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FMR and domain structure in joule-heated glass-covered microwires
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 272–276 (2004) 1858–1859
FMR and domain structure in joule-heated glass-covered microwires R.B. da Silva, M. Carara, A.M.H. de Andrade, A.M. Severino, R.L. Sommer* ! Laboratorio de Magnetismo e Materiais Magn!eticos, Departamento de F!ısica, Santa Maria, RS UFSM 97105-900, Brazil
Abstract The magnetic domain structure of the Co70.4Fe4.6Si10B15 glass-covered amorphous microwires Joule-heated of different annealing currents (temperatures) is studied. From the magnetization curves and ferromagnetic resonance features obtained from the impedance spectra measured at different magnetic fields, a domain structure is proposed for the as-produced and Joule-heated microwires. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Kj; 75.60.Ch; 76.50.+g; 75.30.Gw Keywords: Amorphous microwires; Impedance; Ferromagnetic resonance; Domain structure; Joule-heating
A domain structure (DS) for the Co70.4Fe4.6Si10B15 glass-covered microwires as cast and after annealing by Joule heating at several currents is proposed. The procedure used was based on the fittings of the resonance frequency (fr ) versus axial magnetic field (H) and on the analysis of the magnetization curves for the samples. Impedance spectra Zðf ; HÞ were measured with spectrum-impedance-analyzer model HP4396B (100 kHzpf p1:8 GHz), performed at 10 dBm (0.1 mW) constant power. The adopted sample holder was a coaxial microwave cavity, with the sample playing the role of the central conductor and a short at one end. The real (R) and imaginary (X) parts of Z were simultaneously measured at a given H in the range 7150 Oe. As the magnetoimpedance and FMR are both governed by the sample permeability, the resonance frequency may be determined by a maximum in R accompanied by a zero crossing in X. The samples were treated under the DC current values of 10, 15 and 20 mA (340 C, 475 C, 590 C, respectively, [1]) during 10 min. Magnetization measurements were carried out in a Helmholtz coil VSM in the same samples used for the Zðf ; HÞ measurements. The absence of a demagnetizing *Corresponding author. Tel.: +55-55-220-8888; fax: +5555-220-8432. E-mail address: [email protected] (R.L. Sommer).
factor along the wire’s circumferential direction allows to treat the wire as a semi-infinite plane [2]. In view of this, the total free energy density of the system can be written as [3] E ¼ H M þ 2pðM nÞ Ku ½M u 2 =M 2 :
ð1Þ
In expression (1), H is the external DC field and M the magnetization, while n and u are unit vectors along the radial direction and along the easy axis, respectively. The fr ðHÞ curves are obtained by calculating the root of the determinant that involves the second derivatives of expression (1) with respect to the equilibrium angles of the magnetization y and f: These angles are found by minimizing the free energy for each applied field [3]. The theoretic fr ðHÞ curve is fitted to the experimental one leaving the saturation magnetization Ms ; the uniaxial anisotropy field Hk and the direction of the anisotropy unitary vector u relative to the circumferential direction (fk ) as free parameters. yk was maintained constant and equal to 90 while the gyromagnetic factor g was taken as g/2p=2.8 MHz/Oe [2]. For the as cast sample the magnetization curve presented in Fig. 1 shows two slopes as the field increases, suggesting two anisotropy directions. The absence of remanence and the low coercivity indicate that these directions are radial and circumferential. The corresponding fr ðHÞ curve is shown in Fig. 2(a). For the
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.831
ARTICLE IN PRESS R.B. da Silva et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 1858–1859
Hc (Oe)
as ca st 1
10 m A
0 10 20 I An n eal . (m A)
15 m A
M/M
s
0
20 m A
-9
-6
-3
0
3
6
9
Field (Oe) Fig. 1. Magnetization curves of the studied samples. All samples were measured up to 25 Oe. Inset shows the evolution of coercivity with the annealing current.
