Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> New sensitive linear-type force transducers are presented using a single amorphous core multivibrator bridge with a dc output. These amorphous-core transducers, in which annealed Metglas 2605A ribbon-wound cores with lumped windings are used, have high linearity (0.5 %FS), high stability against temperature variation (0.02 %FS/°C), high maximum operating temperature (200°C), and high output voltage (350 mV) compared with conventional unbonded resistance wire strain gages and semiconductor transducers. The amorphous-core force transducers are considered to be suitable for application in industrial automatic control under high temperature and high noise level conditions. <s> BIB001 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Presents a review of fluxgate magnetometry based on a survey of the literature and on the work of the author and colleagues. The theory is outlined and an evaluation of the merit of the different types of sensors is made based on the sensor geometry. The design of a second-harmonic feedback magnetometer is discussed with respect to sensor configuration, frequency response, noise, offset, temperature dependence and long-term stability. Examples of the parameters are compiled from the literature and some new results on the long-term stability are presented. <s> BIB002 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> A new torque transducer of the noncontact type employing the magnetostrictive effect is presented. In this torque transducer, two stress-sensitive amorphous ribbons are glued to a torsion bar which is used as a part of the shaft. Unidirectional magnetoelastic magnetic anisotropy is created in each ribbon in such a manner that one of the anisotropies lies along 45° to the shaft axis and another along -45°. The applied torque is detected as a difference in permeability between the amorphous ribbons by an ac bias field. The amorphous ribbon used in experiments is of Fe-Si-B system whose saturation magnetostriction \lambda_{s} \simeq 24\times10^{-6} and I_{s} \simeq 1.5 T. With this torque transducer, instantaneous torque as well as static torque is detected with sufficient accuracy. Due to the easy-to-mount structure, this torque transducer is well suited for the torque control application. <s> BIB003 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> The high stress sensitivity and high yield stress properties of amorphous ribbon materials make them suitable for magnetic sensors and tranducer applications. Recently the authors have shown that ac systems eliminate the offset voltage and drift problems of the previously published dc systems. Further investigations proved that these transducers could be operated with a linear characteristic up to 1000 g in multiwrap toroidal configurations. The cause of the transducing behavior of the materials was proved to be variation of permeability with stress. It was previously suggested that the optimum operating frequency of the ac transducers is dependent on the physical configuration of the core. Further investigations have shown that the optimum operating frequency is linearly dependent on the amplitude of the input signal to the transducer. Double‐core systems have been previously described in the literature where one core acts as a dummy core and the force is applied to the active core. The disadvantage of t... <s> BIB004 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> The residual stresses in deformed magnetic metal rods are estimated by measuring the electromotive force induced from a propagation of ultrasonic waves. When a longitudinal ultrasonic wave is transmitted to magnetic metals, a magnetic field with an ultrasonic wave frequency is generated in specimens by the inverse effect of magnetostriction. The magnetic field is detected as an electromotive force induced in a sensing coil. In this paper, it is shown that the amplitude of electromotive force due to ultrasonic waves depends on both the effective magnetic field and the residual stress in magnetic materials deformed. As a result, the residual strain of as-received specimens estimated is the same as a 10% deformed rod. <s> BIB005 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Abstract Fe 20 Ni 74 Co 6 and Fe 20 Ni 64 Co 16 1 μm thick magnetic tubes electroplated onto Cu 98 Be 2 conductive wire have been investigated in as-deposited state, after heat treatment under longitudinal magnetic field for 1 h at 330°C, and after rf-sputtering deposition of the additional 2 μm Fe 19 Ni 81 layer. Heat treatments and an additional layer deposition modify the shape of hysteresis loops. Magnetically bistable behaviour, observed after the field annealing at a temperature of 330°C, is studied as a function of the length of the samples. This is the first report by our knowledge on the bistable behaviour of the electroplated wires. The bistability of these wires is promising for applications such as tagging or pulse generator applications. <s> BIB006 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> In this work, we show the induction of bistability in amorphous ribbons with low magnetostriction (Metglas 2705 M) using the exchange coupling in zones with a continuously varying anisotropy direction. It is shown that the magnetization processes under the action of a longitudinal magnetic field can be controlled by the non-uniform field produced by an alternating current, of the same frequency as the exciting field, flowing through the sample. Hysteresis loops with very different susceptibilities and coercive fields have been obtained by varying the amplitude of the current intensity and the phase differences between the exciting magnetic field and the current through the sample. <s> BIB007 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Circular magnetic bistability associated with a large Barkhausen jump between two states with opposite directions of circular magnetization have been observed by magneto-optical Kerr effect in