Bimagnetic Microwires, Magnetic Properties, and High-Frequency Behavior

Abstract

Bimagnetic microwires are cylindrically multilayered systems consisting of two magnetic metallic microlayers, a cylindrical nucleus, and an external shell, separated by an insulating layer. Such microwires are synthesized by combined quenching and drawing, sputtering, and electrodeposition, and the magnetic configuration of each phase can be suitably tailored to result in soft/soft, soft/hard, or hard/soft biphase microwires. Several families of alloy composition for each phase are considered in this overview: magnetostrictive Fe-based and non-magnetostrictive CoFe-based amorphous alloys for the nucleus and soft FeNi and harder CoNi alloys with polycrystalline character for the shell. The phenomenology of the magnetic behavior of the different microwires under low-frequency applied field is firstly described. Particularly the influence of the thickness of layers and that of thermal annealing are presented. A specific study is performed as a function of the measuring temperature in the range of below (15–300 K) and above (300–1000 K) room temperature. Magnetic and structural phase transitions are determined.

Special attention is paid to the ferromagnetic resonance and microwave absorption experimentally investigated with the help of network analyzer, NA-FMR, as a function of applied field in the frequency range up to 14 GHz and with perturbation cavity at X-band (9.5 GHz) and K-band (69 GHz) under different applied fields. The network analyzer-FMR allows us to conclude the presence of multipeak resonance spectra for soft/soft biphase systems while no absorption is detected for the hard phase. In addition, the observed non-Kittel absorption in bimetallic microwires allows us to confirm the equivalency to a capacitor.

The analysis in perturbation cavity is carried out as a function of the measuring dependence (X-band) where the role of the different contributing phases is determined. A correlation between FMR absorption data with that obtained through NA-FMR is performed. Further analysis at room temperature allows us to conclude the need of magnetic saturation of the hard phase to observe properly its FMR absorption. In addition, the screening effect induced by the external metallic shell on the nucleus is observed.

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7.1 Outlook Around Multilayer Microwires

Amorphous magnetic metals are being investigated because of their outstanding magnetic behavior that makes them especially suitable as sensing elements in various devices [1]. Their particular magnetic behavior is a consequence of the intrinsic atomic disordering that in addition results in very interesting fundamental phenomena. Glassy metals are prepared by rapid solidification techniques that enable their preparation in planar (ribbons or thin films [2]) or cylindrical (wires) shapes [3]. Alternatively, amorphous alloys with interesting magnetic behavior can be also obtained as bulk material or can give rise to ultrasoft magnetic alloys after suitable thermal treatment s resulting in nanocrystallization [4, 5]. Amorphous magnetic wires show specific characteristics deriving from their cylindrical symmetry, and they are prepared by two different techniques: (1) by in-rotating-water quenching (100–150 μm diameter) and (2) by quenching and drawing (1–30 μm diameter). The microwires with larger diameter were systematically investigated along the 1980s, showing fascinating magnetic effects as magnetic bistability, characterized by the propagation of a single-domain wall resulting in a giant Barkhausen jump, and very high initial susceptibility that gives rise to giant magnetoimpedance effect [6]. Along the last 20 years, interest has been readdressed toward thinner glass-coated microwires [7], profiting of the similar effects and rather smaller size of interest for miniaturization. Particularly, they have been shown to be very relevant because of their dynamic properties around the ferromagnetic resonance and for a number of applications in electronic devices as sensing element [8].

Early attempts to fabricate multilayer microstructures with cylindrical geometry were performed on in-rotating-water-quenched microwires [9, 10] or by electrodeposition and sputtering techniques showing an interest for their magnetic bistability and microwave absorption [11–13]. Microwires with multilayer geometry structure containing two magnetic phases separated by an insulating layer have been introduced more recently [14, 15]. A schematic view of such multilayer microwire is depicted in Fig. 7.1. The fabrication process with micrometer size diameter requires an intermediate step where noble metal is sputtered onto the glass which serves as electrode in the subsequent electroplating as well as buffer layer insuring the substrate roughness reduction. Multilayer microwires present interesting properties in terms of magnetic couplings, while the electrical insulation between the two metallic layers plays an important role for certain technological applications . The fabrication process allows one the selection of a wide range of alloy compositions with tailored magnetic character for the magnetic nucleus and shell – soft/soft, soft/hard, or hard/hard – where the nucleus is typically amorphous or nanocrystalline [16] and the shell polycrystalline. The presence of the external shell induces significant mechanical stresses (i.e., magnetoelastic anisotropy ) in the internal nucleus, and in addition, its stray field can bias the magnetic behavior of the system [17–19]. These magnetic interactions between magnetic layers give rise to tailored magnetic behavior as asymmetrical magnetoimpedance [20] and multiabsorption phenomena or enhanced stress sensitivity to mechanical stresses [21]. These properties make multilayer microwires very suitable for several applications as elements in field, stress or temperature sensor devices [22], orthogonal flux-gates [23, 24], biomedical applications [25], or microactuators [26]. For an overall information about the state of the art and applications, the reader is addressed elsewhere [27, 28].

Fig. 7.1

Scheme of glass-coated (single-phase) microwire (a) and multilayer (biphase) microwire (b), with indication of thickness and composition of respective layers

This article reviews most relevant magnetic properties of bimagnetic microwires based on glass-coated microwires. The introductory sections focus on the preparation techniques and the phenomenology of magnetization process, aspects that have been thoroughly studied in recent manuscripts. Afterwards, we pay particular attention to the latest experimental results about the microwave properties and the influence of the measuring temperature. We conclude with a general overview about present trends around fundamental and applied research on this family of microwires.

7.2 Synthesis of Biphase Magnetic Microwires

Multilayer microwires are designed to consist of two electrically isolated magnetic phases, namely, a ferromagnetic nucleus and a ferromagnetic outer shell separated by an intermediate insulating dielectric layer. They are prepared by the combination of rapid quenching , sputtering and electrodeposition techniques. Firstly, the precursor magnetic nucleus covered by a Pyrex layer is directly obtained by quenching and drawing, a modified Taylor–Ulitovsky technique. Figure 7.2 shows images of the fabrication facility and a picture during the quenching process. This rapid solidification procedure to fabricate amorphous microwires has been described in detail in earlier works [3, 5]. The quenching rate is of the order of 10⁵ K/s to enable the magnetic metallic nucleus to exhibit amorphous structure. The diameter of the metallic nucleus ranges typically between 1 and 20 μm while the thickness of the Pyrex-like glass cover can be tailored roughly between 2 and 10 μm. Three types of alloys with soft magnetic behavior have been considered in this chapter according to its saturation magnetostriction : Fe -based (λ_s = 3 × 10⁵), Co -based (λ_s = −1 × 10⁶), and CoFe-based alloys (λ_s = −1 × 10⁷). The amorphous microstructure of these alloys is confirmed by X-ray diffraction analysis.

