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—We showed that stress-annealing performed under proper conditions can improve magnetic softness, domain wall (DW) velocity and giant magneto-impedance (GMI) effect of Fe-based microwires. One order of magnitude improvement of GMI ratio and more than 100% increase of DW velocity have been achieved by stress-annealing. Observed dependencies have been related to the domain structure modification evidenced from the evolution of the hysteresis loops upon stress-annealing. We discussed observed results considering that the outer domain shell with transverse magnetic anisotropy affects the travelling DW in a similar way as the application of transverse bias magnetic field. GMI ratio improvement is attributed to beneficial magnetic anisotropy distribution achieved by stress-annealing.

[EN] We report on the influence of graded magnetic anisotropy designed by stress-annealing of magnetic microwire at variable annealing temperature on domain wall propagation. We found that the domain wall propagation in a medium with graded magnetic anisotropy is substantially nonuniform. Domain wall can be trapped in the microwire region with strong enough stress-annealing induced magnetic anisotropy. On the other hand, faster domain wall propagation and a decrease in the domain wall length are observed in the region with moderate stress-annealing induced magnetic anisotropy. Beneficial effect of stress annealing on the domain wall dynamics is associated with the induced transverse magnetic anisotropy in the outer domain which affects the travelling domain wall in a similar way as application of transversal bias magnetic field. Observed decreasing of the half-width of the electromagnetic force (EMF) peak in stress-annealed microwires can be associated to the decreasing of the characteristic domain wall length. This work was supported by the Spanish MCIU, under PGC2018099530-B-C31 (MCIU/AEI/FEDER, UE), by the Government of the Basque Country, under PIBA 2018-44, PUE_2021_1_00 09 and Elkartek (CEMAP and AVANSITE) projects, and by the University of Basque Country, under the scheme of "Ayuda a Grupos Consolidados"(Ref.: GIU18/192) and COLAB20/15 project. The authors are thankful for the technical and human support provided by SGIker of UPV/EHU (Medidas Magneticas Gipuzkoa) and European funding (ERDF and ESF).

Processing by stress-annealing (450 MPa, 300 °C, 1 h) the glass-coated microwire of Fe 75 B 9 Si 12 C 4 composition a macroscopic magnetic anisotropy with a circular component is developed. This anisotropy very significantly improves the giant magnetoimpedance (GMI) effect with respect to the observed in the as-prepared microwire. The analysis of the GMI response as a function of the frequency (10–1000 MHz) opens new lights to understand the distribution of the magnetic anisotropy inside the glass-coated microwire. We have investigated the GMI response of the stress-annealed Fe 75 B 9 Si 12 C 4 glass-coated microwire. From the frequency dependence of the GMI we have analyzed the distribution of the magnetic anisotropy inside the metallic nucleus obtaining good agreement with the average value of the anisotropy field deduced from the hysteresis loop of the bulk. From measured magnetic field dependences of GMI ratio we evaluated the frequency and magnetic field dependences of the penetration depth. We found that the minimum penetration depth of Fe 75 B 9 Si 12 C 4 microwire decreases from about 1.5 μm down to 0.8 μm after stress annealing. Obtained dependences demonstrate that the minimum penetration depth value as well as the frequency and magnetic field dependences are considerably affected by the stress-annealing.

Processing by Joule-heating the Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 glass-coated microwire allows considerable improvement of magnetic softness and giant magnetoimpedance (GMI) effect. At optimal joule heating conditions we observed GMI ratio up to 650%. Observed magnetic softening and GMI ratio improvement have been discussed considering magnetic anisotropy induced by Oersted magnetic field during current annealing, internal stresses relaxation and radial distribution of magnetic anisotropy. The analysis of the GMI ratio as a function of the frequency (10–1000 MHz) opens new lights to understand the distribution of the magnetic anisotropy inside the glass-coated microwire.

Applications in security and electronic surveillance require a combination of excellent magnetic softness with good mechanical and anticorrosive properties and low dimensionality. We overviewed the feasibility of using glass-coated microwires for electronic article surveillance and security applications, as well as different routes of tuning the magnetic properties of individual microwires or microwire arrays, making them quite attractive for electronic article surveillance and security applications. We provide the routes for tuning the hysteresis loops’ nonlinearity by the magnetostatic interaction between the microwires in the arrays of different types of amorphous microwires. The presence of neighboring microwire (either Fe- or Co-based) significantly affects the hysteresis loop of the whole microwires array. In a microwires array containing magnetically bistable microwires, we observed splitting of the initially rectangular hysteresis loop with a number of Barkhausen jumps correlated with the number of magnetically bistable microwires. Essentially, nonlinear and irregular hysteresis loops have been observed in mixed arrays containing Fe- and Co-rich microwires. The obtained nonlinearity in hysteresis loops allowed to increase the harmonics and tune their magnetic field dependencies. On the other hand, several routes allowing to tune the switching field by either postprocessing or modifying the magnetoelastic anisotropy have been reviewed. Nonlinear hysteresis loops have been also observed upon devitrification of amorphous microwires. Semihard magnetic microwires have been obtained by annealing of Fe–Pt–Si microwires. The observed unique combination of magnetic properties together with thin dimensions and excellent mechanical and anticorrosive properties provide excellent perspectives for the use of glass-coated microwires for security and electronic surveillance applications. This work was funded by Spanish MCIU under PGC2018-099530-B-C31 (MCIU/AEI/FEDER, UE) by the Government of the Basque Country under PIBA 2018-44 project and Elkartek (CEMAP and AVANSITE) projects and by the University of Basque Country under the scheme of “Ayuda a Grupos Consolidados” (Ref.: GIU18/192).

