Tuning of magnetic bistability and domain wall dynamics in magnetic microwires

A unique combination of unusual magnetic properties, such as magnetic bistability associated with ultrafast domain wall propagation or ultrasoft magnetic properties, together with excellent mechanical and corrosion properties can be obtained in amorphous microwires. Such ferromagnetic microwires coated with insulating and flexible glass-coating with diameters ranging from 0.1 to 100 can be prepared using the Taylor-Ulitovsky method. Magnetic properties of glass-coated microwires are affected by chemical compositions of the metallic nucleus and can be substantially modified by post-processing. We provide an overview of the routes allowing tuning of hysteresis loops and domain wall dynamics in amorphous microwires and new experimental results on the dependence of hysteresis loops on external stimuli, such as applied stress and temperature.

Introduction.-Magnetic materials of cylindrical shape have attracted continuous attention for many years due to their unusual magnetic properties suitable for various technological applications [1,2].The development of technology for the preparation of magnetic materials allowed to substantially improve physical properties (mechanical, corrosion) of magnetic wires.Thus, use of rapid melt quenching is suitable for preparation of amorphous magnetic materials with superior mechanical and corrosion properties [3][4][5][6].However, the main distinctive feature of amorphous materials is their excellent magnetic softness [7][8][9].In the case of amorphous magnetic wires excellent magnetic softness is combined with other properties, like giant magnetoimpedance (GMI) effect or magnetic bistability related to remagnetization through fast domain wall (DW) propagation [9][10][11][12][13].
(a) E-mail: arkadi.joukov@ehu.es(corresponding author) Both the above-mentioned phenomena, the GMI effect and magnetic bistability, have attracted considerable attention owing to both fundamental physical interest and numerous promising technological applications.Thus, the extraordinary high magnetic field sensitivity (up to fewhundred-percent change of impedance under applied magnetic field) is attractive for the development of magnetic sensors and magnetometers and smart composites with magnetic microwire inclusions [10,[14][15][16].On the other hand, fast and controllable DW propagation was proposed for magnetic logics and memory applications [17,18], while magnetic bistability was involved in electronic article surveillance, magnetic and magnetoelastic sensors applications [10,19,20].
Recent development of the fabrication methods for preparation of amorphous wires allowed to substantially extend the diameters range towards nanoscale and simultaneously provide the biocompatibility and improve the corrosion resistance and mechanical properties by using glass-coating microwire preparation method.Using this method (commonly called Taylor-Ulitovsky) glasscoated microwires with metallic nucleus diameters, d, from 0.1 to 100 μm covered by thin insulating and flexible glass-coating (typically of a few μm thickness) and up to few km in length can be prepared within a few minutes [21][22][23].
Evidently, optimization of the GMI effect and the DW dynamics are essentially relevant for the proposed applications.Most of previous publications deal with studies of as-prepared glass-coated microwires, paying the main attention to the effect of chemical composition or geometry on magnetic properties [24].However, magnetic properties of glass-coated microwires can be substantially affected by post-processing.Accordingly, this paper is focused on engineering of hysteresis loops and DW dynamics in amorphous glass-coated microwires by appropriate post-processing and on new experimental studies of the effect of external stimuli, such as applied stress and temperature, on hysteresis loops of amorphous glass-coated microwires presenting magnetic bistability.
Experimental details and samples preparation.-We studied Fe-, Fe-Co-and Fe-Co-Ni-based glass-coated microwires with either positive or low negative magnetostriction coefficients, λ s , using the modified Taylor-Ulitovsky technique, described in detail elsewhere [21][22][23].Briefly, the fabrication process consists of melting a preprepared metallic alloy (usually weighing a few grams) using a high-frequency inductor (typically 350-500 kHz) inside a Pyrex-like glass tube, forming a capillary from the softened glass tube (see fig. 1).The molten metallic alloy then fills the glass capillary, forming a microwire with a metallic nucleus completely covered by a continuous, thin and flexible glass coating (see fig. 1(c) for the Fe 75 B 9 Si 12 C 4 microwire).Such glass-coated microwire is drawn through the inductor and captured by a rotating receiving spool [22][23][24].The coolant stream (see fig. 1(b)) allows to obtain amorphous microwires by achieving a sufficiently high quenching rate [23].As demonstrated [23], such glass-coated microwires present rather homogeneous metallic nucleus diameters and glass-coating thickness (see fig. 1(d  The chemical compositions, metallic nucleus, d, and total, D, diameters and magnetostriction coefficient, λ s , values of the studied microwires (average values obtained from at least 10 measurements) are provided in table 1.