Fig. 7.2

Fabrication of glass-coated microwires . Images of the facility for quenching and drawing at the Instituto de Ciencia de Materiales de Madrid, ICMM/CSIC

Afterwards, an Au nanolayer (typically 20–30 nm thick) is grown on top of the glass surface using commercial sputtering (metallizer) system which is later used as an electrode for the final electroplating of the magnetic outer layer. Figure 7.3 illustrates the process of Au sputtering and electrochemical deposition of the external shell. Pictures of the simple equipments employed at the ICMM/CSIC, Madrid, are shown together with the cross-section image of a final multilayer bimagnetic-phase microwire. For the final galvanostatic electrodeposition, the sputtered Au is used as cathode and a Pt mesh with cylindrical geometry as anode. The control of the current density (j = 12 mA/cm² in the experiments) was carried out using a potentiostat/galvanostat power supply AMEL Instruments 2053, the temperature was adjusted to 40 °C and 55 °C, and the electrodeposited was performed under magnetic stirring for a maximum time between 60 and 90 min.

Fig. 7.3

Images illustrate the process of sputtering an intermediate Au nanolayer on top of the glass-coated microwire as well as the final electrochemical deposition of the external magnetic shell to obtain the multilayer microwire (its cross section is also visualized by optical microscopy after polishing)

Regarding the composition of the external shell, we have selected FeNi and CoNi alloys with soft and relatively hard magnetic behavior, respectively. As for the electrolytes, in the case of FeNi plating, the bath was composed of FeSO₄ × 7H₂O (8 g/l), NiSO₄ × 6H₂O (125 g/l), NiCl₂ × 6H₂O (20 g/l), H₃BO₃ (40 g/l), and saccharin (6 g/l) in demineralized water [29]. Boric acid (H₃BO₃) is employed as an agent to stabilize the pH which in this case was adjusted to 2 and 2.80, by adding KOH to the solution. In the case of CoNi, the electroplating was performed in an aqueous solution of NiSO₄ × 6H₂O (150 g/l), NiCl₂ × 6H₂O (22.5 g/l), H₃BO₃ (45 g/l), 7H₂O CoSO₄ (150 g/l), and CoCl₂ × 6H₂O (22.5 g/l) [30]. CoNi solution has a pH of 4.4. The particular composition of the alloys is controlled tailoring the current density of the electroplating, and verified by EDS, microanalysis at surface and X-ray fluorescence analysis. The thickness, varied up to around 10 μm, is nearly proportional to both electrodeposition time and current density. Crystalline structure of FeNi and CoNi alloys shows fcc (face-centered cubic) and hcp (hexagonal close-packed) crystalline phases, respectively, as determined by XRD.

Several biphase magnetic configurations have been selected. The amorphous nucleus exhibits always soft magnetic behavior either with vanishing (CoFe-based) or large positive (Fe -based) magnetostriction , while the polycrystalline shell shows soft (FeNi ) or hard (CoNi) behavior:

• 1. Soft/soft (CoFe/ FeNi ): (Co_0.94Fe_0.06)_72.5Si_12.5B₁₅/Fe₂₀Ni₈₀ and Co_67.1Fe_3.8 Ni_1.4Si_14.5B_11.5Mo_1,7/Fe₂₀Ni₈₀

• 2. Soft/soft ( Fe / FeNi ): Fe₇₆Si₉B₁₀P₅/Fe₂₀Ni₈₀ and Fe_77,5Si_7,5B₁₅/Fe₂₀Ni₈₀

• 3. Soft/hard (CoFe/CoNi): (Co_0.94Fe_0.06)_72.5Si_12.5B₁₅/Co₉₀Ni₁₀ and Co_67.1Fe_3.8 Ni_1.4Si_14.5B_11.5Mo_1,7/Co₉₀Ni₁₀

• 4. Soft/hard ( Fe /CoNi): Fe_77,5Si_7,5B₁₅/Co₉₀Ni₁₀

For simplicity, along the chapter nuclei composition is labeled as CoFe and Fe , while the shell alloys are termed as CoNi or FeNi .

7.3 The Magnetization Reversal in Bimagnetic Microwires

7.3.1 Room Temperature Hysteresis Loops

A first magnetic characterization of the magnetic multilayer microwires is performed through the hysteresis loop s taken in vibrating sample magnetometer (KLA Tencor EV7 VSM, LOT-Oriel) installed at the ICMM/CSIC, Madrid, under applied magnetic field parallel to the microwire axis (temperature range 100–400 K). Biphase microwires present a double magnetization process whose individual contributions are better differentiated for soft/hard magnetic configuration. A typical example is shown in Fig. 7.4 for a soft/hard CoFe/CoNi microwire. Figure 7.4a shows the hysteresis loop of the precursor soft CoFe glass-coated amorphous microwire. This loop is typical of a microwire with relatively small and negative magnetostriction : this is nearly non-hysteretic and exhibits a well-defined transverse (circular) magnetic anisotropy with anisotropy field of around 7 Oe. Its domain structure is characterized by a main circumferential domain but containing an inner axial vortex structure [31]. Figure 7.4b depicts the loop for the CoNi hard magnetic shell (it was prepared for the experiment on a Pyrex capillary with similar diameter as in the sample of Fig. 7.4a). Figure 7.4c shows the hysteresis loop for the bimagnetic microwire where the magnetization processes of the two magnetic phases are clearly identified. Note that the fractional volume of each magnetic phase is given by the fractional magnetization jump (very similar in this particular example).

Fig. 7.4

Low-field (a) and high-field (b, c) hysteresis loop s corresponding to single-phase CoFe soft amorphous nucleus, thickness t _CoNi = 8.5 μm (a), to single-phase CoNi external shell, t _CoNi = 2 μm (b), and CoFe/CoNi biphase microwire

The overall magnetic behavior of the bimagnetic microwires is determined by the nature of the phases as well as by the strength and nature of magnetic interactions, magnetoelastic and magnetostatic, between them. The magnetoelastic contribution appears in all the cases as a consequence of the stresses induced by the shell. The magnetostatic interactions are observed in the case of soft/hard microwires after submitting the sample to a saturating field so that, after its release, at remanence or under low field, the soft phase is magnetically biased by the stray field. In this overview we will consider the effect of magnetoelastic interactions in more detail. Figure 7.5a shows the hysteresis loop of FeSiB single-phase microwire with typical bistable magnetic behavior originating in its high and positive magnetostriction . The influence of the external shell is deduced in Fig. 7.5b, where the bistable behavior is deteriorated owing to the compressive stresses induced in the nucleus as has been reported elsewhere (see [27] and references inside).