Stress-annealing enabled a considerable improvement in the GMI effect in both Fe- and Co-rich glass-coated microwires. Additionally, a remarkable magnetic softening can be achieved in stress-annealed Fe-rich microwires. Observed stress-annealing induced magnetic anisotropy is affected by annealing conditions (temperatures and stresses applied during annealing). The highest GMI ratio up to 310% was obtained in stress-annealed Co-rich microwires, although they presented rectangular hysteresis loops. A remarkable magnetic softness and improved GMI ratio over a wide frequency range were obtained in stress-annealed Fe-rich microwires. Irregular magnetic field dependence observed for some stress-annealing conditions is attributed to the contribution of both the inner axially magnetized core and outer shell, with transverse magnetic anisotropy.

The influence of post-processing (annealing and stress-annealing) on the magnetic softness, Giant magnetoimpedance (GMI) effect and domain wall dynamics of Fe3.6Co69.2Ni1B12.5Si11Mo1.5C1.2 glass-coated microwires is studied. As-prepared Co-rich glass-coated microwire presents linear hysteresis loops and rather higher magnetoimpedance ratio with double-peak magnetic field dependence, typical for materials with transverse magnetic anisotropy. Considerable magnetic hardening and transformation of linear hysteresis loop with low coercivity (Hc ≈ 4 A/m) into rectangular with Hc ≈90 A/m upon annealing without stress is observed. However, we observed remarkable MI effect improvement at certain annealing conditions. Stress-annealing of studied microwire allows considerable magnetoimpedance ratio and domain wall velocity increasing. Additionally, remanent magnetization growth and coercivity decrease are generally observed upon stress annealing. Frequency dependence of maximum GMI ratio for as-prepared and annealed samples is evaluated. The obtained frequency dependence of the maximum GMI ratio allows determination of the optimal GMI measurement conditions for each sample. The observed stress-induced anisotropy and related changes in magnetic properties are discussed considering the internal stresses relaxation and "back-stresses". This work was supported by Spanish MCIU under PGC2018-099530-B-C31 (MCIU/AEI/FEDER, UE), by the Government of the Basque Country under PIBA 2018-44 projects, by Russian Foundation for Basic Research (Grant 16-53-48012) and partially supported by Act 211 Government of the Russian Federation, contract # 02.A03.21.0011. The authors thank for technical and human support provided by SGIker of UPV/EHU and European funding (ERDF and ESF).

We report changes of coercivity, induced magnetic anisotropy, magneto-optical domain structure and frequency dependencies of coercivity and energy loss (up to 10 MHz) associated with the structural modifications produced by thermal treatments under applied magnetic field (field annealing) in toroidal wound cores of Fe 73.5 Cu 1 Nb 3 Si 15.5 B 7 amorphous alloy. The thermal treatment (535 °C, 1 h) leads to the typical nanocrystalline structure of α-Fe(Si) nanograins (60–65% relative volume, 10–20 nm average grain size embedded in a residual amorphous matrix, while the magnetic field with the possibility to be applied in two directions to the toroidal core axis, that is in transverse (which is equivalent to the transverse direction of the ribbon) or longitudinal (equivalent to the longitudinal direction of the ribbon), develops a macroscopic uniaxial magnetic anisotropy in the transverse (around 245 J/m 3 ) or longitudinal (around 85 J/m 3 ) direction of the ribbon, respectively. It is remarkable the quasi-unhysteretic character of the cores with these two kinds of field annealing as comparing with that of the as-quenched one. Magneto-optical study by Kerr-effect of the ribbons provides useful information on the domain structure of the surface in agreement with the direction and intensity of the induced magnetic anisotropy. This induced uniaxial magnetic anisotropy plays a very important role on the H c ( f ) and E L ( f ) curves, ( f : frequency), being drastic the presence and direction of the induced magnetic anisotropy. In addition, these frequency dependencies show a significant change at the frequency around 100 Hz.

The effect of Joule-heating on hysteresis loops and giant magnetoimpedance effect, GMI; of Co69.2Fe3.6Ni1B12.5Si11Mo1.5C1.2 glass-coated microwire is studied. Joule heating performed at suitable conditions prevents the magnetic hardening observed during conventional furnace annealing of the studied microwires. A remarkable GMI ratio improvement is observed as compared to as-prepared annealed and even stress-annealed microwires. Observed magnetic softening and GMI ratio improvement have been discussed considering magnetic anisotropy induced by Oersted magnetic field during Joule heating and internal stresses relaxation.

We studied the magnetic properties and domain wall (DW) dynamics of Fe 47.4 Ni 26.6 Si 11 B 13 C 2 and Fe 77.5 Si 7.5 B 15 microwires. Both samples present rectangular hysteresis loop and fast magnetization switching. Considerable enhancement of DW velocity is observed in Fe 77.5 Si 7.5 B 15 , while DW velocity of samples Fe 47.4 Ni 26.6 Si 11 B 13 C 2 is less affected by annealing. The other difference is the magnetic field range of the linear region on dependence of domain wall velocity upon magnetic field: in Fe 47.4 Ni 26.6 Si 11 B 13 C 2 sample is considerably shorter and drastically decreases after annealing. We discussed the influence of annealing on DW dynamics considering different magnetoelastic anisotropy of studied microwires and defects within the amorphous state in Fe 47.4 Ni 26.6 Si 11 B 13 C 2 . Consequently we studied the structure of Fe 47.4 Ni 26.6 Si 11 B 13 C 2 sample using X-ray diffraction and the atom probe tomography. The results obtained using the atom probe tomography supports the formation of the B-depleted and Si-enriched precipitates in the metallic nucleus of Fe-Ni based microwires.

