- Email: [email protected]
Investigation of helical magnetic structure in Co-rich amorphous microwires
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 316 (2007) 332–336 www.elsevier.com/locate/jmmm
Investigation of helical magnetic structure in Co-rich amorphous microwires A. Chizhika,, C. Garciaa, A. Zhukova, P. Gawronskib, K. Kulakowskib, J. Gonzaleza, J.M. Blancoc a Departamento Fı´sica de Materiales, Facultad de Quı´mica, UPV 1072, 20080 San Sebastia´n, Spain Faculty of Physics & Applied Computer Science, AGH University of Science & Technology, 30-059 Cracow, Poland c Departamento Fı´sica Aplicada I, EUPDS, UPV/EHU, Plaza Europa, 1, 20018 San Sebastia´n, Spain
b
Available online 12 March 2007
Abstract The magnetization reversal process in Co-rich glass-covered amorphous microwires has been studied in presence of the torsion stress. The experiments have been performed using the transverse magneto-optical Kerr effect in crossed axial and circular magnetic fields. The influence of the torsion stress on the surface domain structure has been investigated. The angle of the surface helical structure has been determined based on the analysis of the stress-induced transformation of the Kerr hysteresis loops. The dependence of the angle of the helical structure on the value of the torsion stress has been obtained. r 2007 Elsevier B.V. All rights reserved. PACS: 75.50.Kj; 75.60.Ch; 75.60.Ej Keywords: Amorphous microwire; Kerr effect; Hysteresis loop
1. Introduction The glass-covered amorphous microwires are recognized to be among the most interesting materials as magnetic sensing elements, owing to their unique magnetic properties related to the magnetic bistability associated with the peculiar magnetization reversal process and giant magnetoimpedance (GMI) effect [1–5]. The interest to the GMI effect is related with the high sensitivity of the impedance to an applied magnetic field. The discovery of the torsion impedance effects [6] showing high sensitivity of the impedance to the applied torsion stress attracted the attention of the researchers to the investigation of the helical magnetic structure in amorphous wires [7–10]. In spite of the existence of a number of papers devoted to the behavior of the helical structure, the experimental investigations of the surface helical structure in amorphous wires were not performed practically up to now. Additionally, taking into account that the GMI effect is mainly a surface Corresponding author. Tel.: +34 943 018611; fax: 34 943 017130.
E-mail address: [email protected] (A. Chizhik). 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.03.007
effect, the investigation of the helical magnetic structure in the surface area of the wire takes special importance. Particularly, interest to the study of the surface helical structure is determined by the fact that the glass coating sheath introduces additional stress in the surface area of the wire due to the difference between the thermal expansion coefficients of the glass coating and the metallic nucleus. The application of the magneto-optical Kerr effect for the study of amorphous microwires demonstrated the advantages of this method for the investigation of magnetization reversal in the surface of non-plane samples. In this article, we present the relevant results on the magneto-optical study of the magnetization reversal in the surface area of a negative magnetorestrictive Co-rich amorphous microwires in the presence of torsion stresses.
2. Experimental details Glass-covered amorphous microwires exhibiting nearly zero negative magnetostriction, of nominal composition Co69.5Fe3.9Ni1B12.8Si10.8Mo2 (metallic nucleus diameter
ARTICLE IN PRESS A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 332–336
19 mm, glass coating thickness 2.6 mm) supplied by TAMAG Iberica S.L., were obtained by the Taylor–Ulitovski method [11]. The experiments have been performed using the transverse magneto-optical Kerr effect in axial and circular magnetic fields. The circular magnetic field (HCIRC) has been produced by an electric current (60 Hz) flowing through the microwire. An axial magnetic field (HAX) has been produced by a pair of Helmholtz coils. A polarized light from a He–Ne laser was reflected from the surface of the microwire to the detector. The incident light was parallel polarized to the plane of incidence. The beam diameter was of 0.8 mm. The intensity of the reflected light is proportional to the magnetization oriented perpendicularly to the plane of the light, i.e., to the circular projection of the magnetization in the surface area of the microwire. A torsion stress up to 40 p rad m1 has been applied during the experiments. 3. Experimental results and discussion Fig. 1(a)–(c) presents the experimental transverse Kerr effect dependencies on the AC axial magnetic field with the torsion stress as a parameter. The increase of the torsion stress causes the transformation of the surface hysteresis,
333