nearly-zero magnetostrictive glass covered Co-rich amorphous microwire. The influence of external axial tensile stress on the circular switching field has been studied. Observed results have been related with a circular magneto-elastic anisotropy induced by a tensile stress in the outer transversally magnetized shell of the microwire. <s> BIB008 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> In this work we show the induction of bistability in amorphous ribbons with low magnetostriction (Metglas 2705M) using the exchange coupling in zones with a continuous varying anisotropy direction. It is shown that the magnetization processes under the action of a longitudinal magnetic field can be controlled by the non-uniform field produced by an alternating current, of the same frequency than the exciting field, flowing through the sample. Hysteresis loops with very different coercive fields have been obtained by varying the amplitude of the current intensity through the sample. <s> BIB009 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> A new sensor for magnetic field detection and mechanical displacement is presented. The active element is a CoFeSiB magnetic amorphous wire having 125 μm in diameter. Using different wire lengths can modify both the magnetic field and the displacement range. Moreover, this sensor could be successfully used for the detection and measurement of 3D magnetic fields. <s> BIB010 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Abstract This paper presents results of the investigation on a novel solution in construction of the magnetoelastic torque sensors. In this solution, ribbon ring-shaped magnetic materials based on both iron and nickel were used. Due to a special backing glued to the ring-shaped core the uniform stresses under the influence of the torque can be achieved. As a result magnetoelastic properties under the influence of the torque can be tested. For investigation both Fe 78 B 13 Si 9 and Fe 40 Ni 38 Mo 4 B 18 alloy compositions in as-quenched and annealed state were used. In annealed Fe 40 Ni 38 Mo 4 B 18 core, under the torque equal 4 Nm, was observed a decreasing of flux density from 301 to 108 mT. <s> BIB011 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Results are presented for the performance of a magnetoelastic torque transducer that converts a torque-induced strain in a nonmagnetic shaft into changes in a measurable magnetic field. The magnetic field is generated by a thin magnetostrictive layer that is coated onto the circumference of the shaft. The layer is magnetized and has an initial residual strain. The magnetization within the layer rotates in response to changes in the strain which occur when the shaft is torqued. The magnetic field produced by the layer changes with the magnetization and this can be sensed by a magnetometer to monitor the torque on the shaft. In this paper, a phenomenological theory is developed for predicting the performance of the transducer. The theory can be used to predict the magnetic field distribution of the transducer as a function of the physical properties of the magnetic coating, its residual strain, and the applied torque. It enables rapid parametric analysis of transducer performance, which is useful for the development and optimization of novel non-contact torque sensors. <s> BIB012 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> The structure evolution of the annealed amorphous microwires of composition Fe40Ni38Mo4B18 and its interplay with magnetism has been studied. It has been shown by x-ray diffraction, that primary crystallization phase has a microstructure of γ-(Fe,Ni) crystallites of about 10 nm embedded in a residual amorphous matrix. Changes of the saturation magnetization and the switching field after different thermal treatments were observed. The dependence of the switching field on the applied mechanical stress was investigated. <s> BIB013 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Abstract Full-fiber optical current sensors utilize the effects of magnetic-field imposed on the change of polarization azimuth of light in the fibers. Due to the sensitivities to external perturbations, the sensing fiber head in practical applications is usually packed in a fixed metallic housing majorly for protection purposes. However, the housing material itself tends to influence the magnetic field distributions of the current carrying wire in question. In this paper, the intrinsic effect and influence of fiber sensor head housing made of different magnetic materials on the magnetic field distributions around the current-carrying wire have been investigated. Simulation and virtual experimentation was carried out in the COMSOL environment. From the results, the housings made of single magnetic material are found to have magnetic disturbances on the magnetic field distribution around the wire. Housing made of some alloy materials has no influence on the magnetic distributions outside the wire. After experimenting with several materials, the former materials inclusive, steel is preferred as the protective housing and/or casing of fiber sensor head in optical fiber current sensors. This is on the basis of both technical and non-technical consideration of low cost of material though biased toward technical aspect of little or no influence on magnetic distribution around the wire. <s> BIB014 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> This paper shows a new displacement-to-frequency transducer based on the variation of a coil inductance when a magnetic core is partially or completely inserted inside. This transducer is based on a Colpitts oscillator due its low manufacturing price, behavior and immunity to noise. A tank circuit with a configuration in parallel was used because it can be employed at lower frequencies and it enables it to make a direct analysis. The sensor has a dynamic range equal to the length of the coil. The cores can exchange sensors (coils with its ferromagnetic core) using the same electronic