Studies of magnetic properties and GMI effect of amorphous Co-Fe rich microwires reveal that they present GMI effect at GHz frequencies. Magnetic field dependences of GMI effect are affected by the post-processing conditions. In particular, we observed that in Co-Fe rich microwires stress-annealing allows improvement of frequency dependence of GMI ratio at high frequencies. We discussed observed experimental dependences considering both different magnetic structure and the anisotropy in the bulk and near the surface and close analogy between giant magnetoimpedance and ferromagnetic resonance.Studies of magnetic properties and GMI effect of amorphous Co-Fe rich microwires reveal that they present GMI effect at GHz frequencies. Magnetic field dependences of GMI effect are affected by the post-processing conditions. In particular, we observed that in Co-Fe rich microwires stress-annealing allows improvement of frequency dependence of GMI ratio at high frequencies. We discussed observed experimental dependences considering both different magnetic structure and the anisotropy in the bulk and near the surface and close analogy between giant magnetoimpedance and ferromagnetic resonance.

We observed a remarkable improvement of domain wall (DW) mobility, DW velocity, giant magnetoimpedance (GMI) effect and magnetic softening at appropriate stress-annealing conditions. Beneficial effect of stress-annealing on GMI effect and DW dynamics is associated with the induced transverse magnetic anisotropy. An improvement of the circumferential permeability in the nearly surface area of metallic nucleus is evidenced from observed magnetic softening and remarkable GMI effect rising. We assumed that the outer domain shell with transverse magnetic anisotropy associated to stress-annealing induced transverse magnetic anisotropy affects the travelling DW in a similar way as application of transversal bias magnetic field allowing enhancement the DW velocity. Observed decreasing of the half-width of the EMF peak in stress-annealed microwires can be associated to the decreasing of the characteristic DW width. Consequently, stress annealing enabled us to design the magnetic anisotropy distribution beneficial for optimization of either GMI effect or DW dynamics. This work was supported by Spanish MCIU under PGC2018-099530-B-C31 (MCIU/AEI/FEDER, UE), by the Basque Country Government under the PIBA 2018-44 project, by the University of Basque Country under the scheme of "Ayuda a Grupos Consolidados" (Ref.: GIU18/192), by the Russian Foundation for Basic Research (Grant 16-53-48012) and by Act 211 Government of the Russian Federation, contract #02.A03.21.0011. The authors thank for technical and human support provided by SGIker of UPV/EHU (Medidas Magneticas Gipuzkoa) and European funding (ERDF and ESF).

The Giant magneto-impedance (GMI) effect in the frequency range 10–1000 MHz and surface magnetic characterization using the magneto-optical Kerr effect (MOKE) in (Co63Ni37)75Si15B10 amorphous ribbon were studied. The GMI ratio increases with a frequency up to around 500 MHz followed by a slow decrease. Observed dependence of GMI ratio is discussed by considering the frequency dependencies of the skin depth penetration and magnetic permeability. MOKE in the transverse and longitudinal applied magnetic field to the ribbon direction configurations provides images of magnetic domain structure and hysteresis loops of the two surface sides of the ribbon. An inclined magnetic structure with respect to the longitudinal direction of the ribbon was observed. This inclined magnetic structure is related to a significant transverse component of the magnetic susceptibility tensor, which is a prerequisite to observe GMI effect. The magnetic anisotropy field evaluated from the hysteresis loop with the transverse applied magnetic field configuration is in agreement with the longitudinal magnetic field necessary to obtain the maximum GMI ratio. The MOKE characteristic of two sides ribbon is quite vertical associated to large Barkhausen jumps because the anisotropy axis is, in this configuration, parallel to the applied magnetic field.

We provide an overview of the routes allowing the optimization of magnetic softness, giant magnetoimpedance (GMI) effect and domain wall dynamics in one of the families of magnetic microwires: glass –coated microwires prepared using Taylor-Ulitovsky method. The magnetic properties of as-prepared microwires are determined mostly by the magnetoelastic anisotropy. Conventional annealing allows a considerable improvement of the domain wall dynamics in Fe-rich microwires and a slight decrease of the coercivity, however, remarkable magnetic hardening is observed after conventional furnace annealing of Co-rich microwires. Stress annealing of Fe-rich microwires allows a considerable magnetic softening and GMI effect enhancement and even more remarkable improvement of the domain wall dynamics. In Co-rich microwires stress-annealing allows the improvement of GMI effect and even the induction of transverse magnetic anisotropy at high enough annealing temperature. However, the highest GMI effect is observed for stress-annealed Co-rich microwires which present rectangular hysteresis loops. Consequently, annealed Co-rich microwires can present both, fast domain wall propagation and GMI effect. Observed induced anisotropy and related changes of the magnetic properties are discussed considering the internal stresses relaxation, “back-stresses” and circumferential magnetic field during proposed post-processing. Consequently, correctly designed post-processing enabled us to design the magnetic anisotropy distribution beneficial for the optimization of the GMI effect and the domain wall dynamics in magnetic microwires.