The fluxmetric method, previously developed for characterization of magnetically soft microwires and described in detail elsewhere [25], was used for the hysteresis loops measurements.The studied samples, placed inside the 120 mm long and thin (8 mm in diameter) solenoid, were magnetized by a homogeneous axial magnetic field, H.The magnetization was measured by pick-up coils surrounding the samples and placed coaxially inside the solenoid [25].The hysteresis loops were represented as the normalized magnetization M/M o vs. H (being M o the magnetic moment of the sample at maximum magnetic field amplitude H o ).
The magnetostriction coefficient, λ s , of studied microwires was evaluated using the small angle magnetization rotation (SAMR) method, recently adapted for measurements of magnetic microwires [30].
The DW dynamics was measured using the modified Sixtus-Tonks technique, described elsewhere [31].In this method the DW velocity, v, is determined using the pickup coils placed along the microwire.Knowing the distance, l, between such pick-up coils and the time difference, Δt, between the induced electromotive force (EMF) peaks in-  duced in pick-up coils by travelling DW, we can estimate the v value as Magnetic properties were measured in as-prepared and annealed (at temperatures, T ann , below the crystallization) microwires [5].
Experimental results and discussion.-The hysteresis loops of as-prepared glass-coated microwires are affected by the chemical composition: the rectangular hysteresis loops with coercivity, H c , about 100 A/m are observed for Fe-rich and Fe-Ni-rich microwires with positive λ s (see fig. 2(a), (b)), while almost linear hysteresis loops with an order of magnitude lower H c are typical for as-prepared Co-rich microwires (see fig. 2(c)).
The magnetic softness (i.e., high magnetic permeability) is the main prerequisite for the GMI effect optimization.Therefore, most efforts in optimization of magnetic softness and GMI effect were focused on Co-rich microwires [32,33].
On the other hand, perfectly rectangular axial hysteresis loops observed for magnetic microwires with positive λ s values (Fe-or Fe-Ni-rich microwires) are related to the magnetic bistability and remagnetization process through the DW propagation [31,34].The demagnetized state cannot be observed in magnetically bistable microwires.As experimentally shown [12,31], the DW propagation starts from the microwire ends, where the closure domains exist because of the demagnetizing field effect.Accordingly, single DW propagation can be studied in amorphous magnetically bistable wires [31,34].
The correlation of the hysteresis loops character and λ s values and sign is commonly attributed to the magnetoelastic anisotropy, K me , given as [11,12,30] where σ = σ i + σ app is the total stresses, σ i and σ app are the internal and applied stresses, respectively.In the absence of applied stresses, the internal stresses magnitude and distribution are a relevant factor affecting the magnetic anisotropy of glass-coated microwires.The preparation process involving rapid solidification of the metallic alloy inside the glass-coating with rather different thermal expansion coefficients results in the onset of elevated internal stresses with predominantly axial origin in most part of the metallic nucleus volume [21][22][23].The magnitude of the internal stresses is affected by the glasscoating thickness, d and D values.In the most simplified approximation σ i has been expressed, as [21,23] σ φ = σ r = P = εEkΔ/(k/3 + 1)Δ + 4/3, being σ φ , σ r and σ z circular, radial and axial stresses, Δ = (1−ρ 2 )/ρ 2 , k = E g /E m , E m , E g are the Young modulus of metallic alloy and glass, ε = (α m −α g )(T m −T room ),  The example provided below (see fig. 3) confirms the significant influence of internal stresses through the ρ-ratio on the hysteresis loops: with an increase in the ρ-ratio (a decrease in the σ i value), the coercivity, H c , decreases in Fe-rich microwires of the same chemical composition.