measuring system. In this way, with only an electronic circuit, the core sensor determines the measurement range. The obtained resolution is higher than 1/100,000, and the sensor also allows the measurement and knowing in real time the effect of vibration, thermal expansion, referred overload movements, etc.., that can occur in the structural elements of a building. <s> BIB015 </s> Magnetic Sensors Based on Amorphous Ferromagnetic Materials: A Review <s> Theory <s> Abstract A high-finesse extrinsic Fabry–Perot interferometric sensor for the measurement of weak dc magnetic fields is demonstrated. The Fabry–Perot cavity is formed by aligning the fiber end-face and the TbDyFe rod end-face, and each end-face is coated by a mirror with a micro-lens. The length of the TbDyFe rod is changed by the variation of an applied dc magnetic field, leading a change of the Fabry–Perot cavity length. By interrogating the white-light interferometric spectrum, the wavelength of the resonant peak is tracked and the length of the Fabry–Perot cavity is obtained. The sensor exhibits a high sensitivity of 1510 nm/mT with a magnetic resolution of 25 nT. <s> BIB016
The application of a mechanical stress, σ, to a ferromagnetic material induces an anisotropy whose energy density is K = (3/2) λs σ in perpendicular or parallel direction to this stress depending on the positive or negative sign of the magnetostriction constant of the material, λs. Therefore, a mechanical stress will cause a change in the susceptibility of the material that can be used to measure stress, strain, torques, forces, etc.  . The susceptibility χ of a ferromagnetic material of λs > 0 with an initial anisotropy K perpendicular to the applied stress, which is magnetized with a magnetic field applied along to the stress direction, can be evaluated by: (1) Figure 1a shows the susceptibility (χ) depending on the stress applied (σ). When the resulting anisotropy takes the direction of the applied field, the material reaches its maximum permeability due to a process of magnetic walls displacement. This maximum permeability limits the maximum sensitivity of the device and is dependent on the above parameters. The maximum sensitivity of the device is obtained for extremely small densities (K), as is shown in Figure 1b , where the sensitivity curve as a function of the stress applied is represented. In this form the sensitivity is: In amorphous materials K is well controlled. Accordingly, it is possible to obtain devices with sensitivities that are equivalent to the best semiconductor strain gauge, although in this form the dynamic range of the devices decreases (Figure 2 ). Therefore it is advisable to select materials with high λs to achieve acceptable dynamic ranges without decreasing their sensitivity. Figure 3 shows a typical application of these devices for the measurement of torques on rotary axes without electrical contacts BIB003 BIB012  . For sensors with the shape of layers or thin tapes, magnetic materials are used in a similar way as extensometric bands are: two sets of equal samples, perpendicularly placed between themselves in an angle of 45° with the rotation axis, are stuck to the shaft in which the torque is to be measured. If the shaft undergoes torsion, one set of samples is tensed whereas the other set is compressed, modifying in a different way the permeability of both of them and inducing an electro-motive force (e.m.f.) on the series connected secondary reels. If there is no torsion both have the same permeability being the outgoing signal zero. If, instead, there is torsion a signal proportional to the relative permeability change is recorded. This system allows one to measure torques on rotary axes without using sliding contacts, which always give problems. The main drawback of this measuring system are the induced stresses on the samples when gluing the layers to the base; this effect can be avoided by using ceramic glues and annealing afterwards the system in order to remove the induced stresses. This sensor has been developed by Pina et al.  to detect and measure the muscle activity in the throat, in order to remedy partial vocal cord paralysis. This ailment concerns the paralysis of one of the vocal cords due to its partial or total weakness. The voice is produced by simultaneous vibration of both vocal cords. An air column coming from the lungs passes through the vocal cords at a certain pressure, causing a natural vibration. In order to reach the right pressure level, the vocal cords move towards each other until reaching the so-called midline, closing the air flow properly. This is the normal function of a healthy throat. In case of paralysis, the damaged cord stays far away from the midline being unable to move itself to reach the right pressure level. As a result, the cords do not vibrate and the phonation is not totally possible. The manufactured device consists of two clearly different parts. The first element is a magnetostrictive sensor which is inserted inside the healthy vocal cord. This sensor can detect the deformation and tension inside de muscle during the normal activity of the vocal cord. The sensor will + respond to a certain deformation with an electric signal which will start up the device's second element. The second element consists of an actuator composed of a set of electrodes connected to the vocal cord nerve. The electrical stimulation of the unhealthy vocal cord will be controlled by the responses off the magnetoelastic sensor located on the cord. This way both vocal cords will move simultaneously and symmetrically. The system is regulated by a feedback control that includes a second magnetoelastic sensor inserted inside de damaged vocal cord. The sensor manufactured for this application was designed to respond to stresses applied in any direction of the insertion plane. Thus the sensor core is composed of a magnetostrictive tape in the shape of a ring with two rolled coils around the core: a drive coil of sine waved voltage within a range of hundreds