the increase of the jump of Kerr effect signal, i.e., the increase of the jump of the circular magnetization DMCIRC and the decrease of the value of the coercive field. Fig. 2 presents the transverse Kerr effect dependencies on the ac electric current flowing along the wires in the presence of a DC axial bias magnetic field and with the torsion stress as a parameter. When the DC axial magnetic field is absent (Fig. 2(a), (d), (i)), the shape of the circular hysteresis loop is rectangular. It is related to the circular magnetic bistability in the form of large Barkhausen jump between two states with opposite direction of the surface circular magnetization. There are three different types of behavior depending on the value of the torsion stress. When the torsion stress is absent (Fig. 2(a)–(c)), the application of the DC axial magnetic field causes the symmetrical change of the switching field, HSW (associated with the switching current). The value of the jump of the Kerr intensity (circular magnetization) also decreases with DC axial magnetic field. The shift of the loop is not observed. For the torsion stress of 20 p rad m1 (Fig. 2(d)–(f)), a bias field-induced shift of the loop along the ‘‘X’’-axis takes place. The jump of the Kerr intensity decreases with bias field and disappears when the bias field is high enough. For the torsion stress of 40 p rad m1 (Fig. 2(i)–(k)), we can see the field-induced decrease of the switching field and the shift of the loop. The main feature of this experiment is the following. The shape of the loop remains rectangular in the presence of the bias field up to the abrupt disappearance of the hysteresis loop. The shape of the loops presented in Fig. 2(j) and (k) is related to existence of the metastable state with the magnetization tilted from the circular direction, which was discussed in our paper [12]. The calculation of the hysteresis loops has been performed taking into account the existence of a helical magnetic anisotropy in the wire. The expression of the energy of the system has the form U ¼ K U cos2 ðy jÞ h m ¼ K U cos2 ðy jÞ haxial m cosðyÞ,
Fig. 1. (a)–(c) Experimental transverse Kerr effect dependencies on axial magnetic field for different values of torsion stress. (d)–(f) Calculated dependences of circular magnetization on normalized axial magnetic field for three angles of the anisotropy direction j.
ð1Þ
where haxial is the applied magnetic field, KU is the uniaxial anisotropy constant, m is the saturation magnetization, j is the angle between the anisotropy axis and the wire axis, and y is the angle between the magnetic moment and the wire axis. The result of the numerical analysis of Eq. (1) is presented in Fig. 3. There is the calculated dependence of the jump of the circular magnetization DMCIRC on the angle of helical anisotropy. Also, the series of the surface hysteresis curves for different values of the helical anisotropy angle (Fig. 1(d)–(f)) has been obtained as a result of the calculation. For the angles close to 901, the magnetization reversal is determined mainly by a fluent rotation of the magnetization and this rotation continues after the moment when the magnetization reaches the exact circular direction. For the angles close to 601, the jump of
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Fig. 2. Transverse Kerr effect dependencies on circular magnetic field for different values of torsion stress with the axial bias field as a parameter. (a)–(c) Torsion stress 0 p rad m1; (d)–(f) torsion stress 20 p rad m1, (i)–(k) torsion stress 40 p rad m1.
Fig. 3. Calculated dependence of the jump of the circular magnetization DMCIRC on the angle of helical anisotropy j.
the magnetization occurs at the moment when the direction of the magnetization is close to the circular magnetization. Because of that, the value of the DMCIRC is large for these angles. The Kerr effect experimental results and the results of the calculation have been compared taking into account the value of the jump of the circular magnetization DMCIRC. This jump is related to the overcoming of the helical hard axis. We can conclude that the angle of the helical anisotropy in the surface of the studied microwire is 881 for the torsion
stress of 0 p rad m1, 841 for the torsion stress of 20 p rad m–1, and 561 for the torsion stress of 40 p rad m1. The results of the comparison are presented in Figs. 1(d)–(f) and 4. The experimental results presented in Fig. 2 are in agreement with the above-performed analysis of the magnetic structure in the surface area of the studied microwire. The observed shift of the hysteresis loops means that the sensitivity of the studied system to the DC axial bias field grows with the increase of the inclination of the helical anisotropy from 901.
ARTICLE IN PRESS A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 332–336
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Fig. 5. Calculated dependencies of circular magnetization on normalized circular axial magnetic in the presence of the normalized axial bias field.
Fig. 4. Helical anisotropy angle dependence on torsion stresses obtained from the comparison of experimental and calculated hysteresis loops.