Fig. 7.5

Hysteresis loops corresponding to several microwires with indicated metallic, d, and total, D _tot, diameters: Fe single-phase (a), Fe/CoNi biphase, t _CoNi = 3 μm with magnetostrictive nucleus (b), and CoFe/FeNi biphase microwire with non-magnetostrictive nucleus (c)

In the case of soft/soft biphase microwires , the reversal process of each phase can overlap. As an example, Fig. 7.5c shows the hysteresis loop s for CoFe/FeNi soft/soft microwire. This figure includes the nearly non-hysteretic loop for the small and negative magnetostriction CoFe nucleus with well-defined circular anisotropy . For the biphase microwires, we observe a large Barkhausen jump at around 1 Oe applied field ascribed to the FeNi (Permalloy) external shell plus a nearly non-hysteretic region corresponding mainly to the CoFe nucleus. In this case, the determination of each magnetic fractional volume is not so straightforward.

7.3.2 Influence of Layers Thickness

While the general magnetic behavior of bimagnetic microwires is obviously determined by the magnetic nature of each magnetic phase, their particular properties can be tailored through the geometry (i.e., thickness) of each layer. The increase of the external layer gives rise to an enhanced fractional volume and to mechanical stresses in the nucleus that couple with the magnetostriction constant to result in the corresponding magnetoelastic anisotropy [32].

Figure 7.6 shows two examples about the influence of the thickness of external layers for the same CoFe soft amorphous nucleus. In Fig. 7.6a, we observe the variation of the high-field hysteresis loop of CoFe/CoNi with an increase of the thickness of the hard shell. Obviously, the total magnetic signal increases with the fractional volume of the CoNi shell which results in an enhanced remanence . Macroscopic coercivity also increases with that thickness. In fact, both remanence and coercivity correspond to those magnitudes of the shell for a sufficiently high thickness.

Fig. 7.6

Hysteresis loops of soft/hard CoFe/CoNi biphase microwire with increasing CoNi thickness (a) and of soft/soft CoFe/FeNi with increasing thickness of intermediate Pyrex layer, glass-coated CoNi diameter, D _tot, (b) [32]

Apart from the external shell, the thickness of the intermediate insulating Pyrex layer also plays a significant role. Figure 7.6b shows the hysteresis loop s of soft/soft CoFe/FeNi bimagnetic microwires for different values of the total diameter, D _tot, of the precursor glass-coated CoFe base microwire with constant metallic diameter (d = 17 μm) and increasing the thickness of Pyrex. Note that after the irreversibility determined by the FeNi shell, the nearly reversible region of the loop corresponding to the nucleus shows a susceptibility that decreases with the thickness of the intermediate Pyrex layer. Such hardening of the soft nucleus is actually determined by the mechanical stresses induced by the Pyrex.

7.3.3 Influence of Thermal Treatments

Thermal treatments at high enough temperature and sufficiently long duration modify irreversibly the microstructure of the materials giving rise to significant changes in the magnetic properties . In the present case, we are dealing with biphase microwires whose internal nucleus is structurally amorphous while the shell shows polycrystalline structure. Their response to thermal annealing is thus somehow different. In this section we will describe some effects of low-temperature heating in the soft nucleus while in a subsequent section we will consider also some modifications in the external shell.

Thermal treatments were performed in the temperature range up to 700°C ranging from 100 to 700 °C in Argon atmosphere for 1 h. The cooling to room temperature took between 1 and 2 h, depending on the annealing temperature. The influence of thermal treatment s has been determined from the hysteresis loop s. We can distinguish two main ranges of annealing temperature, below and above the crystallization temperature of the soft amorphous nucleus. The crystallization temperature of Fe and CoFe-based amorphous alloys is in the range 500–600 °C for heating rates of around 10 °C/min. We consider here the case of soft/hard Fe/CoNi bimagnetic microwires whose Fe-base single-phase nucleus exhibits bistable behavior.

Figure 7.7a shows the hysteresis loop s as a function of annealing temperature in the range from 500 to 700 °C. The two magnetization regions are still observed after annealing at 500 °C. After annealing below that temperature, the hysteresis loops retain very similar magnetic behavior, and only relatively small variations in the coercivity and remanence are observed which are ascribed to the partial relaxation of the amorphous structure and consequently of its internal mechanical stress. However, after annealing above 500 °C, a quite noticeable magnetic hardening is observed, and finally, magnetization takes place in apparently a single process. This is ascribed to the crystallization of the amorphous nucleus. In the present example particularly, the result of crystallization is the growth of α-FeSi and Fe -borides grains [1].

Fig. 7.7

Hysteresis loops of soft/hard FeSiB/CoNi (a) biphase microwires after annealing at indicated temperatures above the crystallization of the amorphous nucleus. Evolution of the coercive field (b) with annealing temperature (adapted from [33])

Figure 7.7b summarizes the evolution of the coercivity of the biphase microwire as a function of annealing temperature. At low annealing temperatures, coercivity is determined by that of the soft nucleus, where even a kind of small softening of stresses is detected just before annealing at above 500 °C where the mentioned crystallization process takes place.

7.4 Temperature Dependence of Magnetic Properties

This family of multilayered biphase magnetic microwires has been recently introduced. The strongest attention has been paid in previous reports to the magnetization process and the magnetic interactions between phases, to some microwave properties , and to their technological applications in sensor devices. However, there are only very few publications around their temperature dependence below (in single-phase microwires [34, 35]) and above room temperature [36, 37]. In this section we summarize most recent results obtained by the coauthors on the temperature dependence of static properties, while in the next section we will deal with the matter at the microwave frequency range.

7.4.1 Low-Temperature Behavior

The hysteresis loop s at low frequency were measured in the temperature range 10–300 K for biphase microwires with different compositional configuration in the VSM facilities at the ICMM/CSIC, Madrid, and the University of the Basque Country, Bilbao. Figure 7.8 shows the data for selected alloy compositions. In Fig. 7.8a, the loops correspond to the soft/hard Fe /CoNi biphase system with magnetostrictive soft nucleus. The different contributions of the two phases to the magnetization process are clearly observed by the different values of the applied fields at which we observe irreversible jumps of the magnetization. Note that low-field jump ascribed to the soft Fe-based nucleus occurs at around 1 Oe applied field while the high-field irreversible jump ascribed to the CoNi shell is observed at around 100 Oe. Figure 7.8b shows the temperature dependence of the coercivity ascribed to the CoNi hard magnetic phase. The corresponding coercivity for the soft nucleus is barely observable at the same scale. The inset shows that variation for the soft phase in the biphase microwire (a significant error is found in its quantification) together with the result for the single-phase glass-coated microwire (which follows a standard monotonic evolution).

Fig. 7.8

Low-temperature dependence of hysteresis loop s for the soft/hard Fe /CoNi biphase system (a) and quantitative values for the irreversibility field (coercivity ) ascribed to the hard phase (b). Inset shows data at an enlarged scale for the soft nucleus which is compared to the single-phase microwire

In the second example, given in Fig. 7.9, we present the data for the soft/soft CoFe/FeNi system. Here, the overall temperature dependence of the low-field loops (see Fig. 7.9a) is much reduced. As indicated above, the irreversibility corresponds to the FeNi external shell while the higher-field nearly non-hysteretic is ascribed to the soft nucleus. The temperature dependence of coercivity is presented in Fig. 7.9b, corresponding to CoFe single-phase microwire and the biphase microwire with two thicknesses of the shell.