Joule heating of the Co-rich glass-coated microwire allows remakrable improvement of magnetic softness and giant magnetoimpedance effect. At optimal joule heating conditions we observed GMI ratio up to 650%, low magnetic anisotropy field of about 25 A/m and coercivity of about 2 A/m. Observed experimental dependencies are discussed considering various factors affecting the magnetic properties of studied microwire upon Joule heating: induced magnetic anisotropy, internal stresses relaxation and radial distribution of magnetic anisotropy.

We observed remarkable optimization of the magnetic softness in Fe-rich magnetic microwires by stress-annealing. It is found that the as-prepared Fe-rich microwires present rectangular hysteresis loops. The magnetic softness and magnetoimpedance effect of the Fe-rich microwires can be considerably improved by annealing. Observed stress-induced anisotropy and related changes of magnetic properties are discussed considering internal stresses relaxation and "back-stresses".

We studied the influence of AC current flowing through microwires, on magnetization dynamics. We used a previously developed Sixtus-Tonks modified setup to evaluate the domain wall (DW) velocity within the microwire. However, instead of a magnetizing solenoid, we used a current flowing through the microwire. We observed that the AC current flowing through the annealed Co-rich microwire leads to remagnetization by fast domain wall propagation. The estimated DW velocity was approximately 4.5 km/s, which is similar to and even higher than that reported for the magnetic-field-driven domain wall propagation in Fe- and Co-rich microwires. We measured the DW velocity under tensile stress, and found that the DW velocity decreases under applied stress. An observed DW propagation induced by the current flowing through the microwire is explained considering the influence of an Oersted magnetic field on the outer domain shell. This field has a circular easy magnetization direction and magnetostatic interaction between the outer circumferentially magnetized shell and the inner axially magnetized core.

We report on the magnetic properties and giant magnetoimpedance (GMI) effect of amorphous glass-coated Co-rich microwires in as-prepared and annealed states. The magnetic field and frequency dependences of GMI, magnetic hysteresis loops, and domain wall (DW) dynamics of ${\rm Co}_{69.2}{\rm Fe}_{4.1}{\rm B}_{11.8}{\rm Si}_{13.8}{\rm C}_{1.1}$ microwires produced by the Taylor–Ulitovski technique were investigated systematically. We have shown that these properties can be tailored either by controlling magnetoelastic anisotropy of the as-prepared microwires or by controlling their magnetic anisotropy via proper annealing. While the GMI effect has been achieved in an as-prepared microwire, high DW velocity and rectangular hysteresis loops have been observed in its annealed counterpart.

We studied effect of magnetoelastic anisotropy and role of defects on domain wall (DW) dynamics and remagnetization process of magnetically-bistable Fe-rich microwires. We manipulated the magnetoelastic anisotropy applying the tensile stresses. Application of stresses resulted in decrease of the DW velocity v, and DW mobility S. Consequently, we observed certain correlation between the magnetoelastic energy and DW dynamics in microwires: decreasing the magnetoelastic energy, Kme, DW velocity can be increased. We are trying to reveal contribution of local defects on DW propagation in amorphous microwires. Below some critical magnetic field, Hn, determined by the microwires inhomogeneities, almost linear DW velocity, v on magnetic field, H, dependence is found. When the applied magnetic field exceeds Hn, new reverse domains can be nucleated and consequently tandem remagnetization mechanism can be realized. The role of defects existing in magnetically bistable microwires is related with nucleation of new reversed domains. Abrupt jumps on v(H) dependences correlate with defects existing in microwires. Magnetic field value, corresponding to such jump on v(H) dependences, correlates with the minimum nucleation field, which determines threshold between single and multiple domain wall propagation regimes. In the latter case, under the action of the magnetic field, a new domain can be spontaneously nucleated in front of the propagating head-to-head closure domain. In this way real structure of microwires limits single DW propagation regime.

In this paper we studied effect of transversal magnetic field, magnetoelastic anisotropy and defects on DW dynamics of amorphous microwires. We observed that the viscous single DW region is limited by the samples defects, which determine the threshold between single and multiple domain wall propagation regimes.

IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, SpainWe studied effect of magnetoelastic anisotropy and role of defects on domain wall (DW) dynamics andremagnetization process of magnetically-bistable microwires. We manipulated the magnetoelastic anisotropychanging the ratio between the metallic nucleus diameter and glass coating thickness and applying the tensilestresses. Application of stresses resulted in increase of the switching field and decrease of the DW velocity, v. Therole of defects existing in magnetically bistable microwires is related with nucleation of new reversed domains.Abrupt jumps on v(H) dependences correlate with defects existing in microwires. Annealing allows considerablyincrease DW velocity, enhances the magnetic field range of single DW propagation regime and domain wall mobility.Key words: amorphous microwires, domain wall dynamics, magnetic anisotropy1. IntroductionStudies of domain wall (DW) propagation in thinmagnetic wires prepared by different methods attractedgrowing attention during last few years [1, 2]. Maintechnological interest is related with proposedapplications involving the information storage,magnetic sensors and logics. For aforementionedapplications the DW speed and the ways for the DWdynamics manipulation are essentially relevant.Reported DWs propagation can be driven by themagnetic field as well as by the electric current flowingthrough the sample. The DW velocity is determined bythe magnetic field value as well as by the shape anddimensions of the wires [1, 3-6]. Thus, for amorphousmicrometric wires with circular cross section fastest DWvelocity (exceeding 1000 m/s) have been reported [7,8].Additionally the DW velocity, v, depends on themagnetoelastic anisotropy depending on themagnetostriction constant value as well as on theinternal or applied stress [9]. On the other hand, forcontrolling the DWs dynamics in thin wires (either withrectangular or cylindrical cross-section), fewmechanisms involving the DW injection, creation ofartificial defects and inhomogeneities, controllable DWcollision etc have been reported [9, 10].Studies of glass-coated microwires withferromagnetic nucleus attracted considerable attentionwithin last few years owing to their reduced dimensionsand unusual soft magnetic properties such asspontaneous magnetic bistability, Giantmagnetoimpedance effect and high magneticpermeability. Magnetic bistability is related with largeand single Barkhausen jump observed in amorphousmicrowires with positive magnetostriction constant isparticularly interesting for studies of the DWpropagation within the inner core of microwire [5-7, 11].On the other hand giant magneto-impedance, GMI,effect and extremely soft magnetic properties can beuseful for magnetic sensors applications [12, 13].Abovementioned magnetic bistability observed inamorphous glass-coated microwires with positivemagnetostriction constant is related with fastmagnetization switching of a large single axiallymagnetized domain by fast DW propagation of a singleDW [5-8, 11, 13]. Therefore these microwires are uniquematerial allowing studying the magnetization dynamicsof a single DW in a cylindrical micrometric wire.Appearance of such peculiar domain structureconsisting of a large single axially magnetized domainsurrounded by outer radially magnetized shell isdetermined by the stresses arising during rapidsolidification of composite thin wire [5, 13-17]. Thestrength of these stresses originated from the differencein thermal expansion coefficients of the metal and glassis determined by the volumes of metallic nucleus andglass coating [14-16]. Consequently the magneticsoftness of glass-coated microwires is determined by themagnetoelastic anisotropy originated from thecomposite character being also depending on themetallic nucleus composition and ratio between themetallic nucleus diameter, and total microwirediameter.Consequently fast magnetization switching ofmicrowires is related with the propagation of the singlehead-to head DW along the wire.Recently we reported, that the samplesinhomogeneities, observed through the measurementsof the distribution of the local nucleation fields, H

We studied magnetic properties and domain propagation in thin magnetic amorphous microwires Fe72 75Co2 25B15Si10. At low metallic nucleus diameters considerable increase of switching field has been observed. Dependence of domain wall velocity, v , measured by abovementioned method shows roughly linear dependence on applied magnetic field, H, achieving about 850 m/s at 18 Oe. This velocity is somehow smaller as compared with similar microwires compositions of thicker diameter. Probably, magnetoelastic contribution plays an important role in domain wall propagation. Results are discussed taking into account the magnetoeleastic contribution.

We have investigated the application of the magnetoimpedance (MI) effect in amorphous microwires for absolute position detection and demonstrated that MI elements arranged in 1D and 2D arrays can be used for contactless proximity and position sensing of a magnetic label attached to an object to be detected. Owing to the high sensitivity of the MI elements to the stray magnetic field produced by the magnetic label, the required density of the MI elements can be rather low, which allows the designing of low-cost in situ reconfigurable sensor networks. An example of application of a 2D proximity and position sensing device for wireless power transfer is considered.

We report on studies of domain wall propagation of magnetically-bistable Fe-Co-rich microwires paying attention on the effect of applied and internal stresses. We measured magnetic domain propagation in various magnetic Fe-Co-rich amorphous microwires with metallic nucleus diameters (from 2.8 microm to 18 microm) using Sixtus Tonks-like experiments. We found that application of applied stresses and increasing of internal stresses result in decreasing of domain wall (DW) velocity. We assume that in order to achieve higher DW propagation velocity at the same magnetic field and enhanced DW mobility, special attention should be paid to the decrease of magnetoelastic energy.

In this paper we experimentally studied GMI effect and soft magnetic behavior of Co-rich microwires. Correlation between magnetoelastic anisotropy and magnetic field dependences of diagonal and off-diagonal impedance components are observed. Low field GMI hysteresis, explained in terms of magnetoelastic anisotropy of microwires, has been suppressed by the bias current.

We studied the domain wall (DW) propagation of magnetically-bistable Fe–Co-rich microwires paying attention to the effect of applied and internal stresses. Magnetic field, H, dependences of DW velocity, v, were measured in Co41.7Fe36.4Si10.1B11.8 microwires with metallic nucleus diameters (from 13 μm to 18 μm) and with different ρ-ratio between the metallic nucleus diameter, d, and total microwire diameter, D. DW velocity decreased under the application of stresses. From measured dependences we evaluated DW mobility, S, dependence on the applied stresses. The results obtained for Co41.7Fe36.4Si10.1B11.8 sample show that S decreases with the increasing of applied stresses, σa. The observed dependences manifest that increasing of magnetoelastic anisotropy results in the decreasing of DW mobility and DW velocity

In this paper, we experimentally studied the effect of applied and residual stresses on the domain-wall (DW) velocity in amorphous Fe-Co-based microwires. We found that application of applied stresses and an increase of internal stresses result in decrease of DW velocity. We assume that in order to achieve higher DW propagation velocity at the same magnetic field and enhanced DW mobility, especial attention should be paid to decrease of magnetoelastic energy.

