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Experimental determination of limit angle of helical anisotropy in amorphous magnetic microwires
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 803–805
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Experimental determination of limit angle of helical anisotropy in amorphous magnetic microwires A. Chizhik a,, A. Zhukov a, J.M. Blanco b, J. Gonzalez a, P. Gawronski c a b c
Departamento Fisica de Materiales, Facultad de Quimica, UPV, 1072, 20080 San Sebastian, Spain Departamento Fisica Aplicada I, EUPDS, UPV/EHU, Plaza Europa, 1, 20018 San Sebastian, Spain Faculty of Physics & Applied Computer Science, AGH University of Science & Technology, 30-059 Cracow, Poland
a r t i c l e in fo
abstract
Available online 30 November 2008
The influence of the torsion stress on the surface magnetic structure in Co-rich amorphous glass covered microwires has been investigated. The limit angle of the surface helical anisotropy induced by the torsion stress has been determined in agreement with the model which considers the torsion stress as a interference of two tensile stresses of opposite signs directed at 451 and 1351 relative to the longitudinal axis of the wire. & 2008 Elsevier B.V. All rights reserved.
PACS: 75.30.Gw 75.50.Kj 81.07.Bc Keywords: Amorphous magnetic wire Hysteresis Magnetooptic Kerr effect Torsion stress
1. Introduction Giant magnetoimpedance (GMI) effect is of great importance in sensor application [1,2]. The role of the helical anisotropy in GMI effect is well known [3–5]. The problem of the experimental determination of the limit value of the angle of the torsion stress induced helical anisotropy in the wires exists since the works of Sablik and Jiles [6,7], in which it was shown that the torsion stress can be assumed to be a sum of two perpendicular stresses, each acting at 451 relative to the longitudinal axis of the wire, with tensile stress along one axis and opposite compressive stress along the another axis. The angular boundaries of the existence of the torsion stress induced helical anisotropy have been theoretically shown, but the value of the inclination of the helical anisotropy from the transverse direction was not experimentally determined up to now. In this situation, therefore, the purpose of our paper is to find the experimental limits of the torsion stress induced inclination of the helical anisotropy in magnetic wires.
2. Experimental details Amorphous microwires of nominal composition Co69.5Fe3.9 Ni1B11.8Si10.8Mo2 (metallic nucleus diameter 19 mm, glass coating thickness 2.6 mm) were supplied by TAMAG Iberica S.L. The Corresponding author. Tel.: 34 943 018611; fax: 34 943 017130.
E-mail address: [email protected] (A. Chizhik). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.11.073
experiments have been performed using the transverse magneto-optical Kerr effect (TMOKE). The details of the TMOKE experimental set-up have been presented elsewhere [8]. A polarized light from the He–Ne laser was reflected from the surface of the wire to the detector. The intensity of the reflected light is proportional to the magnetization oriented perpendicularly to the plane of the light polarization, i.e. to the circular projection of the magnetization in the surface area of the microwire. The torsion stress has been applied to the microwire during the experiments. To avoid a distortion of the magnetooptical signal related to the reflection from the non-planar surface of the wire, the part of light which corresponds to a small area of the wire surface was cut by the diaphragm. The part of the surface of the microwire from which the light hits to the detector could be considered as almost plane one, because the diaphragm cuts the sector of the light, which has a angle about of 11.