Fig. 7.9

Low-temperature dependence of hysteresis loop for the soft/soft CoFe/FeNi biphase system (a) and coercivity , ascribed to the FeNi soft phase (b) [39]

We should underline that the magnetization process in these biphase systems is actually determined in a significant manner by the differential temperature dependence of the metallic layers and that of the intermediate insulating layer. Mechanical thermal stresses are introduced as the measuring temperature is reduced as a consequence of the different thermal expansion coefficients of the layers. That contributes to the thermal dependence of coercivity and other magnetic magnitudes. A proper systematic study is thus required for a proper quantification of the presented behavior.

7.4.2 High-Temperature Behavior

The high-temperature-dependent properties have been independently measured for the whole set of biphase microwires in the temperature range from 25 to 925 °C at the Lake Shore VSM (7400 series) magnetometer installed in Immanuel Kant Baltic Federal University, Kaliningrad. The commercial equipment was optimized for a high magnetic field resolution of 0.02 Oe to measure the magnetic moment at high temperature. Figure 7.10 shows the temperature dependence for two selected biphase systems, namely, soft/hard Fe /CoNi (Fig. 7.10a) and soft/soft CoFe/FeNi (Fig. 7.10b). Very complex dependence is observed in both families of microwires where various magnetic behaviors appear as a consequence of the structural changes occurring during the heating.

Fig. 7.10

High-temperature dependence of hysteresis loop s for soft/hard Fe /CoNi (a) and soft/soft CoFe/FeNi (b) biphase microwire systems

In order to analyze in more detail those changes, the temperature dependence of the received magnetic moment under 10 Oe applied magnetic field is shown for the CoFe-based and Fe -based single- and biphase systems in Fig. 7.11a, b, respectively. That enables us to follow the structural and magnetic-phase transformations sensitively detected by the thermomagnetic analysis. Figure 7.11a depicts the results for CoFeSiB single-phase and biphase microwires . We firstly identify the Curie point of the amorphous CoFe nucleus, T _C,am-CoFe ≈ 377 °C, in the cases of CoFe single-phase and of the CoFe/FeNi biphase microwires. Data for similar CoFeSiB amorphous alloy ribbons give values in the same range [41, 42]. The crystallization into Co -rich phases is expected to occur at the temperature T _x,CoFe ≈ 567 °C [43]; however, it seems that the applied field is likely not large enough to receive a significant magnetic response. From the data for the CoFe/FeNi biphase system, we can also identify the magnetic-phase transition of the FeNi shell, at T _c,FeNi ≈ 601 °C, that agrees well with data reported in the literature [44, 45]. The reduction of the magnetic signal at the Curie point of the CoFe amorphous phase is less pronounced owing to its small fractional magnetic weight. We should mention that the Curie point, 1075 °C [37], of the crystalline CoNi external shell is not reached at the highest measuring temperature.

Fig. 7.11

Temperature dependence of the magnetic moment for single, CoFe, and CoFe/FeNi biphase or CoFe/CoNi biphase systems (a) and for single, Fe , and Fe/FeNi biphase or Fe/CoNi biphase systems (b). Arrows denote the Curie temperature , T _c, of different phases [40]

The results in Fig. 7.11.b correspond to Fe -based microwires . In the case of Fe/FeNi biphase microwire, we evaluate the magnetic -phase transitions for the amorphous nucleus at T _c,am-Fe ≈ 427 °C (similar to that reported for ribbons in [41]) and T _C,FeNi ≈ 601 °C for the crystalline FeNi shell. Also, we estimate the crystallization temperature of the amorphous core at around T _x,Fe ≈ 525 °C and its Curie point at T _C,Fe-crys ≈ 645 °C. Finally, for the Fe/CoNi biphase microwire, we evaluate T _c,Fe ≈ 427 °C and T _C,Fe-cryst ≈ 675 °C. Note that similar values of Curie and crystallization temperatures are experimentally measured for individual magnetic phases in the different single- and biphase microwires.

7.5 Network Analyzer-Ferromagnetic Resonance in Biphase Magnetic Microwires

The ferromagnetic resonance, FMR, or, to be more precise, the resonant absorption under external electromagnetic radiation is a technique that has been successfully employed for the investigation of magnetic substances, not only about their fundamental magnitudes but also for their technological applications . The microwave properties of amorphous magnetic alloys have been reported by several groups [12, 46–53]. The main features of FMR in amorphous microwires have been analyzed in several reports [54, 55]. The interpretation of rather complex experimental data for multilayer wires with and without intermediate glassy layer has been, however, sometimes contradictory. In the case of biphase wires with glassy interlayer, several difficulties have been pointed out to interpret their multiabsorption spectra [33, 56]. While single-phase microwires are characterized by single FMR absorption, biphase microwires show two or more different absorptions depending on the soft/hard nature of the two magnetic phases. The evolution of the resonance frequency with DC applied field has been fitted to Kittel’s equation for thin films which is applicable also to metallic wires if the skin depth is small compared to the wire diameter [51]. Thus, the diversity of interpretation specifically occurs if the skin effect in ferromagnetic metal is not properly taken into account. This fact justifies the present updating of recent progress in understanding FMR aspects of ferromagnetic metallic wires.

FMR experiments collected in the present overview are basically divided into two categories: (1) under a fixed DC magnetic field varying the microwave frequency of the AC electromagnetic field by means of so-called network analyzer-FMR (NA-FMR) and coaxial or microstrip microwave circuits and (2) at constant frequency varying the amplitude of the DC magnetic field making use of classical FMR spectrometers and waveguide microwave techniques. The first type of measurements is presented in this section while the second ones are collected in the next one.

The microwave characterization was carried out at room temperature with a network analyzer (Agilent, model E8362B) and a transmission coaxial line in the frequency range between 10 MHz and nominally 20 GHz. DC magnetic field (up to 5 kOe) was applied parallel to wire axis by an electromagnet. SMA connectors and adapters are used suitable for measurements at a maximum frequency of 20 GHz. The adapted sample holder is based on a commercial SMA (SubMiniature version A) connector where the inner pin was removed to avoid radiation effects. The inner and outer conductors of the holder are shorted by means of the microwire nucleus: the Au and magnetic coatings are removed from the wire ends and the amorphous nucleus (around 50 Ω DC resistance) is welded using silver paint. The reflection coefficient S 11 is analyzed, from which real R and imaginary X components of impedance are determined.

Pieces of microwires 5 mm in length were taken for these measurements. The electric contacts between the inner metallic core and the measuring circuit were made by a silver paint. The microwave current passing through the wire induced a circumferential AC field in the core and the surrounding external shell (FeNi or CoNi) microtube. A schematic view of the whole measurement system is depicted in Fig. 7.12, while additional experimental details can be found elsewhere [33, 38].