In this work we study the effect of applied stresses on magnetic-domain propagation in magnetic amorphous Fe-Co based microwires using Sixtus―Tonks-like experiments. The dependence of domain-wall (DW) velocity, v, measured by the above-mentioned method shows a roughly linear dependence on applied magnetic field, H. We experimentally studied the effect of applied stresses on single DW dynamics in a number of Fe-Co rich microwires. Quite fast DW propagation (ν up to 2500m/s at H about 30 A/m) has been observed in low magnetostrictive Co 56 Fe 8 Ni 10 Si 10 B 16 microwires. Applied and internal stresses result in decreasing of DW velocity. The observed dependences have been discussed considering the magnetoelastic contribution to the DW mobility.

We are trying to reveal the contribution of local defects on DW propagation in amorphous microwires. Con- sequently, we present a comparative study of single domain wall dynamics and local nucleation fields in Fe- and Co-rich amorphous glass-coated microwires. For this we modified experimental set-up based on the classical Sixtus-Tonks ap- proach introducing additional pick-up coil in order evaluate defects contribution in domain wall propagation. Below some critical magnetic field, HN , determined by the microwires inhomogeneities, an almost linear DW ve- locity, v, dependence on magnetic field, H , is found. Quite fast DW propagation (v till 3000 m/s at H about 65 A/m) has been observed. When the applied magnetic field ex- ceeds HN , new reverse domains can be nucleated and con- sequently tandem remagnetization mechanism can be real- ized. The role of defects existing in magnetically bistable microwires is related with nucleation of new reversed do- mains.

The remagnetization process of Fe-rich wires as dependent on the circular magnetic field induced by the AC current flowing through the wire is investigated experimentally. We present the dependence of the switching field on the amplitude and frequency of the circular magnetic field and its variance with the applied tensile stress. The results are interpreted in terms of magnetic domain structure of the wire.

The giant magneto-impedance (GMI) attracted growing attention especially owing to the large sensitivity of the electrical impedance to the DC magnetic field, when the relatively high-frequency electrical current flows along the magnetic conductor. Such GMI effect is the highest in soft magnetic wires with vanishing magnetostriction constant. The last strong tendency in miniaturization of the magnetic sensing elements has resulted in the development of the thinner glass-coated wires produced by the Taylor–Ulitovsky method (1–30 μm in diameter). Recent significant progress in tailoring of magnetically soft Co-rich glass-coated microwires allows to enhance significantly the GMI ratio (up to about 600%) in compositions with vanishing magnetostriction constant, λ s , at frequencies between 100 kHz and 20 MHz. In this paper we report novel results on the GMI effect at high-frequency region (between 10 MHz and 500 MHz) in different families of amorphous microwires (Fe-rich, with positive magnetostriction constant, Co-rich with negative magnetostriction constant and Co–Fe-rich with nearly-zero magnetostriction constant) fabricated by the Taylor–Ulitovsky method. The differences in observed dependencies for these families of compositions have been interpreted in terms of difference in the magnetoelastic anisotropy.

In this paper we studied the hysteresis loop and GMI effect (real component of impedance, Z, and the off-diagonal impedance tensor ζ Φz (H ex )) in ultra-thin amorphous glass-coated microwires with nearly-zero and negative magnetostriction constant with metallic nucleus diameter ranging from 6 μm to 16 μm paying special attention to the effect of the metallic nucleus diameter on the aforementioned properties. Both GMI effect and hysteresis loops of nearly-zero magnetostrictive Co 67.1 Fe 3.8 Ni 1.4 Si 14.5 B 11.5 Mo 1.7 microwires exhibit strong sensitivity to the ratio, p, the metallic nucleus diameter, d, to the total microwire diameter, D. Selecting the right chemical composition we achieved low coercivity (generally below 15 A/m). The magnetic anisotropy field, H k , increases when p decreases. The shape of the magnetic field dependence of Z is also affected by the ρ-ratio. The field dependence of the off-diagonal voltage response of nearly zero magnetostrictive (λ s ≈ -3 x 10 -7 ) Co 67.1 Fe 38 Ni 1.4 Si 14.5 B 11.5 Mo 1.7 microwires with metallic nucleus diameters ranging between 6.0 μm and 16.8 μm exhibits anti-symmetrical shapes. At certain magnetic field, H m , the off-diagonal voltage reaches the maximum value. Between -H m and H m at certain field range almost linear dependence of the off-diagonal voltage on magnetic field has been observed. This linear region of the curve depends on microwires geometry, but in any case is smaller than whole -H m to H m range. Joule heating significantly affects the off-diagonal MI curves of Co 67.1 Fe 3.8 Ni 1.4 Si 14.5 B 11.5 Mo 1.7 microwires with vanishing magnetostriction constant. Under DC current annealing the H m decreases. The obtained results allow us to tailor the microwire magnetic properties for applications in magnetic sensors through the selection of their composition and/or thermal treatment conditions.

Off-diagonal component of magneto-impedance tensor with pulse excitation is very promising for high sensitivity magnetic field sensor applications. We report novel results on studies of off-diagonal MI effect and magnetic properties in amorphous glass-coated microwires with nearly-zero and negative magnetostriction constant and metallic nucleus diameter ranging between 6 μm and 10 pm. Off-diagonal impedance tensor ζ φz (H ex ) has been investigated in ultra-thin amorphous glass-coated microwires in as-cast state and after Joule heating treatment.