3. Experimental result and discussion The transformation of the surface hysteresis loops has been produced by the external torsion stress. The most important feature of this transformation is the stress induced change of the value and direction (sign) of the jump of the Kerr intensity DI (the circular magnetization DMCIRC). For the torsion stress of 2.2 p rad m1 value (Fig. 1(b)) there is no jump of the circular magnetization. The increase of the applied stress of negative
ARTICLE IN PRESS 804
A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 803–805
Fig. 1. TMOKE dependencies in the presence of torsion stress. (a) t ¼ 22 p rad m1, (b) t ¼ 2.2 p rad m1, (c) t ¼ 0, and (d) t ¼ 8.9 p rad m1.
value (22 p rad m1) causes the appearance of the DMCIRC of the opposite sign (Fig. 1(a)). The observed transformation is related to the torsion induced change of the surface helical anisotropy. The pictures presented in Fig. 2 demonstrate schematically the change of the direction of the surface helical anisotropy. The Kerr intensity is proportional to the transverse magnetization in the surface area of the wire, DI/IMAX DMCIRC/MMAX, where MMAX is the maximal value of the transverse (circular) magnetization during the magnetization reversal. Fig. 3 presents the experimental dependence of the normalized value of the jump of the Kerr intensity DI/IMAX (IMAX is the maximal intensity of the Kerr signal during the magnetization reversal) on the applied torsion stress. We put the attention to this parameter because the value of the jump of the circular magnetization DMCIRC is the key parameter which permits to establish the correlation between the shape of the surface hysteresis loop and the angle of the helical anisotropy and also to determine this angle. We consider that the observed transformation of the surface hysteresis loops is related to the transformation of the surface helical magnetic structure. Therefore, the calculation of the hysteresis loops has been performed taking into account an existence of a helical magnetic anisotropy in the surface area of the wire. We treat the wire surface as a two-dimensional system in our calculations, because the curvature of the area of wire surface, from which the light is reflected to detector, is about 11, as it was mentioned above. The applied magnetic field can be expressed as a superposition of two mutually perpendicular fields (haxial and hcirc). The direction of the anisotropy was changed from axial to circular direction. 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 cos ðyÞ hcirc sin ðyÞ
(1)
where KU is uniaxial anisotropy constant, m is the saturation magnetization, j is an angle between the anisotropy axis and the wire axis and y is the angle between the magnetic moment and the wire axis.
Fig. 2. Schematic pictures of the inclination of the axis of helical anisotropy induced by the torsion stress. (a) without stress; (b), (c) left torsion; (d), (e) right torsion.
The numerical calculation was done by the coherent rotation approach [9]. The hysteresis loops was computed by the minimization of the energy term described by the Eq. (1). For given values of the angle j the minimization procedure can be outlined in the following way: each time the value of the axial field was changed, the search of the value of the angle y, that gave the minimal value of the energy term (1) was done.
ARTICLE IN PRESS A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 803–805
Fig. 3. Experimental dependence of the normalized value of the jump of the Kerr intensity DI/IMAX on applied torsion stress.
805
angle of the helical anisotropy. The jump is equal to zero for the angle of 901 (the case of the transverse anisotropy). The calculated dependence of the DMCIRC has two maximum for the values of the angle of 621 and 1181. Fig. 5 presents the result of the comparative analysis of the experimental results presented in Fig. 3 and the results of the calculations presented in Fig. 4. We have determined and constructed the dependence of the angle of the helical anisotropy on the applied torsion stress. In the absence of the applied stress the anisotropy was directed almost to the transverse direction but not exactly to this one. The small peak marked in Fig. 1(c), means that the small jump of circular magnetization takes place and that the angle of anisotropy is not exactly 901. The application of relatively small stress of 2.2 p rad m1 value induces the disappearance of this small peak and the transverse anisotropy but not the helical one exists at this value of the torsion stress. The increase of the absolute value of the stress causes the growth of the absolute value of the angle of the helical anisotropy. This growth ends at the applied stress value of around 740 p rad m1. Therefore, as it was predicted in Refs. [6,7], the torsion stress induced inclination of the helical anisotropy does not exceed the 451 from the transverse direction in spite of the value of the applied stress was high enough.
4. Conclusion
Fig. 4. Calculated dependence of the jump of the circular magnetization DMCIRC/ MMAX on the angle of helical anisotropy j.