Fig. 7.12

Scheme of the experimental setup for FMR measurements in transmission coaxial line in the network analyzer: Diagram of measurement (a) with detail of the sample holder (b) and view of the whole system and electromagnet (c)

7.5.1 Effect of Two Phases into the FMR Spectrum

Let us first summarize the main characteristics of FMR absorption spectra for single- and biphase magnetic systems. Figure 7.13a shows typical spectra for the real component of impedance corresponding to non-magnetostrictive CoFe-based single-phase glass-coated microwire for a range of indicated DC applied field. As observed, a clear resonance peak, FMR1, is observed which is naturally ascribed to the soft magnetic glass-coated microwire. Note that the amplitude of DC applied field is high enough so that the microwire is assumed to be magnetically saturated.

Fig. 7.13

Evolution of FMR spectra (real component of impedance) with static magnetic field for CoFe single-phase glass-coated microwire (17 and 42 μm metallic and total diameter) (a), CoFe/CoNi (2 μm CoNi thick) (b), and CoFe/FeNi (2 μm FeNi thick) (c). Adapted from [32]

The evolution of the resonance frequency with applied field has been typically performed using the Kittel’s condition of resonance for a tangentially magnetized planar film which corresponds to the skin -depth layer at the metallic microwire surface [39, 57–59]. The following equation holds:

$$ {\left(\frac{\omega }{\gamma}\right)}^2=\left({H}_{\mathrm{r}}+{H}_{\mathrm{K}}\right)\;\left({H}_{\mathrm{r}}+{H}_{\mathrm{K}}+4\pi {M}_{\mathrm{S}}\right) $$

(7.1)

where ω = 2πf _r is the angular frequency of the microwave field and γ is the gyromagnetic ratio (γ/2π = 2.8 ×10⁶ Hz/Oe). The evolution of f _r ² is typically represented as a function of the DC applied field and fitted top, a linear behavior which allows one to determine a fitting value for the anisotropy field, H _k, and of the saturation magnetization . As deduced from the fitting in Fig. 7.14, the fitted value for the saturation magnetization is 4πM _s = 7.1 kG which agrees well with the expectations for the CoFe-based alloy composition.

Fig. 7.14

Evolution of the square frequency at resonance as a function of applied magnetic field for CoFe/FeNi biphase microwires (CoFe glass-coated microwire with total diameter, D _tot = 42, 34, and 20, and 2 μm thick FeNi layer) where the linear fits correspond to Eq. (7.1) (a). Absorption spectra of CoFe, CoFe/Au, and CoFe/FeNi (2.5 μm thick) (b). Dependence of the absorption frequency for FMR2 with different dielectric thickness, t _g (c). Adapted from [32]

In the case of biphase magnetic microwires , we obtain in general multipeak spectra. For example, for the soft/hard CoFe/CoNi biphase microwire, we observe in Fig. 7.13c the presence of two peaks that are ascribed to two absorption phenomena. That one at higher frequency can be ascribed to the soft CoFe nucleus as this is observed at similar frequency as FMR1, and it follows a similar trend with applied field as can be deduced in Fig. 7.14 as well as the value of the saturation magnetization fitted according to Eq. (7.1). However, the peak observed at the lower frequency range in Fig. 7.13c, that we will label FMR2, follows a different evolution (see Fig. 7.14) with applied field which cannot be ascribed to any magnetic phase as the fitted parameters would give us nonsense values for the external CoNi shell.

In soft/soft CoFe/FeNi microwire in Fig. 7.13b, we detect three peaks; FMR1 is ascribed to the CoFe nucleus, while the new peak, FMR3, should correspond to the soft FeNi shell as the fitted value (see Fig. 7.14) for the saturation magnetization is 4πM _s = 11.5 kG, near to the expected value for Permalloy. Again, we observe a FMR2 peak which cannot be fitted to any of the two magnetic phases.

7.5.2 Influence of Layers Thickness: The Microwire as a Capacitor

The FMR study has been performed for biphase microwires with different thicknesses of the layers. First, we consider the influence of the thickness of the intermediate Pyrex layer. In fact, this thickness introduces mechanical stresses in the internal nucleus as has been commented in a previous section. Variations of that thickness also modify the FMR behavior of single- and biphase microwires. Measurements taken in CoFe-based single- and biphase non-magnetostrictive microwires show not very significant influence in the FMR peaks ascribed to each magnetic phase. Figure 7.14a depicts the fitting to Kittel’s Eq. (7.1) for the data collected for soft/soft CoFe/FeNi biphase microwires with different total diameter, D _tot, of precursor glass-coated microwire (i.e., thickness of Pyrex layer).

However, that is relevant to unveil the nature of the FM2 absorption. Since it depends on the insulating intermediate layer, it seems reasonable to correlate the effect to a geometrical feature, particularly to the capacitance formed between the two magnetic metallic conductors and the insulating Pyrex layer [60, 61]. The multilayer microwire can be taken as a cylindrical capacitor of internal and external radii a and b, respectively, filled by a dielectric (Pyrex) with a given capacity, C:

$$ C=\frac{2\pi {\varepsilon}_0{\varepsilon}_{\mathrm{r}}l}{ \ln \left(b\Big|a\right)} $$

(7.2)

Therefore, the microwire and the measurement system form a LRC resonant circuit which resonance frequency is given by:

$$ {f}_{\mathrm{r}}=\frac{1}{2\pi \sqrt{L(H)C}} $$

(7.3)

where L(H) is the inductance of the two magnetic -phase structure. This circuit reproduces qualitatively the FMR behavior observed for the biphase microwires CoFe/FeNi . As a result, the alternating current passes through both the inner metallic nucleus and the outer metallic shell of the microwires. Thus, the biphase microwire can be taken as two impedances in parallel (one much larger than the other since for a 5 mm long microwire, the resistance values are R _nucleus ≈ 50 Ω, R _shell = 1.5 Ω). Thus, the observed shift of FMR2 resonance with the applied field can be understood as due to the field dependence given in Eq. (7.3). Figure 7.14b presents the absorption spectra at a constant applied field (H _ap = 0.375 kOe) for single-phase microwire CoFe (black), for the same microwire sputtered with a thin Au nanolayer (orange), and after electroplated by FeNi soft external shell (green). Indeed, the resistance of biphase microwires (electroplated by magnetic or not magnetic metal layer) is much smaller than the single-phase microwires. On the other hand, we observe that the FMR2 appears also in the case of a nonmagnetic coating of Au, which confirms the capacitance origin of its absorption peak. This phenomenon illustrates that the composite microwire can be taken by itself as a LRC circuit, and that its absorption should depend on the geometry of the associated capacitor as confirmed in Fig. 7.14c.

7.5.3 Effect of Thermal Treatments: The Influence of the Not-Saturated Phase

The objective of this section has been to investigate the effect of the thermal treatment s on the FMR behavior of Fe /CoNi soft/hard bimagnetic microwires whose static magnetic properties were analyzed in a previous section. An additional objective has been trying to understand why no apparent absorption is received from the external hard shell.