(b) 10 mA
(a) as cast
1.5
1.5
1.0
1.0
f r (GHz)
Hk = 5 Oe
Hk = 5.1 Oe φk = 0
0.5 0.0
0.0
(d) 20 mA
(c) 15 mA
1.5
0.5
o
φk = 5
1.5 1.0
1.0 0.5
Hk = 4.6 Oe
0.0
φk = 12
Hk = 3.4 Oe
0
10
20
30
0.5
o
φk = 15
o
0
10
20
0.0 30
Field (Oe) Fig. 2. fr ðHÞ curves for the studies samples (circles) and the fitting (line) as discussed in the text.
fitting shown in this figure, a circumferential anisotropy field of magnitude 5.1 Oe has been assumed. This means that the outer shell (fraction of the DS probed by FMR) has a circumferential anisotropy. Thus, it can be concluded that for the as cast sample the domain structure is composed by a circumferential anisotropy in the outer shell and radial anisotropy in the inner core. In the case of the sample annealed at 10 mA, the MðHÞ curve exhibits low remanence and coercivity, as seen in Fig. 1. However, the transverse anisotropy character is still present in this curve. Two factors can be the responsible for this: (i) the presence of a dispersion in the circumferential anisotropy, characterized by a skew angle fk or (ii) an alignment of the inner core domains in the longitudinal direction. The skew angle can be introduced in the FMR fitting, by dislocating the unitary vector u by an angle fk from the circumferential direction. The result is a less defined valley in fr ðHÞ curve at HDHk when compared with the pure circumferential anisotropy. In the Fig. 2(b) the fr ðHÞ curve of the 10 mA annealed sample fitted with the
1859
Hk ¼ 5 Oe and fk ¼ 5 is shown. The skew angle can also be obtained through the remanence value as fk ¼ arcsinðMr =Ms Þ [4] which produces a value remarkably close to that obtained by the fitting of the resonance condition. It can then be concluded that, for the 10 mA sample, the outer shell has a helical anisotropy while the inner core keeps the radial anisotropy character. For samples annealed at 15 and 20 mA, a strong increase in the remanence and coercivity is observed as shown in Fig. 1. The fitting of the fr ðHÞ curves, resulted in the values of fk ¼ 12 for the sample annealed at 15 mA, and fk ¼ 15 for the sample annealed at 20 mA, as shown in Figs. 2(c and d). However, these values are smaller than that obtained from the magnetization curves, 20 and 23 for the 15 and 20 mA annealed samples, respectively. It has to be pointed out that, with these parameters, the fr ðHÞ curve can be adjusted only for fields near Hk and higher. For HoHk ; the calculated fr are smaller than the measured ones. In other words, the skew angle alone cannot explain the observed FMR and magnetization curves, meaning that an additional portion of the sample is aligned to the longitudinal direction. It is possible that, for these samples, the inner core has a longitudinal anisotropy and the skin-depth is such that the FMR probes this part of the DS affecting the observed spectra. That means, the inner core has it radius increased when compared with the as cast and annealed at 10 mA samples, as the skin depth is roughly the same for all samples. To conclude, the annealing at 10 mA has produced only a stress relief without major modifications of the DS besides the increase in dispersion of the anisotropy characterized by the skew angle. In the case of the samples annealed at 15 and 20 mA the difference in the thermal expansion coefficient between the glass cover and the metallic nucleus, impose a compressive stress in both directions, radial and axial. This stress, associated with the negative sign of the magnetostriction, will produce an effective field in the longitudinal direction. The circumferential field produced by the annealing current (higher in the surface than in the core) can explain the longitudinal and helical anisotropy in the inner core and outer shell, respectively. The stress relief promoted by the increase in the annealing temperature explains the increase in the inner core radius and the reduction of the effective anisotropy, observed by the FMR. References ! ari, Mater. Sci. Forum [1] H. Chiriac, M. Knobel, T.A. Ov! 302–302 (1999) 239. [2] D. M!enard, M. Britel, P. Ciureanu, A. Yelon, J. Appl. Phys. 84 (1998) 2805. [3] L. Kraus, J. Magn. Magn. Mater. 195 (1999) 764. [4] G. Bertotti, Hysteresis in Magnetism, Academic Press, San Diego, 1998.