The experimental limit values of the angle of the helical anisotropy have been obtained as the result of the analysis of the torsion stress induced transformation of the surface magnetization reversal in the Co-rich amorphous microwires. The relation between the value of the torsion stress and the angle of helical anisotropy angle has been established. Now we have the method which permits us to present the results of the experiments with torsion stress as a dependence on the angle of helical anisotropy. This work was supported by MEyC under project PCI2005-A70230. References
Fig. 5. Dependence of angle of helical anisotropy on applied torsion stress.
The jump of the circular magnetization DMCIRC considerably depends on the value of the angle of the helical anisotropy. Fig. 4 shows the calculated dependence of the DMCIRC/MMAX on the
[1] K.T.K. Mohri, T. Yagi, T. Uchiyama, L.P. Shen, IEEE Trans. Mag. 33 (1997) 3358. [2] A. Zhukov, J. Gonzalez, M. Vazquez, V. Larin, A. Torcunov, Nanocrystalline and amorphous magnetic microwires, in: H.S. Nalwa (Ed.), Encyclopedia of Nanoscience and Nanotechnology, American Scientific Publishers, 2004, p. 23. [3] C. Tannous, J. Gieraltowski, R. Valenzuela, J. Magn. Magn. Mater. 308 (2007) 273. [4] J.G.S. Duque, C. Gomez-Polo, A. Yelon, P. Ciureanu, A.E.P. de Araujo, M. Knobel, J. Magn. Magn. Mater. 271 (2004) 390. [5] C.G. Kim, S.S. Yoon, M. Va´zquez, J. Magn. Magn. Mater. 223 (2001) L199. [6] M.J. Sablik, D.C. Jiles, Phys. D: Appl. Phys. 32 (1999) 1971. [7] M.J. Sablik, D.C. Jiles, IEEE Trans. Magn. 35 (1999) 498. [8] Chizhik, J. Gonzalez, A. Zhukov, J.M. Blanco, J. Appl. Phys. 91 (2002) 537. [9] G. Bertotti, Hysteresis in Magnetism, Academic Press, San Diego, 1998.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Experimental determination of limit angle of helical anisotropy in amorphous magnetic microwires A. Chizhik a,, A. Zhukov a, J.M. Blanco b, J. Gonzalez a, P. Gawronski c a b c
Departamento Fisica de Materiales, Facultad de Quimica, UPV, 1072, 20080 San Sebastian, Spain Departamento Fisica Aplicada I, EUPDS, UPV/EHU, Plaza Europa, 1, 20018 San Sebastian, Spain Faculty of Physics & Applied Computer Science, AGH University of Science & Technology, 30-059 Cracow, Poland
a r t i c l e in fo
abstract
Available online 30 November 2008
The influence of the torsion stress on the surface magnetic structure in Co-rich amorphous glass covered microwires has been investigated. The limit angle of the surface helical anisotropy induced by the torsion stress has been determined in agreement with the model which considers the torsion stress as a interference of two tensile stresses of opposite signs directed at 451 and 1351 relative to the longitudinal axis of the wire. & 2008 Elsevier B.V. All rights reserved.
PACS: 75.30.Gw 75.50.Kj 81.07.Bc Keywords: Amorphous magnetic wire Hysteresis Magnetooptic Kerr effect Torsion stress
1. Introduction Giant magnetoimpedance (GMI) effect is of great importance in sensor application [1,2]. The role of the helical anisotropy in GMI effect is well known [3–5]. The problem of the experimental determination of the limit value of the angle of the torsion stress induced helical anisotropy in the wires exists since the works of Sablik and Jiles [6,7], in which it was shown that the torsion stress can be assumed to be a sum of two perpendicular stresses, each acting at 451 relative to the longitudinal axis of the wire, with tensile stress along one axis and opposite compressive stress along the another axis. The angular boundaries of the existence of the torsion stress induced helical anisotropy have been theoretically shown, but the value of the inclination of the helical anisotropy from the transverse direction was not experimentally determined up to now. In this situation, therefore, the purpose of our paper is to find the experimental limits of the torsion stress induced inclination of the helical anisotropy in magnetic wires.
