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Magnetocrystalline anisotropy and magnetostriction in ordered and disordered Fe–Ga single crystals
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 2060–2061
Magnetocrystalline anisotropy and magnetostriction in ordered and disordered Fe–Ga single crystals A. Kumagaia,*, A. Fujitaa, K. Fukamichia, K. Oikawab, R. Kainumaa, K. Ishidac a
Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 02, Sendai 980-8579, Japan b National Institute of Industrial Science and Technology, Sendai 983-8551, Japan c New Industry Creation Hatchery Center, Aoba-yama, Sendai 980-8579, Japan
Abstract On the basis of our new equilibrium phase diagram, Fe1xGax (x ¼ 0:2420:25) single crystals with the A2, B2 and D03 structures have been prepared in order to investigate the magnetocrystalline anisotropies and magnetostrictions. The [1 1 0] direction was identified as a hard axis and the anisotropy coefficients were jK2 j > K1 > 0; 0 > K2 in the A2 and B2 structures. Lowering the symmetry of the atomic arrangement, the magnetostriction of the [1 0 0] direction becomes larger. These results agree with qualitatively the theoretical calculations. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Gw; 75.80.+q Keywords: Equilibrium phase diagram; Fe–Ga; Magnetocrystalline anisotropy; Magnetostriction
A large magnetostriction in Fe1xGax has been observed around x¼ 0:19 [1]. The magnetostriction of Fe–Ga alloys with x > 0:19 is decreased due to the change in the crystal structure from an A2-disorder to a D03-order phase. Recently, a new equilibrium phase diagram for Fe–Ga system has been demonstrated ð0:10pxp0:35Þ [2]. Strain dependence of magnetocrystalline anisotropy (MCA) energies of Fe3Ga have been calculated by the first-principles calculations using the full potential linearized augmented plane wave method [3]. The spin–orbit interaction occurs between two nondegenerated dxz and dyz states in the minority spin band of Fe d-electrons in a B2 structure resulting in a positive magnetostriction. For the D03 structure, the dxz and dyz states in the minority spin band remain to degenerate because of high symmetry, while the spin– orbit interaction between the dxz and dyz states in the majority spin band brings about a negative magnetostriction. *Corresponding author. Tel.: +81-22-217-7317; fax: +8122-217-7316. E-mail address: [email protected] (A. Kumagai).
In the present paper, Fe1xGax (x ¼ 0:2420:25) single crystals with the A2, B2 and D03 structures were prepared on the basis of a new equilibrium phase diagram and the changes in the magnetic anisotropies and magnetostrictions were discussed by taking the symmetry change in these crystal structures into consideration. The Fe–Ga single crystals were prepared by an optical floating-zone method, and annealed for homogenization at 1273 K for 60 h. The Ga compositions of these phases were determined to be 24–25 at% by an electron probe micro-analyzer method. The crystal structures of D03, B2 and A2 were confirmed after quenching from 923, 963 and 1273 K, respectively. The crystallographic directions were analyzed by electron backscattering pattern and back-reflection Laue diffraction. The magnetization curves at T ¼ 10 K for these specimens with the A2, B2 and D03 structures are shown in Fig. 1. The saturation magnetic field becomes highest in the [1 1 0] direction for the A2 and B2 structures. On the other hand, the difference in the saturation magnetic field was scarcely observed among the [1 0 0], [1 1 0] and [1 1 1] directions for the specimen with the D03 structure. The difference in energies due to
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.827
ARTICLE IN PRESS A. Kumagai et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 2060–2061 200
200
150
150
100 A2
[110 ]
A2
[110]
[111 ]
50
[111]
0
0
150
150
B2
-6
λ// (10 )
Magnetization (emu / g)
50
[100 ]
100
[100]
2061
100 50
100 50
B2
0
0
150
150
D0
3
100
100 50
50
D03
0
0 0
10
20
30
40
50
0
10
20
30
40
50
Magnetic Field (50 kOe)
Magnetic Field (50 kOe)
Fig. 1. Magnetization curves at T ¼ 10 K for the specimens with the A2, B2 and D03 structures.
