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* Laborat ! orio de Magnetismo e Materiais Magn ! eticos, Departamento de F! ısica, Santa Maria, RS UFSM 97105-900, Brazil Abstract The magnetic domain structure of the Co 70.4 Fe 4.6 Si 10 B 15 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 Co 70.4 Fe 4.6 Si 10 B 15 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 (f r ) 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 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 K u 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 f r 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 f r ðHÞ curve is fitted to the experimental one leaving the saturation magnetization M s ; the uniaxial anisotropy field H k and the direction of the anisotropy unitary vector u relative to the circumferential direction (f k ) as free parameters. y k 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 f r ðHÞ curve is shown in Fig. 2(a). For the ARTICLE IN PRESS *Corresponding author. Tel.: +55-55-220-8888; fax: +55- 55-220-8432. E-mail address: sommer@ccne.ufsm.br (R.L. Sommer). 0304-8853/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2003.12.831