2. Experimental details Amorphous microwires of nominal composition Co69.5Fe3.9 Ni1B11.8Si10.8Mo2 (metallic nucleus diameter 19 mm, glass coating thickness 2.6 mm) were supplied by TAMAG Iberica S.L. The Corresponding author. Tel.: 34 943 018611; fax: 34 943 017130.
E-mail address: [email protected] (A. Chizhik). 0304-8853/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2008.11.073
experiments have been performed using the transverse magneto-optical Kerr effect (TMOKE). The details of the TMOKE experimental set-up have been presented elsewhere [8]. A polarized light from the He–Ne laser was reflected from the surface of the wire to the detector. The intensity of the reflected light is proportional to the magnetization oriented perpendicularly to the plane of the light polarization, i.e. to the circular projection of the magnetization in the surface area of the microwire. The torsion stress has been applied to the microwire during the experiments. To avoid a distortion of the magnetooptical signal related to the reflection from the non-planar surface of the wire, the part of light which corresponds to a small area of the wire surface was cut by the diaphragm. The part of the surface of the microwire from which the light hits to the detector could be considered as almost plane one, because the diaphragm cuts the sector of the light, which has a angle about of 11.
3. Experimental result and discussion The transformation of the surface hysteresis loops has been produced by the external torsion stress. The most important feature of this transformation is the stress induced change of the value and direction (sign) of the jump of the Kerr intensity DI (the circular magnetization DMCIRC). For the torsion stress of 2.2 p rad m1 value (Fig. 1(b)) there is no jump of the circular magnetization. The increase of the applied stress of negative
ARTICLE IN PRESS 804
A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 803–805
Fig. 1. TMOKE dependencies in the presence of torsion stress. (a) t ¼ 22 p rad m1, (b) t ¼ 2.2 p rad m1, (c) t ¼ 0, and (d) t ¼ 8.9 p rad m1.
value (22 p rad m1) causes the appearance of the DMCIRC of the opposite sign (Fig. 1(a)). The observed transformation is related to the torsion induced change of the surface helical anisotropy. The pictures presented in Fig. 2 demonstrate schematically the change of the direction of the surface helical anisotropy. The Kerr intensity is proportional to the transverse magnetization in the surface area of the wire, DI/IMAX DMCIRC/MMAX, where MMAX is the maximal value of the transverse (circular) magnetization during the magnetization reversal. Fig. 3 presents the experimental dependence of the normalized value of the jump of the Kerr intensity DI/IMAX (IMAX is the maximal intensity of the Kerr signal during the magnetization reversal) on the applied torsion stress. We put the attention to this parameter because the value of the jump of the circular magnetization DMCIRC is the key parameter which permits to establish the correlation between the shape of the surface hysteresis loop and the angle of the helical anisotropy and also to determine this angle. We consider that the observed transformation of the surface hysteresis loops is related to the transformation of the surface helical magnetic structure. Therefore, the calculation of the hysteresis loops has been performed taking into account an existence of a helical magnetic anisotropy in the surface area of the wire. We treat the wire surface as a two-dimensional system in our calculations, because the curvature of the area of wire surface, from which the light is reflected to detector, is about 11, as it was mentioned above. The applied magnetic field can be expressed as a superposition of two mutually perpendicular fields (haxial and hcirc). The direction of the anisotropy was changed from axial to circular direction. 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 cos ðyÞ hcirc sin ðyÞ
(1)
where KU is uniaxial anisotropy constant, m is the saturation magnetization, j is an angle between the anisotropy axis and the wire axis and y is the angle between the magnetic moment and the wire axis.
Fig. 2. Schematic pictures of the inclination of the axis of helical anisotropy induced by the torsion stress. (a) without stress; (b), (c) left torsion; (d), (e) right torsion.