the rotation of the directions of magnetization is expressed by K1 ð1Þ E1 1 0 E1 0 0 ¼ ; 4 K1 K2 þ ; ð2Þ 3 27 where K1 and K2 are the anisotropy constants of uniaxial and in-plane components, respectively. For the A2 and B2 structures, the value corresponding to the left-hand side of Eq. (1) is positive because the magnetization for the [1 1 0] direction is harder to be saturated, compared with that for the other two directions. Furthermore, E1 1 1 E1 0 0 is almost zero in these structures as seen from the figures. As a result, we obtain the following relations: E1 1 1 E1 0 0 ¼
jK2 j > K1 > 0;
0 > K2
ð3Þ
These relations are qualitatively in accord with the magnetocrystalline anisotropy (MCA) energy EMCA obtained from the first principles band calculations [3]. From the strain dependence of EMCA ; the magnetostriction for these structures has been also calculated. According to the calculated results, it is expected that the magnetostriction in the B2 structure is larger than that in the D03 structure. This difference is attributed to the symmetry change of the atomic arrangements. Namely, the lower symmetry of the atomic arrangement, the stronger the spin–orbit interac-
Fig. 2. The magnetostrictions lJ measured parallel to the magnetic field at T ¼ 300 K for the specimens with the A2, B2 and D03 structures.
tions in the minority spin band due to nondegenerated dxz and dyz states, resulting in a larger positive magnetostriction. Consequently, the magnetostriction in the A2 structure is expected to be larger than that in the B2 structure. Fig. 2 shows the linear magnetostrictions lJ measured parallel to the magnetic field direction at T ¼ 300 K for the specimens with the A2, B2 and D03 structures. The magnetostriction of the [1 0 0] direction in both the A2 and B2 structures is larger than that of other two directions. It should be noted that the magnetostriction of [1 0 0] in the A2 structure is larger than that in the B2 structure. On the other hand, only a slight difference in the magnetostrictions among three directions is observed in the D03 structure. Accordingly, it is confirmed that lJðA2Þ > lJðB2Þ > lJðD03Þ in harmony with the theoretical calculations [3].
References [1] A.E. Clark, M. Wun-Fogle, J.B. Restorff, T.A. Lograsso, Proceedings of the Pacific Rim International Conference on Advanced Material and Proceedings (PRICM-4), Honolulu, Hawaii, December, 11–15, 2001, p. 7. [2] O. Ikeda, R. Kainuma, I. Ohnuma, K. Fukamichi, K. Ishida, J. Alloys Comp. 347 (2002) 198. [3] R. Wu, J. Appl. Phys. 91 (2002) 73.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 2060–2061
Magnetocrystalline anisotropy and magnetostriction in ordered and disordered Fe–Ga single crystals A. Kumagaia,*, A. Fujitaa, K. Fukamichia, K. Oikawab, R. Kainumaa, K. Ishidac a
Department of Materials Science, Graduate School of Engineering, Tohoku University, Aoba-yama 02, Sendai 980-8579, Japan b National Institute of Industrial Science and Technology, Sendai 983-8551, Japan c New Industry Creation Hatchery Center, Aoba-yama, Sendai 980-8579, Japan
Abstract On the basis of our new equilibrium phase diagram, Fe1xGax (x ¼ 0:2420:25) single crystals with the A2, B2 and D03 structures have been prepared in order to investigate the magnetocrystalline anisotropies and magnetostrictions. The [1 1 0] direction was identified as a hard axis and the anisotropy coefficients were jK2 j > K1 > 0; 0 > K2 in the A2 and B2 structures. Lowering the symmetry of the atomic arrangement, the magnetostriction of the [1 0 0] direction becomes larger. These results agree with qualitatively the theoretical calculations. r 2003 Elsevier B.V. All rights reserved. PACS: 75.30.Gw; 75.80.+q Keywords: Equilibrium phase diagram; Fe–Ga; Magnetocrystalline anisotropy; Magnetostriction
A large magnetostriction in Fe1xGax has been observed around x¼ 0:19 [1]. The magnetostriction of Fe–Ga alloys with x > 0:19 is decreased due to the change in the crystal structure from an A2-disorder to a D03-order phase. Recently, a new equilibrium phase diagram for Fe–Ga system has been demonstrated ð0:10pxp0:35Þ [2]. Strain dependence of magnetocrystalline anisotropy (MCA) energies of Fe3Ga have been calculated by the first-principles calculations using the full potential linearized augmented plane wave method [3]. The spin–orbit interaction occurs between two nondegenerated dxz and dyz states in the minority spin band of Fe d-electrons in a B2 structure resulting in a positive magnetostriction. For the D03 structure, the dxz and dyz states in the minority spin band remain to degenerate because of high symmetry, while the spin– orbit interaction between the dxz and dyz states in the majority spin band brings about a negative magnetostriction. *Corresponding author. Tel.: +81-22-217-7317; fax: +8122-217-7316. E-mail address: [email protected] (A. Kumagai).