Journal of Magnetism and Magnetic Materials 272–276 (2004) 1858–1859
FMR and domain structure in joule-heated glass-covered microwires R.B. da Silva, M. Carara, A.M.H. de Andrade, A.M. Severino, R.L. Sommer* ! Laboratorio de Magnetismo e Materiais Magn!eticos, Departamento de F!ısica, Santa Maria, RS UFSM 97105-900, Brazil
Abstract The magnetic domain structure of the Co70.4Fe4.6Si10B15 glass-covered amorphous microwires Joule-heated of different annealing currents (temperatures) is studied. From the magnetization curves and ferromagnetic resonance features obtained from the impedance spectra measured at different magnetic fields, a domain structure is proposed for the as-produced and Joule-heated microwires. r 2003 Elsevier B.V. All rights reserved. PACS: 75.50.Kj; 75.60.Ch; 76.50.+g; 75.30.Gw Keywords: Amorphous microwires; Impedance; Ferromagnetic resonance; Domain structure; Joule-heating
A domain structure (DS) for the Co70.4Fe4.6Si10B15 glass-covered microwires as cast and after annealing by Joule heating at several currents is proposed. The procedure used was based on the fittings of the resonance frequency (fr ) versus axial magnetic field (H) and on the analysis of the magnetization curves for the samples. Impedance spectra Zðf ; HÞ were measured with spectrum-impedance-analyzer model HP4396B (100 kHzpf p1:8 GHz), performed at 10 dBm (0.1 mW) constant power. The adopted sample holder was a coaxial microwave cavity, with the sample playing the role of the central conductor and a short at one end. The real (R) and imaginary (X) parts of Z were simultaneously measured at a given H in the range 7150 Oe. As the magnetoimpedance and FMR are both governed by the sample permeability, the resonance frequency may be determined by a maximum in R accompanied by a zero crossing in X. The samples were treated under the DC current values of 10, 15 and 20 mA (340 C, 475 C, 590 C, respectively, [1]) during 10 min. Magnetization measurements were carried out in a Helmholtz coil VSM in the same samples used for the Zðf ; HÞ measurements. The absence of a demagnetizing *Corresponding author. Tel.: +55-55-220-8888; fax: +5555-220-8432. E-mail address: [email protected] (R.L. Sommer).
factor along the wire’s circumferential direction allows to treat the wire as a semi-infinite plane [2]. In view of this, the total free energy density of the system can be written as [3] E ¼ H M þ 2pðM nÞ Ku ½M u 2 =M 2 :
ð1Þ
In expression (1), H is the external DC field and M the magnetization, while n and u are unit vectors along the radial direction and along the easy axis, respectively. The fr ðHÞ curves are obtained by calculating the root of the determinant that involves the second derivatives of expression (1) with respect to the equilibrium angles of the magnetization y and f: These angles are found by minimizing the free energy for each applied field [3]. The theoretic fr ðHÞ curve is fitted to the experimental one leaving the saturation magnetization Ms ; the uniaxial anisotropy field Hk and the direction of the anisotropy unitary vector u relative to the circumferential direction (fk ) as free parameters. yk was maintained constant and equal to 90 while the gyromagnetic factor g was taken as g/2p=2.8 MHz/Oe [2]. For the as cast sample the magnetization curve presented in Fig. 1 shows two slopes as the field increases, suggesting two anisotropy directions. The absence of remanence and the low coercivity indicate that these directions are radial and circumferential. The corresponding fr ðHÞ curve is shown in Fig. 2(a). For the
0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.831
ARTICLE IN PRESS R.B. da Silva et al. / Journal of Magnetism and Magnetic Materials 272–276 (2004) 1858–1859
Hc (Oe)
as ca st 1
10 m A
0 10 20 I An n eal . (m A)
15 m A
M/M
s
0
20 m A
-9
-6
-3
0
3
6
9
Field (Oe) Fig. 1. Magnetization curves of the studied samples. All samples were measured up to 25 Oe. Inset shows the evolution of coercivity with the annealing current.