The numerical calculation was done by the coherent rotation approach [9]. The hysteresis loops was computed by the minimization of the energy term described by the Eq. (1). For given values of the angle j the minimization procedure can be outlined in the following way: each time the value of the axial field was changed, the search of the value of the angle y, that gave the minimal value of the energy term (1) was done.
ARTICLE IN PRESS A. Chizhik et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 803–805
Fig. 3. Experimental dependence of the normalized value of the jump of the Kerr intensity DI/IMAX on applied torsion stress.
805
angle of the helical anisotropy. The jump is equal to zero for the angle of 901 (the case of the transverse anisotropy). The calculated dependence of the DMCIRC has two maximum for the values of the angle of 621 and 1181. Fig. 5 presents the result of the comparative analysis of the experimental results presented in Fig. 3 and the results of the calculations presented in Fig. 4. We have determined and constructed the dependence of the angle of the helical anisotropy on the applied torsion stress. In the absence of the applied stress the anisotropy was directed almost to the transverse direction but not exactly to this one. The small peak marked in Fig. 1(c), means that the small jump of circular magnetization takes place and that the angle of anisotropy is not exactly 901. The application of relatively small stress of 2.2 p rad m1 value induces the disappearance of this small peak and the transverse anisotropy but not the helical one exists at this value of the torsion stress. The increase of the absolute value of the stress causes the growth of the absolute value of the angle of the helical anisotropy. This growth ends at the applied stress value of around 740 p rad m1. Therefore, as it was predicted in Refs. [6,7], the torsion stress induced inclination of the helical anisotropy does not exceed the 451 from the transverse direction in spite of the value of the applied stress was high enough.
4. Conclusion
Fig. 4. Calculated dependence of the jump of the circular magnetization DMCIRC/ MMAX on the angle of helical anisotropy j.
The experimental limit values of the angle of the helical anisotropy have been obtained as the result of the analysis of the torsion stress induced transformation of the surface magnetization reversal in the Co-rich amorphous microwires. The relation between the value of the torsion stress and the angle of helical anisotropy angle has been established. Now we have the method which permits us to present the results of the experiments with torsion stress as a dependence on the angle of helical anisotropy. This work was supported by MEyC under project PCI2005-A70230. References
Fig. 5. Dependence of angle of helical anisotropy on applied torsion stress.
The jump of the circular magnetization DMCIRC considerably depends on the value of the angle of the helical anisotropy. Fig. 4 shows the calculated dependence of the DMCIRC/MMAX on the
[1] K.T.K. Mohri, T. Yagi, T. Uchiyama, L.P. Shen, IEEE Trans. Mag. 33 (1997) 3358. [2] A. Zhukov, J. Gonzalez, M. Vazquez, V. Larin, A. Torcunov, Nanocrystalline and amorphous magnetic microwires, in: H.S. Nalwa (Ed.), Encyclopedia of Nanoscience and Nanotechnology, American Scientific Publishers, 2004, p. 23. [3] C. Tannous, J. Gieraltowski, R. Valenzuela, J. Magn. Magn. Mater. 308 (2007) 273. [4] J.G.S. Duque, C. Gomez-Polo, A. Yelon, P. Ciureanu, A.E.P. de Araujo, M. Knobel, J. Magn. Magn. Mater. 271 (2004) 390. [5] C.G. Kim, S.S. Yoon, M. Va´zquez, J. Magn. Magn. Mater. 223 (2001) L199. [6] M.J. Sablik, D.C. Jiles, Phys. D: Appl. Phys. 32 (1999) 1971. [7] M.J. Sablik, D.C. Jiles, IEEE Trans. Magn. 35 (1999) 498. [8] Chizhik, J. Gonzalez, A. Zhukov, J.M. Blanco, J. Appl. Phys. 91 (2002) 537. [9] G. Bertotti, Hysteresis in Magnetism, Academic Press, San Diego, 1998.