The shape of the hysteresis loop presented in Fig. 2(c) means that the DC axial field inclines the magnetization toward the axial direction in the surface area of the microwire. Therefore, the jump happens between the conditions with the inclined magnetization. The shift of the hysteresis loop reflects the action of the bias field on the nucleation process of the circular domains. For the helical anisotropy inclined enough from the circular direction, the DC axial field favors and delays the nucleation of the domains with different directions of the magnetization. This effect becomes stronger as the inclination increases. Fig. 5 presents the calculated dependences of circular magnetization on normalized circular axial magnetic field for the angle of the anisotropy direction j ¼ 561 in the presence of the normalized axial bias field. This figure reflects the main features which were observed in the experiment (Fig. 2): the shift of the loop along the ‘‘X’’-axis and the field-induced decrease of the switching field. For the torsion stress of 40 p rad m1, the strong rectangular shape of the hysteresis is observed up to the abrupt disappearance along with the shift of the loop. In the presence of the DC axial field, the magnetization reversal occurs in the form of large Barkhausen jump between two states with helical direction of the magnetization. For the torsion stress of 40 p rad m1, the appearance of the hysteresis loop has a threshold character. The observed behavior could be considered as the confirmation of the torsion stress-induced growth of the value of the helical anisotropy in the surface area of the studied microwire. For the relatively weak helical anisotropy (Fig. 2(c) and (f)), the fluent rotation of the magnetization takes place along with the jump of the magnetization, while for the strong helical anisotropy the rotation is lacking and only the sharp jump of the surface magnetization is observed (Fig. 2(k)).
The results presented in the Fig. 4 are in the frame of the above performed analysis: the inclination of the helical anisotropy from the circular direction induced by the strong torsion stress does not exceed the value of 451, because as it was shown in Ref. [13], the torsion stress induces an easy axis at the angle of p/4 with respect to the circumferential direction. 4. Conclusion The magnetization reversal has been studied for the first time in the surface area of Co-rich amorphous glasscovered microwire in the presence of the torsion stress. The torsion stress induces strong inclination of the direction of the helical anisotropy from the circular direction toward the axial one. It was experimentally confirmed, as predicted, that this torsion stress-induced inclination does not exceed the value of 451.This inclination along with the growth of the value of the helical anisotropy is the key phenomenon determining the main mechanism of the surface magnetization reversal. As the helical anisotropy increases, this mechanism strongly changes. The value of the jump of the circular magnetization DMCIRC for different vales of the torsion stress was obtained experimentally, and also, the calculated dependence of the jump of the circular magnetization DMCIRC on the angle of helical anisotropy. Based on the numerical analysis of the obtained experimental results, the dependence of the angle of the helical anisotropy on the torsion stress has been obtained for the first time in amorphous wires. Acknowledgments The authors acknowledge MEyC for the financial support under project PCI2005-A7-0230. References [1] L.V. Panina, K. Mohri, Appl. Phys. Lett. 65 (1994) 1189. [2] R.S. Beach, A.E. Bertowitz, Appl. Phys. Lett. 64 (1994) 3652. [3] Y. Honkura, J. Magn. Magn. Mater. 249 (2002).
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[4] M. Han, D.F. Liang, L.J. Deng, J. Mater. Sci. (2005) 5573. [5] D.C. Jiles, Acta Mater. 51 (2003) 5907. [6] J.M. Blanco, A. Zhukov, J. Gonzalez, J. Magn. Magn. Mater. 196 (1999) 377. [7] C. Gomez-Polo, M. Vazquez, M. Knobel, Appl. Phys. Lett. 78 (2001) 246. [8] C.G. Kim, S.S. Yoon, M. Vazquez, J. Magn. Magn. Mater. 223 (2001) L199.
[9] D.P. Makhnovskiy, L.V. Panina, D.J. Mapps, Phys. Rev. B 63 (2001) 144424. [10] I. Betancourt, R. Valenzuela, Appl. Phys. Lett. 83 (2003) 2022. [11] M. Vazquez, A. Zhukov, J. Magn. Magn. Mater. 160 (1996) 223. [12] A. Chizhik, J. Gonzalez, A. Zhukov, J.M. Blanco, J. Phys. D 36 (2003) 419. [13] P. Ciureanu, I. Khalil, L.G.C. Melo, P. Rudkowski, A. Yelon, J. Magn. Magn. Mater. 249 (2002) 305.