We studied the velocity of domain wall propagation, v, of Fe 69 Si 10 B 15 C 6 with different metallic nucleus diameter, d, and different total diameter, D (d = 14 μm, D = 33 μm and d= 18 μm, D = 23.4μm, respectively) in the temperature range between 78 and 300K and at different frequencies of applied magnetic field. It is worth mentioning that v(H) dependence is essentially not linear, showing significantly higher domain wall mobility, S=dv/dH, at lower field limit. Domain wall mobility, S, increases significantly with increase in temperature. From v(H) dependence, the critical field, H cr , associated with the change of the slope on v(H) dependence and critical propagation fields H 01 and H 02 for the lower and higher field regions, respectively, are determined. All characteristics, v(H) dependence, S(H) dependence and Her are sensitive to the sample geometry, i.e., to the internal stresses. The origin of such dependence on internal stresses is discussed in terms of magnetoelastic energy contribution.

The giant magneto-impedance (GMI) effect has been studied in 3 different families of amorphous wires: con- ventional amorphous wires (125 μm in diameter), cold drawn wires (50 and 20 μm in diameter) and thin glass coated amorphous microwires (with metallic nucleus diameter of about 15 μm). These wires have been investigated in the fre- quency range 1 - 500 MHz. A remarkable difference in the magnetic field dependence of the GMI effect can be attributed to the different magnetoelastic anisotropy of these three families of the wires.

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.

We studied Giant magnetoimpedance (GMI) effect and magnetic properties of amorphous Fe-Co rich as-prepared and annealed microwires. We measured the GMI magnetic field and frequency dependences, hysteresis loops and domain walls (DWs) dynamics of composite microwires produced by the Taylor-Ulitovski technique. We observed that these properties can be tailored either controlling magnetoelastic anisotropy of as-prepared CoFeBSiC microwires or controlling their magnetic anisotropy by heat treatment. High GMI effect has been observed in as-prepared Co-rich microwires. High DW velocity and rectangular hysteresis loops we observed in heat treated Co-rich microwires. We observe increasing of the DW velocity under stress in some annealed samples. At certain annealing conditions we observed coexistence of GMI effect and fast DW propagation in the same annealed sample.

Experimental and theoretical studies on the influence of ac magnetic field frequency on the axial diagonal (ζzz) and off-diagonal (ζz) components of the magnetoimpedance (MI) tensor in (Co0.94Fe0.06)72.5Si12.5B15 amorphous wires have been performed. The frequency (f) of an ac current flowing along the wire was varied from 1 to 20 MHz with the current amplitude less than 15 mA. In order to enhance the ζz component, the amorphous wire was submitted to torsion annealing for developing and preserving a helical magnetic anisotropy in the surface of the wire. The experimental measurements show that the value of the impedance is proportional to the square-root of the ac current frequency, , in the vicinity of Hex < HK and this increase is due to the contribution of the resistance (real part of the impedance). The measurements also indicate that the peaks of the MI curve shift slightly towards higher field values with increasing f.In a theoretical study the magnetoimpedance expressions ζzz and ζz have been deduced using the Faraday law in combination with the solutions of the Maxwell and Landau–Lifshitz–Gilbert (LLG) equations. By analysing quantitatively the spectra of ζzz and ζz, the phenomenon of the shift in the peaks of the MI curve with f has been considered as a characteristic of the helical anisotropy in the domain structure of the wire surface.

The effect of high frequency electric current on surface coercive properties has been studied in glass covered Co-rich amorphous microwires. The experiments have been carried out using the transverse magneto-optical Kerr effect in a circular magnetic field. During the experiments, an additional electric current with the frequency of 50 kHz - 80 MHz has been applied to the wire. The strong influence of the high frequency current on the circular switching field has been found. Also it has been discovered that the high frequency current induces the appearance of circular bistability in small circular magnetic fields. The results obtained have been discussed in the frame of thermoactivation mechanism of the nucleation of the circular magnetic domains and domain wall propagation. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The influence of an ac magnetic field and the induced magnetic anisotropy (by field annealing and torsion annealing) on the magnetoimpedance (MI) tensor in an amorphous wire has been analysed. The experimental measurements were carried out in an amorphous wire of composition (Co0.94Fe0.06)72.5Si12.5B15, with a negative, nearly zero magnetostriction constant, excited either by an ac circular, h, or an axial, hz, magnetic field created by an ac electric current passing along the wire or through an exciting coil mounted on the wire, respectively. The ac current amplitude was changed from 7.5 to 40 mA and the current frequency f was varied from 1.5 to 20 MHz. The induced magnetic anisotropies modify the MI response drastically. The field annealed sample shows a unique peak of the MI effect, while the torsion annealed sample presents an asymmetric giant magnetoimpedance ratio associated with the induced magnetic anisotropy which provokes such thermal treatments.

We have performed experimental and theoretical studies on the influence of ac magnetic field amplitude on the magnetoimpedance tensor in an amorphous wire with helical magnetic anisotropy. For the experimental measurements, we used an amorphous wire of composition (Co/sub 0.94/Fe/sub 0.06/)/sub 72.5/Si/sub 12.5/B/sub 15/ with negative, nearly zero magnetostriction constant, excited either by an ac circular h/sub /spl phi// or by an axial h/sub z/ magnetic field created by an ac electric current. We changed the ac current amplitude from 7.5 to 40 mA and the current frequency f from 1.5 to 20 MHz. The values of the asymmetric giant magnetoimpedance ratio associated with the sweeping direction of the dc field H/sub ex/ and the corresponding sensitivity were 211% and 0.64 V/Oe, respectively, for an ac current of 37.5 mA at 3 MHz. For the theoretical study based on the magnetization rotation, we obtained the second-order harmonic of the ac magnetization m/spl I.oarr//sup (2)/ induced by the relatively high ac magnetic field by solving the Landau-Lifshitz-Gilbert (LLG) equation. We also considered a second-order surface impedance tensor /spl sigmav//spl circ//sup (2)/, which allowed us to analyze quantitatively the influence of the ac magnetic field amplitude on the impedance tensor of the wire. We obtained the domain model of the wire with helical magnetic anisotropy having multidomains and the magnetization vector /spl plusmn/M/sub 0/ directed in the easy direction, and the corresponding static magnetic configurations, by solving the static LLG equation. For the given magnetic configurations, we calculated the second-order impedance tensor /spl sigmav//spl circ//sup (2)/. The results can well explain the irregular field characteristics of the voltage responses at low dc field value, when the wire was excited at high frequency and at large ac magnetic field.