Measurements have been performed in Fe /CoNi microwires with different metallic, d = 18, 18, and 20 μm, and total diameters, D _tot = 24, 26, and 26 μm, (ρ = d _m/D _tot), respectively, for the glass-coated nucleus and a polycrystalline CoNi shell 3 μm thick. Annealing treatments were performed up to 700 °C and, as in the static case, we find two annealing temperature ranges for which the microwave response is clearly identified. After annealing up to around 500 °C, only relatively small changes are observed in the FMR absorption characteristics in comparison with as-prepared microwire (see Fig. 7.15a). Two absorption spectra, labeled above as FMR1 and FMR2, are observed. FMR1 is again ascribed to the Fe-based nucleus through the fitting to Kittel’s Eq. (7.1) (see Fig. 7.15c).

Fig. 7.15

Evolution of FMR spectra (real part of impedance, R) with applied field for FeSiB/CoNi biphase microwires in as-prepared state (a) and after annealing at 650 °C (b). Square of the resonance frequency as a function of applied static magnetic field for FeSiB/CoNi biphase microwires before and after annealing at 500 °C. Adapted from [33]

However, after annealing at higher temperatures, the two absorption peaks can be still visible as observed in Fig. 7.15b for the sample after annealing at 650 °C. FMR1 corresponding to the soft nucleus now shows much less amplitude, and eventually, it should be ascribed to the partially crystallized FeSiB core. Fitting to Kittel’s equation cannot be properly performed.

Regarding the data for FMR2, they do not follow the resonance condition and are ascribed to the mentioned capacitive effect. We should finally underline that no absorption can be ascribed to the CoNi external shell even after those thermal treatment s. Thus, we understand that owing to its harder magnetic character, the CoNi shell is not sufficiently saturated magnetically. In this case, it does not show properly ferromagnetic absorption, and to observe its FMR a different experiment should be designed.

7.6 Ferromagnetic Resonance Through Cavity-Perturbation Measurements

In this section we summarize the experimental work and its analysis performed in biphase microwires with hard external shell obtained by means of cavity-perturbation technique at two different microwave frequencies, 9.5 GHz (X-band) and 69 GHz (K-band). Apart from the intrinsic interest of this technique to achieve broader and complementary information, an additional reason to perform this study was related to the fact that the maximum available magnetic field in the network analyzer equipment was not high enough to saturate magnetically neither the CoNi shell nor the crystallized FeSiB nucleus after the thermal annealing .

By this classical FMR experiment, we obtain the DC magnetic field dependence of the microwave absorption as a function of strong enough DC applied field (up to 30 kOe) which was parallel to the wire (with field modulation 1 Oe at 100 kHz) at given frequency. Measurements were taken at X-band at an extended temperature range (−269 to 25 °C) at the microwave cavity setup installed at the University of the Basque Country in Bilbao (a scheme of the experimental equipment is depicted in Fig. 7.16 together with a photograph of the whole commercial setup). Experiments at the Czech Academy of Sciences in Prague were performed at room temperature at X-band (rectangular TE10 waveguide) and K-band (on small pieces of microwires , around 2 mm long, cut from the selected wires, inserted into quartz capillary, and placed into the middle of circular waveguide with sample axis along the electric field vector).

Fig. 7.16

Schematic view (a) and image (b) of the cavity-perturbation measurement setup installed at SGIker services of the University of the Basque Country

Measurements were taken on two families of microwires based on single-phase glass-coated microwires of nominal composition FeSiB (positive and large magnetostriction ) and CoFeSiB (vanishing magnetostriction), with metallic nucleus diameter d = 12.5 and 8 μm and total diameters D _tot = 40 and 24 μm, respectively. The corresponding biphase microwires contain a hard CoNi external shell with 3 μm thickness.

7.6.1 Temperature Dependence of Microwave Properties

The objective in this section has been to obtain a deeper knowledge on the microwave phenomena in single- and biphase microwires through the temperature dependence of their FMR absorptions peaks. To reach this goal, we have selected a soft/soft biphase microwire. It consists of an 8 μm diameter non-magnetostrictive CoFeSiB single-phase glass-coated microwire and a 2 or 4 μm thick FeNi external shell.

The results corresponding to the single- and biphase microwires are shown in Fig. 7.17, and they can be compared to the data obtained with the NA-FMR, at 9.5 GHz frequency. As discussed in [39], the spectrum displays one resonant peak for CoFe single-phase microwire at 1.08 kOe which compares with 1.17 kOe of FMR1 as deduced from the data obtained with the network analyzer. For t _NiFe = 2 μm biphase microwire, a main absorption is observed at 1.10 kOe which should correspond to that at 1.16 kOe from FMR1 in NA-FMR measurements which was correlated to the CoFe metallic core. However, for biphase microwires we should expect in principle that the main absorption should be ascribed to the external FeNi phase. This is the case of t _NiFe = 4 μm, where the main absorption at 0.77 kOe corresponds to H _r = 0.87 kOe for FMR3 in NA-FMR measurements. Small additional absorptions at applied magnetic field below the main peak can be hardly identified in Fig. 7.17, and its origin is not clear.

Fig. 7.17

Resonance spectra at 9.5 GHz of soft/soft CoFe/FeNi biphase microwires with different thickness (0, 2 and 4 μm) of the external FeNi shell [39]

The derivative of microwave absorption versus external magnetic field resonance spectra of single-phase microwire measured at selected temperatures is shown in Fig. 7.18a. A single absorption peak is observed which resonance field, H _r, and the total line width, ΔH, are plotted in Fig. 7.18b as a function of temperature. As observed, both parameters increase monotonically with temperature, although ΔH shows a small maximum at low temperature.

Fig. 7.18

Resonance spectra at 9.5 GHz of CoFe-based single-phase glass-coated microwire at selected temperatures (a) and temperature dependence of applied field at resonance, H _r (experimental and calculated), and total line width, ΔH (b) [39]

Considering Eq. (7.1) and that 4πM _s ≫ H _r ≫ H _k in the first approximation, we derive the following expression for the temperature dependence of the resonance field, H _r:

$$ {H}_{\mathrm{r}}(T)\approx \frac{f_{\mathrm{r}}^2}{\pi {\gamma}^2{M}_{\mathrm{S}}(T)}-{H}_{\mathrm{K}}(T) $$

(7.4)

where the two contributions to H _r on the right-hand side increase with increasing temperature (note the negative-circular anisotropy field value). Figure 7.18b shows the experimental temperature dependence of H _r,exp as deduced from data in Fig. 7.18a which is compared with calculated value, H _r,cal, obtained using Eq. (7.4) (taking saturation magnetization and anisotropy field values deduced from low-temperature hysteresis loop s). The difference in both series of data can be justified after taking into consideration that hysteresis loops were obtained at very low frequency while those from FMR absorption were measured at the GHz frequency range.