Journal of Magnetism and Magnetic Materials 316 (2007) 332–336 www.elsevier.com/locate/jmmm
Investigation of helical magnetic structure in Co-rich amorphous microwires A. Chizhika,, C. Garciaa, A. Zhukova, P. Gawronskib, K. Kulakowskib, J. Gonzaleza, J.M. Blancoc a Departamento Fı´sica de Materiales, Facultad de Quı´mica, UPV 1072, 20080 San Sebastia´n, Spain Faculty of Physics & Applied Computer Science, AGH University of Science & Technology, 30-059 Cracow, Poland c Departamento Fı´sica Aplicada I, EUPDS, UPV/EHU, Plaza Europa, 1, 20018 San Sebastia´n, Spain
b
Available online 12 March 2007
Abstract The magnetization reversal process in Co-rich glass-covered amorphous microwires has been studied in presence of the torsion stress. The experiments have been performed using the transverse magneto-optical Kerr effect in crossed axial and circular magnetic fields. The influence of the torsion stress on the surface domain structure has been investigated. The angle of the surface helical structure has been determined based on the analysis of the stress-induced transformation of the Kerr hysteresis loops. The dependence of the angle of the helical structure on the value of the torsion stress has been obtained. r 2007 Elsevier B.V. All rights reserved. PACS: 75.50.Kj; 75.60.Ch; 75.60.Ej Keywords: Amorphous microwire; Kerr effect; Hysteresis loop
1. Introduction The glass-covered amorphous microwires are recognized to be among the most interesting materials as magnetic sensing elements, owing to their unique magnetic properties related to the magnetic bistability associated with the peculiar magnetization reversal process and giant magnetoimpedance (GMI) effect [1–5]. The interest to the GMI effect is related with the high sensitivity of the impedance to an applied magnetic field. The discovery of the torsion impedance effects [6] showing high sensitivity of the impedance to the applied torsion stress attracted the attention of the researchers to the investigation of the helical magnetic structure in amorphous wires [7–10]. In spite of the existence of a number of papers devoted to the behavior of the helical structure, the experimental investigations of the surface helical structure in amorphous wires were not performed practically up to now. Additionally, taking into account that the GMI effect is mainly a surface Corresponding author. Tel.: +34 943 018611; fax: 34 943 017130.
E-mail address: [email protected] (A. Chizhik). 0304-8853/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2007.03.007
effect, the investigation of the helical magnetic structure in the surface area of the wire takes special importance. Particularly, interest to the study of the surface helical structure is determined by the fact that the glass coating sheath introduces additional stress in the surface area of the wire due to the difference between the thermal expansion coefficients of the glass coating and the metallic nucleus. The application of the magneto-optical Kerr effect for the study of amorphous microwires demonstrated the advantages of this method for the investigation of magnetization reversal in the surface of non-plane samples. In this article, we present the relevant results on the magneto-optical study of the magnetization reversal in the surface area of a negative magnetorestrictive Co-rich amorphous microwires in the presence of torsion stresses.
2. Experimental details Glass-covered amorphous microwires exhibiting nearly zero negative magnetostriction, of nominal composition Co69.5Fe3.9Ni1B12.8Si10.8Mo2 (metallic nucleus diameter
ARTICLE IN PRESS A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 332–336
19 mm, glass coating thickness 2.6 mm) supplied by TAMAG Iberica S.L., were obtained by the Taylor–Ulitovski method [11]. The experiments have been performed using the transverse magneto-optical Kerr effect in axial and circular magnetic fields. The circular magnetic field (HCIRC) has been produced by an electric current (60 Hz) flowing through the microwire. An axial magnetic field (HAX) has been produced by a pair of Helmholtz coils. A polarized light from a He–Ne laser was reflected from the surface of the microwire to the detector. The incident light was parallel polarized to the plane of incidence. The beam diameter was of 0.8 mm. The intensity of the reflected light is proportional to the magnetization oriented perpendicularly to the plane of the light, i.e., to the circular projection of the magnetization in the surface area of the microwire. A torsion stress up to 40 p rad m1 has been applied during the experiments. 3. Experimental results and discussion Fig. 1(a)–(c) presents the experimental transverse Kerr effect dependencies on the AC axial magnetic field with the torsion stress as a parameter. The increase of the torsion stress causes the transformation of the surface hysteresis,
333
