Magnetic materials showing giant magnetoimpedance effect (GMI) are a subject of increasing interest because of fundamental applied electrodynamic interest and focus on technological and biomedical applications [1-3]. There were many studies of ferromagnetic resonance and GMI effects in electroplated wires [4,5]. It is established that high GMI value connected with the high sensitivity of the magnetic system to a circular magnetic field near the spin-reorientation magnetic phase transitions [6,7]. The magnetoimpedance phenomenon consists of the change of the total impedance, Z, and its real (R) and imaginary (X) parts of a ferromagnetic conductor under the application of an external magnetic field (H) when high frequency (f) alternating current flows through it [1].

For the first time GMI in FeNi/CuBe electroplated wires was reported and clearly explained using a nonlinear nature of the observed phenomena-strong dependence of the induced voltage on the value of the external magnetic field by Beach et al in 1996 [4]. Although term “impedance” belongs to the linear theory historically they use term “magnetoimpedance” for all cases [6,7]. Both linear and non-linear GMI sensitive elements are promising for the detectors of small magnetic fields offering the sensitivities up to the detection levels requested for biosensors [3]. At the same time non-linear excitation regimes require higher values of the driving current (usually with an intensity above 40 mA [4]) and therefore they are more energy consuming. Despite of the lower total value of the GMI effect and its sensitivity with respect to applied field, some studies were focused on the GMI features for the energy low consuming regimes, i.e. regimes with low intensities of the driving current [8-10].

Electrodeposition is well known and relatively cheap technique [4,11]. Electroplated wires are composite materials consisting of a conducting non-magnetic core and magnetically soft tube covering, which can be FeNi [4, 10], FeCoNi [5,6], CoP [12,13], Co [14], NiFeMo [10], NiFeRu [15]. A wide variety of compositions of magnetic layer was investigated in order to obtain as high as possible values of the GMI variations and high values of sensitivity with respect to an external magnetic field. The last parameter is a strict request for the design of small magnetic field sensors. Since 1996 [4] when the firs work on GMI in electroplated wires was published, huge progress was made in the understanding of both linear and non-linear GMI: the highest values of the sensitivity for reasonably low frequencies were reported for FeNiCo/ CuBe electroplated wires in case of non-linear (high energy consuming) regimes [6,16]. Their deposition conditions like electrolytic current density, pH, in bath additives etc. were carefully studied [13,17].

The GMI responses depend on many parameters like alternating current amplitude and frequency, on effective magnetic permeability, magnetostriction, induced anisotropy etc. One therefore should search for optimised number of parameters to satisfy special condition of each particular application. It can be particular frequency, power consumption limit, the size of the sensitive GMI element, working field interval, working point for magnetic field, level of admitted hysteresis or the price of the circuit to solve the hysteresis problem etc. [18]. In a majority of the studies of the GMI effect in electroplated wires with focus on applications they evaluated Z(H) features or simply induced voltage behaviour [16] without complex analysis of different technological requests. For example, GMI responses of Fe₂₀Ni₆₄Co₁₆/Cu₉₈Be₂ electroplated wire were extremely high [16] for the exciting current of 40 mA and frequency of 4 MHz but the working interval was as narrow as almost zero: the magnetisation process looked rather like magnetisation reversal/discontinuity jump.

One of the requests of the market is automatic measurement of the angular dependence of the GMI. These studies are especially limited in case of the electroplated wires [19] which, in contrast with rapidly quenched amorphous ribbons [20] or thin films [21] as it will be proved here show certain advantages.

In this work the non-magnetic Cu₉₈Be₂ wires were covered by Fe₂₀Co₆Ni₇₄ layers by electroplating for development of GMI sensitive elements. The correlation between static magnetisation processes, the GMI effect value for the total impedance variation and its real and imaginary parts and angular dependence of the GMI with respect to an external magnetic field were studied with focus on electroplated wire particular applications as sensitive elements of the magnetic field angular detectors.

Composite CuBe/FeCoNi wires were prepared by the electroplating of 1 μm Fe₂₀Co₆Ni₇₄ magnetic layer onto highly conductive Cu₉₈Be₂ nonmagnetic cylinders of 100 μm f by elctrodeposition of 1 μm diameter electropolished prior to magnetic layer deposition. The electrochemical experiments were carried out in an electrochemical cell. Cu₉₈Be₂ wires were used as cathode having an exposed area of approximately 0.12 cm²; the current density was as high as current density of about 25 mA/cm². The thickness of the deposited magnetic layer was determined by the time of the deposition in carefully calibrated system. The composition, geometry and structure of the samples were studied by A JEOL 60 kV scanning electron microscope, SEM, equipped by energy-dispersive X-ray spectroscopy system, EDX.

As a consequence of the technology (the electric current flowing along the wire during the electroplating creates a circular magnetic field and causes the appearance of the induced magnetic anisotropy and a circumferential magnetisation component) [4] the longitudinal GMI in a magnetic field applied parallel to the wire axis in asprepared electroplated wires very often consisted of a very sharp impedance variation, i.e. discontinuity jumps which are not useful for application providing a very narrow working field range [16]. Therefore in order to increase the working field range one can design appropriate magnetic anisotropy using corresponding post deposition heat treatments in external magnetic field or torsion annealing [6,20].

Magnetic field annealing in an Ar atmosphere was done under a constant magnetic field of 160 A/m applied along the axis of the wire at a temperature of 320˚C for 1 hour in order to induce effective longitudinal magnetic anisotropy. These conditions were defined using the procedure described in previous research works [5,6]. Fast cool down to room temperature allowed to conserve a magnetic anisotropy induced during the heat treatment. The value of the magnetic field of 160 A/m for above mentioned annealing was selected on the basis of the evaluation of the features of magnetisation curves, M(H), of non-annealed samples, measured at room temperature. It was much higher comparing to the value of the saturation field for the sample in the initial state. All studies were done at room temperature. The total length of the samples used for GMI measurements was 70 mm.

