, Germany c Department of Electrical Engineering and Electronics, Nagasaki University, Nagasaki 852-8521, Japan d Research and Development Center, Kubota Co., 1-1 Hama 1-Chome, Amagasaki, Hyogo 661-8567, Japan a
b
Abstract Magnets were prepared by mixing powders of Ba-ferrite BaFe12 O19 and soft magnetic amorphous ðFe0:97 Cr0:03 Þ76 ðSi0:5 B0:5 Þ22 C2 : The shape of the hysteresis loops of these magnets is typical of a single phase material. The saturation magnetisation increases and the remanence decreases proportionally to the mass quantity of the amorphous phase. Computer simulation on magnetostatic interaction among the powders was made using magnetic charge and the fast Fourier transformation. Excellent agreement between the measured and calculated loop shapes was found. r 2004 Elsevier B.V. All rights reserved. PACS: 75.50 Tt; 75.50.Ww; 75.60.Ej Keywords: Fine-particle system; Permanent magnet; Magnetisation curve; Hysteresis
Nanocomposite magnets composed of high coercivity hard magnetic phase and large magnetisation soft phase result in high-energy product if both phases are sufficiently exchange coupled [1]. The exchange coupling favours remanence enhancement [2]. Generally, the understanding of the magnetisation process in such heterogeneous systems is discussed neglecting magnetostatic interactions between soft and hard nanograins. For bulk nanocomposite magnets it is difficult to optimise the magnetic properties due to microstructural complexities. Mixed powder technique, however, can permit the preparation of artificial nano-disperse magnetic structures and facilitates to study fundamental magnetisation processes both experimentally and numerically. Therefore, in this work, magnets were prepared by mixing powders of hard and soft magnetic materials to study demagnetisation process in such *Corresponding author. Tel.: +43-1-58801-13150; fax: +431-58801-13199. E-mail address: [email protected] (R.S. Turtelli).
heterogeneous systems. Demagnetisation curves obtained from the computer simulation, based on the effect of magnetostatic interaction between the powders were compared with experimental results. Nanocrystalline hard magnetic Ba-ferrite BaFe12 O19 powder (grain size B30 nm; particle size = 80 mm; saturation polarisation Js ¼ m0 Ms ¼ 0:477 T and anisotropy constant Ku ¼ 70 kJ=m3 ) prepared by intensive milling technique [3] was mixed with ‘‘Kubota-powder’’ that is soft magnetic amorphous ðFe0:97 Cr0:03 Þ76 ðSi0:5 B0:5 Þ22 C2 powder (particle size o40 mm and Js ¼ 1:24 T) produced by spinning water atomisation process [4] by means of a high-energy ball mill for 10 min: The mixed powders were glued with a high-temperature glue in the cylinder form, obtaining a sample of 4.13 mm diameter and 5:93 mm length. Three compositions of the mixed powders ðBa ferriteÞx ðKubota powderÞ1x were prepared with a Ba-ferrite volume fraction of x ¼ 0:8; 0:5 and 0.2. Fig. 1 shows the hysteresis loops evolution with x at 300 K measured with SQUID magnetometer with a
0304-8853/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.1422
ARTICLE IN PRESS R.S. Turtelli et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) e497–e498
e498 1.2 0.8
800 nm
0.8
(a)
(b) x=
0.8
400 nm
800 nm
hard powder
0.4
x=
1
0.0
0.0
x = 0.5
x=
-1.2
0.5
x = 0. x= 2 0
x = 0.2 x=0
-2
0
2
-0.2
H (MA/m)
-0.8 0.0
0.2
0.08
0.8 µ 0Mr µ 0Ms
0.04
0.00
0.0 0.0
0.2
0.4
0.6
0.8
Coercive field (MA/m)
µ0Ms; µ0Mr (T)
0.12
Hc = 0.0039exp(x/0.2922)
0.4
Fig. 3. Model magnet composed of powders with low- and high-anisotropy fields.
H (MA/m)
Fig. 1. (a) Hysteresis loops of different compositions. (b) Enlarged scale in the vicinity of coercive field.
1.2
soft powder
-0.4
1.0
Ba-ferrite volume fraction x
Magnetisation [T]
-0.8
800 nm
Averaged Static Field [kA/m]
-0.4
x=1 x = 0.8
µ 0 M (T)
µ0M (T)
0.4
1.0
100
Applied Field [kA/m] -300 -150
0
150
300 -300
-150
total magnet
hard powder 0
150
300
Applied Field [kA/m] -100 Field on Hard Powder Field on Soft Powder
(a)
soft powder
-1.0
(b)
Fig. 4. Averaged static magnetic field (a) and demagnetisation curves (b) for model magnet, e.g., with x ¼ 0:5:
Fig. 2. Coercive field, remanence and saturation magnetisation as function of composition.
maximum applied field H of 6:5 T: The magnetisation M as function of H in the vicinity of HB0 is smooth like that of a single phase material, but the remanence decreases linearly with decreasing x as shows Fig. 2. Ms decreases linearly with x; however, the coercive field decreases exponentially by adding the amorphous phase (see Fig. 2). These results suggest that in these compositions the exchange interaction has not been achieved and the smooth curves in the vicinity of remanence can have been caused by the magnetostatic interaction among powders. In order to investigate the origin of the these experimental results, computer simulations considering the effect of magnetostatic interaction on the demagnetisation curves were performed. Cubic model magnets composed of, in total, 512 isotropic Ba-ferrite and amorphous cubic-powders were assumed and the periodic boundary condition was used for the three directions. Each powder was subdivided into 64 grains. The powder and grain sizes considered in this model are shown in Fig. 3. M in a grain was assumed to interact with M in other grains by the exchange and magnetostatic interactions. The energy of magnetic anisotropy, magnetostatic interaction and H were taken into account, but an exchange interaction with grains in different powders was not assumed. The direction of M in each grain was determined by minimising the total energy for a given applied field.
Magnetostatic field created by div. M were calculated using magnetic charge and the fast Fourier transform. Details of the calculation method are reported elsewhere [5]. As can be seen in Fig. 4(a), the static field averaged for all the grains is zero. Thus, M of the soft powder couples with that of hard powder, and is prevented from M reversal when a negative field is applied. An opposite tendency was observed for the hard powder, and M in the hard powder was reversed easily when a negative field was applied. The demagnetisation curve for a model magnet is smooth despite of the existence of magnetically soft and hard powders (see Fig. 4(b)). As there exists no exchange interactions between powders, this smoothing can be attributed to the magnetostatic interaction between the powders.
References [1] T. Schrefl, H. Kronmuller, . J. Fidler, Phys. Rev. B 49 (1994) 6100. [2] E.F. Kneller, R. Hawig, IEEE Trans. Magn. 27 (1991) 3588. [3] P. Kerschl, Diplomarbeit, Institute for Solid State Physics, TU Vienna, 2000. [4] I. Endo, I. Otsuka, R. Okuno, A. Shintani, M. Yoshino, M. Yagi, IEEE Trans. Magn. 35 (1999) 3385. [5] H. Fukunaga, J. Kuma, Y. Kanai, IEEE Trans. Magn. 35 (1999) 3235.