the increase of the jump of Kerr effect signal, i.e., the increase of the jump of the circular magnetization DMCIRC and the decrease of the value of the coercive field. Fig. 2 presents the transverse Kerr effect dependencies on the ac electric current flowing along the wires in the presence of a DC axial bias magnetic field and with the torsion stress as a parameter. When the DC axial magnetic field is absent (Fig. 2(a), (d), (i)), the shape of the circular hysteresis loop is rectangular. It is related to the circular magnetic bistability in the form of large Barkhausen jump between two states with opposite direction of the surface circular magnetization. There are three different types of behavior depending on the value of the torsion stress. When the torsion stress is absent (Fig. 2(a)–(c)), the application of the DC axial magnetic field causes the symmetrical change of the switching field, HSW (associated with the switching current). The value of the jump of the Kerr intensity (circular magnetization) also decreases with DC axial magnetic field. The shift of the loop is not observed. For the torsion stress of 20 p rad m1 (Fig. 2(d)–(f)), a bias field-induced shift of the loop along the ‘‘X’’-axis takes place. The jump of the Kerr intensity decreases with bias field and disappears when the bias field is high enough. For the torsion stress of 40 p rad m1 (Fig. 2(i)–(k)), we can see the field-induced decrease of the switching field and the shift of the loop. The main feature of this experiment is the following. The shape of the loop remains rectangular in the presence of the bias field up to the abrupt disappearance of the hysteresis loop. The shape of the loops presented in Fig. 2(j) and (k) is related to existence of the metastable state with the magnetization tilted from the circular direction, which was discussed in our paper [12]. The calculation of the hysteresis loops has been performed taking into account the existence of a helical magnetic anisotropy in the wire. The expression of the energy of the system has the form U ¼ K U cos2 ðy jÞ h m ¼ K U cos2 ðy jÞ haxial m cosðyÞ,
Fig. 1. (a)–(c) Experimental transverse Kerr effect dependencies on axial magnetic field for different values of torsion stress. (d)–(f) Calculated dependences of circular magnetization on normalized axial magnetic field for three angles of the anisotropy direction j.
ð1Þ
where haxial is the applied magnetic field, KU is the uniaxial anisotropy constant, m is the saturation magnetization, j is the angle between the anisotropy axis and the wire axis, and y is the angle between the magnetic moment and the wire axis. The result of the numerical analysis of Eq. (1) is presented in Fig. 3. There is the calculated dependence of the jump of the circular magnetization DMCIRC on the angle of helical anisotropy. Also, the series of the surface hysteresis curves for different values of the helical anisotropy angle (Fig. 1(d)–(f)) has been obtained as a result of the calculation. For the angles close to 901, the magnetization reversal is determined mainly by a fluent rotation of the magnetization and this rotation continues after the moment when the magnetization reaches the exact circular direction. For the angles close to 601, the jump of
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Fig. 2. Transverse Kerr effect dependencies on circular magnetic field for different values of torsion stress with the axial bias field as a parameter. (a)–(c) Torsion stress 0 p rad m1; (d)–(f) torsion stress 20 p rad m1, (i)–(k) torsion stress 40 p rad m1.
Fig. 3. Calculated dependence of the jump of the circular magnetization DMCIRC on the angle of helical anisotropy j.
the magnetization occurs at the moment when the direction of the magnetization is close to the circular magnetization. Because of that, the value of the DMCIRC is large for these angles. The Kerr effect experimental results and the results of the calculation have been compared taking into account the value of the jump of the circular magnetization DMCIRC. This jump is related to the overcoming of the helical hard axis. We can conclude that the angle of the helical anisotropy in the surface of the studied microwire is 881 for the torsion
stress of 0 p rad m1, 841 for the torsion stress of 20 p rad m–1, and 561 for the torsion stress of 40 p rad m1. The results of the comparison are presented in Figs. 1(d)–(f) and 4. The experimental results presented in Fig. 2 are in agreement with the above-performed analysis of the magnetic structure in the surface area of the studied microwire. The observed shift of the hysteresis loops means that the sensitivity of the studied system to the DC axial bias field grows with the increase of the inclination of the helical anisotropy from 901.
ARTICLE IN PRESS A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 316 (2007) 332–336
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Fig. 5. Calculated dependencies of circular magnetization on normalized circular axial magnetic in the presence of the normalized axial bias field.
Fig. 4. Helical anisotropy angle dependence on torsion stresses obtained from the comparison of experimental and calculated hysteresis loops.