The value of the room temperature saturation magnetisation, M_s, of the magnetic layer (about 9 × 10⁵ A/m) was obtained from the measurements with a vibrating sample magnetometer of shorter samples of about 9 mm long. The estimated thicknesses of the magnetic layers calculated by structural and magnetic methods were close to each other. The inductive M(H) hysteresis loops were also measured by a conventional fluxmetric method at 30 Hz frequency for 70 mm samples. Resistivity of the non-magnetic CuBe wire was about 4 μΩ-cm and that of the FeCoNi magnetic layer was about 15 μΩ-cm.

The voltage drop across the electroplated wire was measured as a function of the external field by using a standard four-point technique both in increasing “up” branch and a decreasing “down” branch magnetic fields. The impedance changes were calculated by the Ohm’s law follow standard procedure [5,6]. The external magnetic field up to the maximum value, H_max = ± 3 kA/m was created by a pair of CENCO 71267 Helmholtz coils. In all cases for each value of an external field the amplitude of the alternating current was adjusted to a requested value in order to maintain it constant, i.e. regardless of the voltage variations. The error in determining the impedance components was below 2%.

The measuring system was specially designed to allow a rotation of the test fixture with the sample in the external field with an accuracy of at least 2˚ for the angle, α, being the angle between the applied magnetic field and the wire axis (Figure 1). Total impedance and its real, and imaginary, parts were measured by HP 4284 A LCR meter for frequency range of 0.6 to 1 MHz with intensities of the sinusoidal driving current (I_ac) of 2.5 to 20 mA. The MI ratios for total impedance ΔZ/Z and its real, ΔR/R, and imaginary, ΔX/X, parts were defined as follows:

where Z(H), R(H) and X(H) represent the impedance and its parts in a magnetic field H and the Z(H_max), R(H_max) and X(H_max) the impedance and its real and imaginary part values in the field H_max = ± 3 kA/m. The sensitivities of the GMI ratios with respect to the external magnetic field were defined as follows:

In case of the total impedance and its components the sensitivities can be also defined as follows:

where DH = 0.2 is the change of the magnetic field. The maximum available sensitivities to a magnetic field, S_max (DZ/Z), S_max (DR/R), and S_max (DX/X) were also calculated when necessary being the maximum observed sensitivities S(Z), S(R) and S(X).

Figure 1 shows the cross-section of the electroplated wire which was twisted and cut on purpose to distinguish better the magnetic layer and central conductor.

The non-magnetic CuBe conducting wire and magnetic Fe₂₀Co₆Ni₇₄ layer are clearly seen. One can evaluate the thickness of the magnetic layer as big as about 1 μm which was in a good agreement with the estimation data taken from the deposition time.

Analysis of VSM measurements and structural studies were consistent to each other indicating thickness of 1 μm for magnetic layer. EDX analysis indicated that actual composition was close to Fe₂₀Co₆Ni₇₄. Figure 1(a) explains geometry of the GMI measurements and gives the angles definition. The longitudinal magnetisation process, i.e. magnetisation process for the magnetic field applied along the wire axis (α = 0˚) and the field dependence of the GMI for smallest and highest of studied frequencies are shown in Figure 2.

For “down” branches of the magnetoimpedance one can see the broad maximum at a negative field and much narrower one in a positive field. In contrast with the Z(H) curves, the hysteresis loop of the electroplated wire have no visible peculiarities in the negative fields. The easy magnetisation direction in the as-prepared samples (not shown here) was nearly circumferential. As a result of the field annealing, the easy magnetisation axis partially rotates to the axial direction of the wire. Previous theoretical and experimental studies [4,5] considered that

the GMI curves of this kind of wires have two differently shaped peaks corresponding to two orientation phase transitions: the broad maximum at a negative field is of the second order and much narrower one in a positive field is of the first order. This explains a significant hysteresis observed both in the positive and negative fields close to the GMI maxima (Figure 1). Although this kind of hysteresis is a disadvantage for technological applications it can be reduced either by the increase of the intensity of the alternating current [19] or by the design of double sensitive element configuration detector [22].

The impedance of the field annealed electroplated wire shows strong dependence on the magnetic field. Both the “up” and the “down” branches of Z(H) curves have two maxima in the field close to the anisotropy field of about 310 A/m estimated from the shape of the inductive hysteresis loop. Even for the smallest intensity of the driving current (I_ac = 2.5 mA), rather high sensitivity of 0.82%/A/m was observed for the low frequency of 1 MHz convenient for many technological applications. The highest value of the total impedance MI ratio sensitivity (5.3%/A/m) was observed for I_ac = 20 mA and f = 1 MHz which were kept for angular dependency studies of the MI response of the sensitive element. Despite of the fact that higher sensitivities were previously reported in the literature one should always compare the sensitivities obtained for different sensor elements in the same or as much as close conditions. For example, the highest sensitivity obtained by Garcia et al. [8] for FeNi/Cu wires for 1 MHz frequency was just as high as 0.038%/A/m for the wire of similar lengths and similar value of the intensity of the driving current.

Figure 3 shows the GMI variation (for total impedance, real and imaginary parts) of Fe₂₀Co₆Ni₇₄ electroplated wire based sensitive element in external magnetic field. It is clearly seen that total impedance and its real and imaginary parts show strong and similar dependence on a magnetic field (see also Table 1): even shapes of the peaks in the positive and negative fields for R and X parts are similar to that observed for Z(H) dependence. In all cases the shape of the GMI curve can be described as characteristic two-peak response [5,16]. The maximum