The resonance spectra of biphase microwires with different thickness of external shell at selected temperatures are shown in Fig. 7.19. In the case of 2 μm thick FeNi shell, we observe a main absorption peak, FMR1, whose applied field at resonance, H _r, changes very noticeably at the low-temperature range and more moderately at higher temperatures. Also, a small pronounced peak can be observed at low field. For the 4 μm thick FeNi microtube, the variation of the corresponding H _r is much more reduced, while the low-field absorption is detected clearly at low temperatures. Inset in Fig. 7.19b depicts an enlarged view of the low-field peak.

Fig. 7.19

Derivative resonance spectra of CoFe/FeNi biphase microwires with 2 μm (a) and 4 μm (b) thickness of the external FeNi shell. Inset in (b) depicts and enlarged view of the low-field peak [39]

Figure 7.20 collects the evolution of the main resonance field, H _r, as a function of temperature. For the CoFe single-phase microwire, a moderate monotonic increase of H _r with temperature is observed. In the case of 2 μm thick NiFe shell microwire, at temperatures above −143 °C, we observe a similar behavior as that of CoFe single-phase microwire. This similarity, maybe accidental, could lead us to ascribe that absorption to the CoFe core, although we should consider as well that it corresponds to the external FeNi microtube. Note that a similar question was found in the interpretation of data obtained with the network analyzer at room temperature. Below −143 °C a pronounced reduction of H _r is observed that could be eventually interpreted if we would consider a change of sign of anisotropy field in Eq. (7.4). That is, assuming that the low-temperature axial anisotropy field (H _k > 0) evolves to circular anisotropy field (H _k < 0) at high temperatures.

Fig. 7.20

Temperature dependence of the applied field at resonance, H_r, for the different microwires [39]

An overall opposite evolution of H _r with temperature is observed in the case of the 4 μm thick FeNi microtube, including a change of trend at around −143 °C which again could be ascribed to the change of sign of the anisotropy field. Now, it should be circular at low temperature (H _k < 0) and become axial (H _k > 0) at temperatures higher than around −143 °C. The low-field absorption is observed at higher temperatures in the 2 μm thick FeNi biphase microwire, while it appears only at low temperatures in the 4 μm biphase microwire, where a circular magnetic anisotropy would be expected. The origin of this phenomenon could be connected with the absorption in non-saturated samples. Note that its correlation with ferromagnetic antiresonance, FMAR, is in principle discarded since the antiresonance could be observed only above some critical frequency (ω/γ > 4πM _s) which for FeNi lies in the order of 30 GHz. The origin for the anomalous behavior observed in biphase microwires can be ascribed to the presence of strong induced anisotropy in FeNi layers at low temperatures, changing its sign at around −143 °C. The substantial difference in the behavior of the two biphase samples can be a consequence of the different magnetostriction constants, in both sign and magnitude, of the two FeNi layer (2 and 4 μm thick).

In order to properly determine the magnetostriction constant of the FeNi external shell, a final test of their compositions was performed by SEM-EDX (FEI Nova NanoSEM 230 high-resolution scanning electron microscope). That analysis confirmed in fact a different composition for the 2 and 4 μm thick external shell, namely, Fe_8.2Ni_91.8 and Fe_24.4Ni_75.6, respectively. If we consider that for bulk FeNi alloys [44], values of saturation magnetostriction at room temperature are 8 × 10⁻⁶ and −16 × 10⁻⁶ for Fe_8.2Ni_91.8 and Fe_24.4Ni_75.6, respectively, which supports our previous concern and assumption.

Summarizing all data, we can conclude that FMR1 definitely corresponds to CoFe single-phase wire. In the case of the biphase microwire with 2 μm thick FeNi (positive magnetostriction ) external shell, FMR1 is hard to be ascribed, clearly owing to the similar data for CoFe nucleus and FeNi shell in both network analyzer and cavity measurements. In the case of the microwire with 4 μm thick FeNi (negative magnetostriction) shell, the main peak in cavity measurement is associated to FMR3 in the network analyzer measurements from the FeNi shell because of the similarity of H _r fields (0.77 and 0.87 kOe) at 9.5 GHz. We should finally comment that a straightforward comparison of network analyzer and classical FMR cavity-perturbation measurements on the biphase wires would require a fully rigorous theoretical analysis. In the cavity measurement, the microwave current passes through both the core and the FeNi external shell. In contrast, in the network analyzer measurement, the microwave current passes mostly through the CoFe core but also through the FeNi shell because it is transmitted via the capacitance bridge between core and shell. However, it seems that in classical FMR cavity experiment, the core is more effectively screened by the shell.

7.6.2 Room Temperature Analysis: The Role of the Hard-Phase Response

The FMR spectra for single- and biphase microwires measured at frequency 9.5 GHz (X-band) are shown in Fig. 7.21. Absorption is observed in single-phase wires at applied fields of around 1.2 and 0.3 kOe for CoFeSiB and FeSiB microwires, respectively. We should note that according to Eq. (7.1), the difference in applied field to reach resonance comes from the different saturation magnetization and magnetic anisotropy (arising from the magnetostriction constant) of the microwires. For biphase microwires, no absorption is observed up to the maximum applied of 3 kOe. That should be understood as a consequence of a double effect of the presence of CoNi shell: (1) the CoNi shell has not reached again its magnetic saturation and (2) it completely screens the internal core.

Fig. 7.21

Resonance absorption spectra at 9.5 GHz for single- and biphase microwires with CoFe-based (a) and Fe -based (b) nucleus

The results obtained from measurements in the microwave frequency of 69 GHz (K-band) are shown in Fig. 7.22. In the case of single-phase microwires , we observe clean FMR absorption at applied fields of 19 and 17 kOe for CoFeSiB and FeSiB single-phase microwires, respectively. Again, the different saturation magnetization and anisotropy fields of microwires account for the distinct applied fields to observe FMR. In the case of biphase microwires, two resonance peaks are observed at the same frequency (around 17.5 kOe) in both biphase microwires, which consequently lead us to ascribe them to the same magnetic phase, that is, the CoNi external shell, while no resonance can be correlated to the internal nucleus. That would confirm that in this experiment, the amorphous internal nucleus is screened by the CoNi external shell. Further analysis of the spectra indicates that in each sample, we are dealing with a symmetric antiresonance FMAR peak observed at the lower frequency at around 4 kOe together with the mentioned FMR peak. The experimental derivative FMR curves are distorted in both biphase microwires which occur most probably because the sample represents a large load to the microwave circuit [51].

Fig. 7.22

Resonance absorption spectra at 69 GHz for single- and biphase microwires with CoFe-based (a) and Fe -based (b) nucleus

The experiments performed with the cavity-perturbation method enable a broader overview to the analysis of experiments performed in the network analyzer-FMR in previous sections:

• 1. The lack of FMR absorption ascribed to CoNi hard shell in biphase wires is a consequence of the fact that it is not magnetically saturated under the maximum applied field.

• 2. The low-frequency FMR2 absorption arises from a capacitive effect.

• 3. The screening of the core is detected in a complementary way in the cavity experiments.