The shape of the hysteresis loop presented in Fig. 2(c) means that the DC axial field inclines the magnetization toward the axial direction in the surface area of the microwire. Therefore, the jump happens between the conditions with the inclined magnetization. The shift of the hysteresis loop reflects the action of the bias field on the nucleation process of the circular domains. For the helical anisotropy inclined enough from the circular direction, the DC axial field favors and delays the nucleation of the domains with different directions of the magnetization. This effect becomes stronger as the inclination increases. Fig. 5 presents the calculated dependences of circular magnetization on normalized circular axial magnetic field for the angle of the anisotropy direction j ¼ 561 in the presence of the normalized axial bias field. This figure reflects the main features which were observed in the experiment (Fig. 2): the shift of the loop along the ‘‘X’’-axis and the field-induced decrease of the switching field. For the torsion stress of 40 p rad m1, the strong rectangular shape of the hysteresis is observed up to the abrupt disappearance along with the shift of the loop. In the presence of the DC axial field, the magnetization reversal occurs in the form of large Barkhausen jump between two states with helical direction of the magnetization. For the torsion stress of 40 p rad m1, the appearance of the hysteresis loop has a threshold character. The observed behavior could be considered as the confirmation of the torsion stress-induced growth of the value of the helical anisotropy in the surface area of the studied microwire. For the relatively weak helical anisotropy (Fig. 2(c) and (f)), the fluent rotation of the magnetization takes place along with the jump of the magnetization, while for the strong helical anisotropy the rotation is lacking and only the sharp jump of the surface magnetization is observed (Fig. 2(k)).
The results presented in the Fig. 4 are in the frame of the above performed analysis: the inclination of the helical anisotropy from the circular direction induced by the strong torsion stress does not exceed the value of 451, because as it was shown in Ref. [13], the torsion stress induces an easy axis at the angle of p/4 with respect to the circumferential direction. 4. Conclusion The magnetization reversal has been studied for the first time in the surface area of Co-rich amorphous glasscovered microwire in the presence of the torsion stress. The torsion stress induces strong inclination of the direction of the helical anisotropy from the circular direction toward the axial one. It was experimentally confirmed, as predicted, that this torsion stress-induced inclination does not exceed the value of 451.This inclination along with the growth of the value of the helical anisotropy is the key phenomenon determining the main mechanism of the surface magnetization reversal. As the helical anisotropy increases, this mechanism strongly changes. The value of the jump of the circular magnetization DMCIRC for different vales of the torsion stress was obtained experimentally, and also, the calculated dependence of the jump of the circular magnetization DMCIRC on the angle of helical anisotropy. Based on the numerical analysis of the obtained experimental results, the dependence of the angle of the helical anisotropy on the torsion stress has been obtained for the first time in amorphous wires. Acknowledgments The authors acknowledge MEyC for the financial support under project PCI2005-A7-0230. References [1] L.V. Panina, K. Mohri, Appl. Phys. Lett. 65 (1994) 1189. [2] R.S. Beach, A.E. Bertowitz, Appl. Phys. Lett. 64 (1994) 3652. [3] Y. Honkura, J. Magn. Magn. Mater. 249 (2002).
ARTICLE IN PRESS 336
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[4] M. Han, D.F. Liang, L.J. Deng, J. Mater. Sci. (2005) 5573. [5] D.C. Jiles, Acta Mater. 51 (2003) 5907. [6] J.M. Blanco, A. Zhukov, J. Gonzalez, J. Magn. Magn. Mater. 196 (1999) 377. [7] C. Gomez-Polo, M. Vazquez, M. Knobel, Appl. Phys. Lett. 78 (2001) 246. [8] C.G. Kim, S.S. Yoon, M. Vazquez, J. Magn. Magn. Mater. 223 (2001) L199.
[9] D.P. Makhnovskiy, L.V. Panina, D.J. Mapps, Phys. Rev. B 63 (2001) 144424. [10] I. Betancourt, R. Valenzuela, Appl. Phys. Lett. 83 (2003) 2022. [11] M. Vazquez, A. Zhukov, J. Magn. Magn. Mater. 160 (1996) 223. [12] A. Chizhik, J. Gonzalez, A. Zhukov, J.M. Blanco, J. Phys. D 36 (2003) 419. [13] P. Ciureanu, I. Khalil, L.G.C. Melo, P. Rudkowski, A. Yelon, J. Magn. Magn. Mater. 249 (2002) 305.