(b) 10 mA
(a) as cast
1.5
1.5
1.0
1.0
f r (GHz)
Hk = 5 Oe
Hk = 5.1 Oe φk = 0
0.5 0.0
0.0
(d) 20 mA
(c) 15 mA
1.5
0.5
o
φk = 5
1.5 1.0
1.0 0.5
Hk = 4.6 Oe
0.0
φk = 12
Hk = 3.4 Oe
0
10
20
30
0.5
o
φk = 15
o
0
10
20
0.0 30
Field (Oe) Fig. 2. fr ðHÞ curves for the studies samples (circles) and the fitting (line) as discussed in the text.
fitting shown in this figure, a circumferential anisotropy field of magnitude 5.1 Oe has been assumed. This means that the outer shell (fraction of the DS probed by FMR) has a circumferential anisotropy. Thus, it can be concluded that for the as cast sample the domain structure is composed by a circumferential anisotropy in the outer shell and radial anisotropy in the inner core. In the case of the sample annealed at 10 mA, the MðHÞ curve exhibits low remanence and coercivity, as seen in Fig. 1. However, the transverse anisotropy character is still present in this curve. Two factors can be the responsible for this: (i) the presence of a dispersion in the circumferential anisotropy, characterized by a skew angle fk or (ii) an alignment of the inner core domains in the longitudinal direction. The skew angle can be introduced in the FMR fitting, by dislocating the unitary vector u by an angle fk from the circumferential direction. The result is a less defined valley in fr ðHÞ curve at HDHk when compared with the pure circumferential anisotropy. In the Fig. 2(b) the fr ðHÞ curve of the 10 mA annealed sample fitted with the
1859
Hk ¼ 5 Oe and fk ¼ 5 is shown. The skew angle can also be obtained through the remanence value as fk ¼ arcsinðMr =Ms Þ [4] which produces a value remarkably close to that obtained by the fitting of the resonance condition. It can then be concluded that, for the 10 mA sample, the outer shell has a helical anisotropy while the inner core keeps the radial anisotropy character. For samples annealed at 15 and 20 mA, a strong increase in the remanence and coercivity is observed as shown in Fig. 1. The fitting of the fr ðHÞ curves, resulted in the values of fk ¼ 12 for the sample annealed at 15 mA, and fk ¼ 15 for the sample annealed at 20 mA, as shown in Figs. 2(c and d). However, these values are smaller than that obtained from the magnetization curves, 20 and 23 for the 15 and 20 mA annealed samples, respectively. It has to be pointed out that, with these parameters, the fr ðHÞ curve can be adjusted only for fields near Hk and higher. For HoHk ; the calculated fr are smaller than the measured ones. In other words, the skew angle alone cannot explain the observed FMR and magnetization curves, meaning that an additional portion of the sample is aligned to the longitudinal direction. It is possible that, for these samples, the inner core has a longitudinal anisotropy and the skin-depth is such that the FMR probes this part of the DS affecting the observed spectra. That means, the inner core has it radius increased when compared with the as cast and annealed at 10 mA samples, as the skin depth is roughly the same for all samples. To conclude, the annealing at 10 mA has produced only a stress relief without major modifications of the DS besides the increase in dispersion of the anisotropy characterized by the skew angle. In the case of the samples annealed at 15 and 20 mA the difference in the thermal expansion coefficient between the glass cover and the metallic nucleus, impose a compressive stress in both directions, radial and axial. This stress, associated with the negative sign of the magnetostriction, will produce an effective field in the longitudinal direction. The circumferential field produced by the annealing current (higher in the surface than in the core) can explain the longitudinal and helical anisotropy in the inner core and outer shell, respectively. The stress relief promoted by the increase in the annealing temperature explains the increase in the inner core radius and the reduction of the effective anisotropy, observed by the FMR. References ! ari, Mater. Sci. Forum [1] H. Chiriac, M. Knobel, T.A. Ov! 302–302 (1999) 239. [2] D. M!enard, M. Britel, P. Ciureanu, A. Yelon, J. Appl. Phys. 84 (1998) 2805. [3] L. Kraus, J. Magn. Magn. Mater. 195 (1999) 764. [4] G. Bertotti, Hysteresis in Magnetism, Academic Press, San Diego, 1998.