An Indirect Method of Micromagnetic Structure Estimation in Microwires

Abstract

The tunable magnetic properties of amorphous ferromagnetic glass-coated microwires make them suitable for a wide range of applications. Accurate knowledge of the micromagnetic structure is highly desirable since it affects almost all magnetic properties. To select an appropriate wire-sample for a specific application, a deeper understanding of the magnetization reversal process is required, because it determines the measurable response (such as induced voltage waveform and its spectrum). However, the experimental observation of micromagnetic structure of micro-scale amorphous objects has strict size limitations. In this work we proposed a novel experimental technique for evaluating the microstructural characteristics of glass-coated microwires. The cross-sectional permeability distribution in the sample was obtained from impedance measurements at different frequencies. This distribution enables estimation of the prevailing anisotropy in the local region of the wire cross-section. The results obtained were compared with the findings of magnetostatic measurements and remanent state analysis. The advantages and limitations of the methods were discussed.

Keywords: glass-coated microwires; impedance; magnetic permeability; micromagnetic structure; soft magnetic materials.

Figure 1

(a) SEM and (b) TEM images of Co₇₀Fe₄B₁₃Si₁₁Cr₂ microwire. (c) SAED from the microwire and subsequent dark-field image obtained in the first diffraction ring. The samples demonstrate an amorphous structure.

Figure 2

Radial dependence of the current density at frequencies of 1, 2, 5 and 10 MHz. The vertical lines bound the layers through which 70% of the total current flows (shaded areas). The average permeability values for each case are marked with the corresponding color (these values were found by experimental data fitting procedure). For a frequency 1 MHz, the permeability ${\mu }_{\phi }$ is of the order of ${10}^4$, which is typical for low-magnetostriction wires.

Figure 3

Schematic of the permeability distribution calculation based on averaging the permeabilities over the penetration depths. The values of the average permeability ${\mu }_{\phi }^1$ and ${\mu }_{\phi }^2$ correspond to the experimental impedance measured at two frequencies $f(f_1 < f_2)$. The permeability values are used to estimate the corresponding penetration depths $h_{70\%}^1$ and $h_{70\%}^2$. From average values, the permeability ${\mu }_{\phi }^r$ of the differential layer (red) can be interpolated.

Figure 4

Schematic diagram showing the principal directions of the measured magnetic moment with respect to the applied magnetic field H_ex: (a) component of the wire magnetic moment along the field H_ex as a function of H_ex, (b) cross-magnetic moment vs. H_ex.

Figure 5

Schematic of the micromagnetic structure of the metallic part with a diameter 2a of a magnetic microwire: axially magnetized core of a diameter 2a_c (pink) and circularly magnetized shell (green). Closure domains are presented by the yellow region.

Figure 6

Normalized hysteresis loops of the Co₇₀Fe₄B₁₃Si₁₁Cr₂ amorphous glass-coated microwires with different diameters. The shape of hysteresis loops evolves depending on the diameter of the metal core.

Figure 7

Axial magnetic moment vs. magnetic field applied perpendicular to the wire axis for ${\mathrm{d}}_{\mathrm{m}}=8\mathsf{\mu }\mathrm{m}$ in (a) and $28\mathsf{\mu }\mathrm{m}$ in (b).

Figure 8

GMI field dependences at different frequencies for microwires with different metallic core diameters from 6.4 to 28 μm (a–f). Enlarged near-zero field region and hysteresis loops for the samples are included. Evolution of GMI curve shape from double peak (a,b) to single-peak (c,d) and back to double-peak (e,f) with increasing metal core diameter is observed.

Figure 9

Radial distribution of the permeability of CoFe-based microwires with different diameters. (a) Schematic representation of the permeability histogram construction reflecting radial permeability distribution, (b–f) permeability distribution histograms for the samples with different metal core diameters. The height of the bar is the local permeability value and the width is the thickness of the corresponding layer. Color is used to contrast the permeabilities of different layers. The permeability calculation was done for zero DC magnetic field.