Magnetic properties of Fe-rich amorphous wires, prepared by in-rotating-water-quenching technique and submitted to a post cold-drawing process (to reduce the initial diameter) have been studied. The experiments have been performed using magneto-optical Kerr effect and fluxmetric methods in crossed axial and circular magnetic fields. The helical magnetic structure has been found in the surface and in the volume of the wire. The angle of helical anisotropy has been evaluated to be around 45° with respect to the axial direction at the surface of the wire decreasing to 39° through the volume of the wire.

The effect of the length sample and applied tensile stress on the hysteresis loop of a Co 72.5 Si 12.5 B 15 amorphous wire has been investigated at the amplitude of applied field just above the switching field. The character of the hysteresis loop changes with the length as well as with the applied stress. Measurements of the magnetic remanence were made by displaying the hysteresis loop of the center of the wire as well as the local hysteresis loop in different points along the wire. Experimental results can be satisfactorily explained by the generalization of the outer-shell model developed for a Co-rich amorphous wire of finite length exhibiting negative magnetostriction, where the outer-shell magnetization configuration is a consequence of a radial dependence of the residual tensile stress.

Investigations of magnetization reversal in Co-rich amorphous glass-covered microwires were performed using the magneto–optical Kerr effect in perpendicular axial and circular magnetic fields. The magnetization reversal consists of the rotation of the magnetization and nucleation of the circular domain in the outer shell of the microwire. The model, which takes into account the influence of DC electric current on the nucleation process, has been applied.

In bistable magnetic wires, the switching field H ∗ is an applied magnetic field sufficient to remagnetise a wire. The spectrum of the fluctuations of H ∗ depends on temperature. We demonstrate that this effect leads to a maximum of the thermal dependence of the amplitude of the wire magnetisation.

Investigations on the magnetic reversal in a system of two glass-covered Co-rich amorphous microwires with circular bistability have been performed using the magneto-optical Kerr effect technique. The experimental configuration, when the electric current producing the circular magnetic field flows through the wires in opposite directions, has been employed first for the glass-covered microwires. The peculiarities of the obtained hysteresis loops reflect the influence of the axial stray fields produced by the inner cores of the microwires on the circular magnetization reversal in the outer shells of the neighbouring microwires of the system. The experimental results have been analysed considering the mutual influence of microwires in the condition of the circular bistability effect.

Investigations on the magnetic reversal in amorphous wire (diameter 125 μm) of nominal composition (Co 94 Fe 6 ) 72.5 Si 12.5 B 15 and glass-covered microwires (diameter around 20 μm) of nominal composition (Co 1− x Mn x ) 75 Si 10 B 15 (0.07 x x =0.07 can be interpreted by considering that the magnetization process takes place by large Barkhausen jumps of circular domain structure, while the rectangular shape of the hysteresis loop with axial magnetic field of the microwire x =0.11 could be connected to large Barkhausen jumps inside the axial domain structure.

Investigation of surface domain walls motion in Co-rich magnetic microwires has been performed in circular and axial magnetic fields. The dc axial magnetic field acceleration of the domain wall motion related to the influence of the axial field on the structure of the moving domain wall has been discovered. Pulsed axial magnetic field induced unidirectional motion of surface domain wall also has been found.

The technique of coupled map lattices is applied to investigate the time dependence of magnetization of a set of bistable wires. Subsequent moments of time tk, between which the mapping is performed, are chosen when a domain wall within a wire starts to move or stops. Iterative maps are formed by means of the integration of the equations of motion of the domain walls. The system is proved to be piecewisely integrable, and it does not exhibit chaos in long time limit. However, the Lyapunov exponent determined numerically is positive during a transient time. For small amplitude of the applied magnetic field, more than one limit cycle is found. Observed random long-time behaviour can be assigned to thermal fluctuations of the switching field, which shift a trajectory from one limit cycle to another one. We show also some experimental results on the hysteresis loops of Fe77.5B15Si7.5 and on the fluctuation distribution of the switching field.

Spontaneous experimental spread, Δ H s , of the switching field, H s , (switching field fluctuations) during the re-entrant magnetization process of Fe-rich (Fe 65 Si 15 B 15 C 5 ) microwire (metallic nucleus diameter of around 10 μm) exhibiting rectangular hysteresis loop has been observed at room temperature. Shape of the switching field distribution has been measured and analyzed in terms of a thermoactivational mechanism. The model predicts the lineal dependence of the logarithm of Barkhausen jump probability, d w , on reduced switching field fluctuation, Δ h =Δ H s / H sm . Observed d w (Δ h ) dependence fits satisfactorily to the predicted semi-logarithmic dependence.