Further systematic experiments are in perspective.

7.6.3 Angular Dependence of Microwave Absorption

The interest of the determination of the angular dependence of the FMR characteristics is in many cases related to its capability to determine the contributions to the total anisotropy field, H _k. In this kind of experiments, the magnetic field is applied making a variable angle with a particular orientation of the investigated sample. Such angular dependence of microwave behavior has been successfully employed in samples with various magnetic and geometry characteristics as amorphous alloy ribbons, multilayer thin films , and ferrites [62, 63]. In the present study, we introduce preliminary results on the angular dependence of microwave absorption in CoFeSiB and FeSiB single-phase microwires . The microwave absorption measurements were carried out by the cavity technique at X-band spectrometer (9.5 GHz) at room temperature.

Figure 7.23 presents the derivative resonance spectrum of both samples for applied field parallel to microwire. In the case of the CoFeSiB glass-coated microwire, the spectrum displays just one peak at the H _r = 1.3 kOe which relates to the circular anisotropy field of the microwire. Note that such circular anisotropy arises from the coupling between internal stresses with the small but negative magnetostriction of that alloy, which takes a value of λ_s ~ −1 × 10⁻⁷. The spectrum in the case of FeSiB glass-coated microwire displays two peaks, both at lower field than in the CoFe-based microwire: a smaller but broader peak is observed at the lower field of 0.25 kOe, and the steep larger one is observed at higher field of 0.65 kOe. These peaks should be ascribed to two different regions inside the metallic Fe -based microwire, namely, the low-field resonance peak would correspond to the FMR response of an inner core which is known to exhibit with strong axial anisotropy, while the peak at high field is seemingly the response of an outer shell of the microwire with transverse anisotropy.

Fig. 7.23

Derivative resonance spectrum of CoFe- and Fe -based single-phase glass-coated microwires

The angular dependence of FMR behavior is shown in Fig. 7.24 for both samples at selected angles between 0° and 180° (note that for 0°, the AC microwave field is in the plane of the wire and the DC field is parallel to the wire axis, while for 90°, the AC field remains parallel to the plane and the DC field is normal to the wire). Measurements in Fig. 7.24a for CoFeSiB (λ ≤ 0) microwire show an increase in the resonant field and a reduction of absorption amplitude as the angle approaches 90°. Similarly, resonance linewidth, ΔH, sharply increases for angles close to 90°. For angles 90° < θ < 180°, a symmetric evolution is observed (see also Fig. 7.24). The angular dependence for the Fe -based microwire is presented in Fig. 7.24b with the two mentioned FMR spectra. A similar angular evolution as in the case of CoFe-based microwire is observed.

Fig. 7.24

Angular dependence (at selected angles) of the derivative resonance spectrum of CoFe- and Fe -based single-phase glass-coated microwires

Figure 7.25 collects all the results for the angular dependence of the field at resonance, H _r, and the absorption width, ΔH, for both samples CoFeSiB and FeSiB (high-field resonance peak). In order to understand that angular broadening, we should consider that because of skin effect, the Kittel resonance conditions for an infinite cylinder cannot be used in general for metallic wires. For an oblique magnetization of the wire, the resonance curve is inhomogeneously broadened. It means that different parts of the wire exhibit different resonance fields, and the resulting resonance curve is given by the envelope of the local resonance curves. The inhomogeneous broadening increases with increasing angle θ and reaches maximum at θ = 90°. However, for thick enough wires, where the skin depth is much smaller than the wire diameter, the skin layer can be approximated by a thin tube at the wire surface . Then, the local resonance field can be calculated from the Kittel resonance condition of an obliquely magnetized thin film [64]. For the transversally magnetized wire (θ = 90°), the minimum and maximum local resonance fields are:

Fig. 7.25

Angular dependence of applied field at resonance, H _r, and of absorption width, ΔH, in CoFe- and Fe -based single-phase glass-coated microwires

$$ \begin{array}{ll}{H}_{\min }=\sqrt{{\left(\omega /\gamma \right)}^2+{\left(2\pi {M}_{\mathrm{s}}\right)}^2},\hfill & {H}_{\max }=\omega /\gamma +2\pi {M}_{\mathrm{s}}\hfill \end{array} $$

(7.5)

This gives very broad resonance curve at fields above the measured field range.

7.7 Final Remarks and Conclusions: Future Perspectives

We have summarized in the chapter some of the most relevant recent results on the magnetic properties of bimagnetic multilayer microwires synthesized over glass-coated amorphous microwires. After describing the synthesis procedure, we have characterized for some selected biphase microwires with soft/soft and soft/hard magnetic behaviors based on magnetostrictive and non-magnetostrictive amorphous nucleus and polycrystalline soft and hard shell.

We have confirmed the role played by the thickness of different layers, particularly that of the intermediate glass cover and of the external shell. Both contribute to induce magnetoelastic anisotropy resulting in a relative hardening of the nucleus. In addition, the fractional volume of the phases is determined by the thickness of the shell which finally determines the magnetic response of the microwire. Less attention has been paid until now to the temperature effects in these microwires . Annealing at temperatures around 500–600 °C results in the crystallization of the amorphous nucleus and its subsequent magnetic hardening. Measurements at high temperature enable the determination of the Curie and crystallization temperature s of the different magnetic phases.

The measurements at microwave frequencies were firstly performed in network analyzer for samples with selected thickness of external layers and after heating at different temperatures. Multipeak absorption has been observed with two and three absorptions for soft/hard and soft/soft microwires . FMR absorption is detected in all the cases corresponding to the soft phases, the nucleus, the shell, or both of them. However, an additional low-frequency absorption is always detected, which does not follow Kittel’s resonance condition, and is ascribed to a resonance of the microwire as bimetallic cylindrical capacitor.

Measurements in perturbation cavity allow us to confirm that the FMR absorption corresponding to the hard phase is only observed when working at high enough frequency (K-band). In addition, the shell produces a screening effect of the soft nucleus. Preliminary data on the angular dependence of FMR for single-phase microwires are analyzed. Further, measurements as a function of the measuring temperature are interpreted in terms of the temperature dependence of the magnetic anisotropy of soft phases. That has allowed us to forecast the particular evolution of FeNi soft shell with different alloy composition and magnetostriction .

Regarding new perspectives of this family of bimagnetic microwires , there is no doubt of the potential opportunities offered by this family of bimagnetic microwires as sensing elements of various devices as has been shown in previous reports. Present data confirm the possibility to employ such materials in sensing devices at moderately high working temperatures. Their magnetic response can be tailored through particular design of alloy composition and geometry (i.e., diameter and thickness of layers or especial coating of external shell) and specific preheating treatments. On the other hand, data at microwave frequencies demonstrate the specific response of bimetallic magnetic systems with cylindrical geometry. New advanced measurements are still open for further deepening into fundamental knowledge. The possibility to deal with two phases of tailored magnetic character opens new opportunities for electromagnetic shielding effects at different working frequencies and for high-frequency sensor devices.