In the present paper, Fe1xGax (x ¼ 0:2420:25) single crystals with the A2, B2 and D03 structures were prepared on the basis of a new equilibrium phase diagram and the changes in the magnetic anisotropies and magnetostrictions were discussed by taking the symmetry change in these crystal structures into consideration. The Fe–Ga single crystals were prepared by an optical floating-zone method, and annealed for homogenization at 1273 K for 60 h. The Ga compositions of these phases were determined to be 24–25 at% by an electron probe micro-analyzer method. The crystal structures of D03, B2 and A2 were confirmed after quenching from 923, 963 and 1273 K, respectively. The crystallographic directions were analyzed by electron backscattering pattern and back-reflection Laue diffraction. The magnetization curves at T ¼ 10 K for these specimens with the A2, B2 and D03 structures are shown in Fig. 1. The saturation magnetic field becomes highest in the [1 1 0] direction for the A2 and B2 structures. On the other hand, the difference in the saturation magnetic field was scarcely observed among the [1 0 0], [1 1 0] and [1 1 1] directions for the specimen with the D03 structure. The difference in energies due to
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.827
ARTICLE IN PRESS A. Kumagai et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 2060–2061 200
200
150
150
100 A2
[110 ]
A2
[110]
[111 ]
50
[111]
0
0
150
150
B2
-6
λ// (10 )
Magnetization (emu / g)
50
[100 ]
100
[100]
2061
100 50
100 50
B2
0
0
150
150
D0
3
100
100 50
50
D03
0
0 0
10
20
30
40
50
0
10
20
30
40
50
Magnetic Field (50 kOe)
Magnetic Field (50 kOe)
Fig. 1. Magnetization curves at T ¼ 10 K for the specimens with the A2, B2 and D03 structures.
the rotation of the directions of magnetization is expressed by K1 ð1Þ E1 1 0 E1 0 0 ¼ ; 4 K1 K2 þ ; ð2Þ 3 27 where K1 and K2 are the anisotropy constants of uniaxial and in-plane components, respectively. For the A2 and B2 structures, the value corresponding to the left-hand side of Eq. (1) is positive because the magnetization for the [1 1 0] direction is harder to be saturated, compared with that for the other two directions. Furthermore, E1 1 1 E1 0 0 is almost zero in these structures as seen from the figures. As a result, we obtain the following relations: E1 1 1 E1 0 0 ¼
jK2 j > K1 > 0;
0 > K2
ð3Þ
These relations are qualitatively in accord with the magnetocrystalline anisotropy (MCA) energy EMCA obtained from the first principles band calculations [3]. From the strain dependence of EMCA ; the magnetostriction for these structures has been also calculated. According to the calculated results, it is expected that the magnetostriction in the B2 structure is larger than that in the D03 structure. This difference is attributed to the symmetry change of the atomic arrangements. Namely, the lower symmetry of the atomic arrangement, the stronger the spin–orbit interac-
Fig. 2. The magnetostrictions lJ measured parallel to the magnetic field at T ¼ 300 K for the specimens with the A2, B2 and D03 structures.
tions in the minority spin band due to nondegenerated dxz and dyz states, resulting in a larger positive magnetostriction. Consequently, the magnetostriction in the A2 structure is expected to be larger than that in the B2 structure. Fig. 2 shows the linear magnetostrictions lJ measured parallel to the magnetic field direction at T ¼ 300 K for the specimens with the A2, B2 and D03 structures. The magnetostriction of the [1 0 0] direction in both the A2 and B2 structures is larger than that of other two directions. It should be noted that the magnetostriction of [1 0 0] in the A2 structure is larger than that in the B2 structure. On the other hand, only a slight difference in the magnetostrictions among three directions is observed in the D03 structure. Accordingly, it is confirmed that lJðA2Þ > lJðB2Þ > lJðD03Þ in harmony with the theoretical calculations [3].
References [1] A.E. Clark, M. Wun-Fogle, J.B. Restorff, T.A. Lograsso, Proceedings of the Pacific Rim International Conference on Advanced Material and Proceedings (PRICM-4), Honolulu, Hawaii, December, 11–15, 2001, p. 7. [2] O. Ikeda, R. Kainuma, I. Ohnuma, K. Fukamichi, K. Ishida, J. Alloys Comp. 347 (2002) 198. [3] R. Wu, J. Appl. Phys. 91 (2002) 73.