Recently, it was shown experimentally that various postprocessing (mainly annealing) can effectively modify the magnetic anisotropy and hence hysteresis loops of glasscoated microwires [23,24].Below we will provide several routes allowing tuning of hysteresis loops and DW dynamics.The commonest way to release internal stresses is thermal treatment.Therefore, the internal stresses relaxation by annealing is the simplest and quite effective method for DW dynamics optimization [34].One of the examples is provided in fig.4, where the influence of annealing on hysteresis loops and DW dynamics of Fe 75 B 9 Si 12 C 4 microwire is shown.Although the hysteresis loops after annealing (T ann = 400 • C, annealing time, t ann = 180 min) at room temperature remain almost unchanged (see fig. 4(a)), a substantial increase of DW velocity, v, is evident from the comparison of v(H) for as-prepared and annealed Fe 75 B 9 Si 12 C 4 microwire (see fig. 4(b)).The voltage peaks (shown in the inset to fig.4(b)) in the pickup coils located along the studied microwire are caused by the propagating DW.
As discussed elsewhere, the v(H) dependences can be described as follows [31,34]: where S is the DW mobility and H 0 is the critical propagation field.Observed substantial improvement of v and S values upon annealing was attributed to the magnetoelastic anisotropy, K me , contribution in the DW dynamics.Thus, the domain wall mobility, S, is affected by the domain wall width, δ w [31,34]: where A is the exchange stiffness constant and K is the magnetic anisotropy constant.On the other hand, in amorphous materials the main source of magnetic anisotropy is the magnetoelastic anisotropy, K me .Initially, better DW dynamics is expected in Fe-Nibased microwires with lower λ s .
However, a substantial magnetic hardening is experimentally observed in Fe-Ni-based microwires, evidenced by the hysteresis loops of as-prepared and annealed Fe 62 Ni 15.5 Si 7.5 B 15 and Fe 49.6 Ni 27.9 Si 7.5 B 15 microwires (see figs.5(a), 6(a)).The origin of such magnetic hardening was attributed to the DW stabilization owing to the ordering of the atomic pairs previously reported in Fe-Ni alloys [35,36].
Similarly to Fe-rich microwires, a substantial DW dynamics improvement is observed in Fe 62 Ni 15.5 Si 7.5 B 15 microwires (see fig. 5(b)).However, the DW dynamics of Fe 49.6 Ni 27.9 Si 7.5 B 15 microwires is less affected by annealing: even lower v values were obtained upon annealing (see fig. 6(b)).Such anomalous behaviour of Fe 62 Ni 15.5 Si 7.5 B 15 microwires has been related to the Invar-like composition (Ni/Fe content about 40/60).The peculiarity of the Invar alloys is a low thermal expansion coefficient.Therefore, a lower influence of internal stresses on magnetic properties and hence on DW dynamics is expected [36].
Even more unexpected is the magnetic hardening observed in Co-rich microwires upon annealing.In The origin of the observed magnetic hardening, observed in several Co-rich microwires, is attributed to the effect of annealing on λ s value and sign: a change from negative to positive λ s is experimentally confirmed in such Co-rich microwires [30].
Accordingly, room temperature hysteresis loops of Fe-rich microwires present improved thermal stability.
The hysteresis loops of Fe-rich microwires maintain the rectangular shape upon application of tensile stress (see fig. 8(a)).Therefore, applied stress dependence of hysteresis loops of Fe-rich microwires looks promising for stresses monitoring.However, the hysteresis loops character of Ferich microwires changes upon heating: a gradual transfor- However, additional studies are needed to improve thermal stability.On the other hand, it should be emphasized that heat treatment of glass-coated microwires can effectively improve the DW dynamics and tune the hysteresis loops.In addition, magnetic bistability in Co-rich microwires can be induced by annealing.However, magnetic bistability in Fe-rich microwires disappears when heated above 100 • C and is restored when cooled to room temperature.
) for the Fe 70 B 15 Si 10 C 5 sample).The samples were prepared in the laboratory of magnetism of the University of Basque Country.

Fig. 1 :
Fig. 1: Image (a) and scheme (b) of the experimental setup for fabrication of microwires and optical microscopy images of Fe75B9Si12C4 (c) and Fe70B15Si10C5 (d) microwires.

Fig. 4 :
Fig. 4: Hysteresis loops (a) and v(H) dependences (b) of asprepared and annealed at Tann = 400 • C Fe75B9Si12C4 microwire.The voltage peaks induced by the propagating DW in the 3 pick-up coils in as-prepared sample are shown in the inset of fig.4(b).

Fig. 8 :
Fig. 8: Effect of applied stresses (a) and heating (b) on hysteresis loops of as-prepared Fe75B9Si12C4 microwires.Low field hysteresis loops measured at room temperature and at 100 • C are provided in the inset of panel (b).Hysteresis loops of Fe75B9Si12C4 microwires measured before and after heating to 300 • C (c).