of kHz frequencies and a secondary coil. The sensor is covered with biocompatible silicone and the sensors head has a 3 mm diameter. The optimal work frequency obtained is of 500 kHz. The sensor has been tried on dogs. The experiment shows clearly two signal peaks that correspond respectively to deglutition and phonation. (c) Deformation Sensor Another possible application of this effect is shown in Figure 4 . This device BIB004 BIB011 BIB001 uses a several layers round core with multiple windings. Any pressure being exerted on the torus modifies the self-induction in the windings, which allows a very accurate measuring of deformations. The sensitivity of the sensor is of 350 mV/V within a range of 10 mg-30 g, showing stability at a temperature of 0.02%FS/°C (FS is full scale) and a maximum operating temperature of 190 °C. There are also sensors to measure magnetic fields, current capacities, deformations, etc. that have been developed using the inverse effect as earlier described: the change in length of ferromagnetic materials when varying their magnetic direction. Optic fibres with nickel cover, acted upon by a magnetic field, vary in length when the length of their cover is altered Through interferometric measures, it is possible to determine with great accuracy the variation of that length which is proportional to the applied magnetic field BIB014 BIB016 . Figure 5 shows a current sensor based on this effect. With some slight changes it can also be used to measure magnetic fields. Position sensors are measured with an optic fibre sensor through a field created by a permanent magnet stuck to the object of which the position is to be determined. Finally, magnetometers with a much lower sensitivity have been developed. They are based on speed variations of acoustic waves that are conveyed through a tape of amorphous material when their magnetization state and, consequently, their Young modulus changes by the action of an outside field BIB005 . The detection of this speed variation is done measuring the phase changing of the elastic waves emitted by the source and those collected by a receiver (Figure 6 ). The wave phase change will be according to: where K is a parameter in proportion to the Young modulus, D the distance between transducers and C the acoustic wave speed. This sensor has an estimated sensitivity of 1 pT (ΔY = 0.05, D = 1 m, ω = 20 MHz, c = 3 Km/s) and an experimental sensitivity of 2.5 nT. A saturated core sensor (or fluxgate magnetometer) is a device which uses the periodic saturation of its ferromagnetic core (or cores) to produce an output signal with harmonic components that are nearly proportional to the device's external magnetic fields. The ferromagnetic core is periodically saturated through a current applied to an exciting winding, while the net variation of the core flow is observed with the help of a measuring winding. If there is no external magnetic field, the electromotive force induced into the measuring winding contains at least the odd harmonics of the exciting current, unless the device is configured (as is usual) in a way that keeps the mutual inductance between exciting and (3) measuring winding to a minimum, in which case the odd harmonics also near zero. When an external magnetic field is applied, the operation becomes asymmetrical, producing even harmonics in the measuring winding BIB002 . Consequently, this device uses the (nonlinear) magnetic features of the ferromagnetic core material to form a directional sensor which measures the component of an external field parallel to the measuring coil's ( Figure 7) axes. The phenomenon of magnetic bistability in amorphous substances was observed firstly in iron-rich and highly magnetostrictive threads. The magnetic and mechanical characteristics of these threads and their possible technological application have been examined in depth. Several authors have studied these materials to establish the dependency of the Young modulus on the applied magnetic field, the longitudinal and transversal magneto-resistance, the magnetostriction, etc. BIB007 BIB006 BIB013 BIB008 . However, the basic mechanisms responsible of magnetic bistability were not determined immediately. Therefore, the bibliography includes many papers of related to various characteristics of these threads, amongst them the Barkhausen and Matteucci effect, the influence of mechanic tensions on magnetization processes and observations of magnetic domains with the Bitter technique. The reason why the threads show a bistable behavior is that, due to the manufacturing process, two areas appear: the inside area that is tense and the magnetization of which is aligned with the thread's axis; and the outside area that is compressed with a magnetization perpendicular to the axis. As a result of this setting, a strong magnetoelastic coupling, responsible of the bistable behaviour, occurs. Initially, the bistable jumps were attributed to the spread, alongside the thread, of a conic magnetic wall that was thought be nucleated at the thread ends like a closing domain to decrease its magnetostatic energy. Spread measurements of these walls were realised. Today, taking into account the braking measurements through induced flows of the propagation wall in the thread, it seems more likely that the wall spread has a plane and not a conic propagation. Since the bistable behavior is a consequence of a magnetoelastic coupling, the parameters of the loop described by the samples under the action of an alternating magnetic field will be strongly influenced by tensions applied from the outside. The thermal treatment of these threads subjected to tension will influence their magnetic features. Likewise, it is possible to obtain bistability on non-magnetostrictive threads by merely applying tensions and torsions to reinforce the magnetostrictive coupling between the inner and outside areas of the thread. Also the influence of an axial electric flow on the magnetization processes of bistable threads has been studied by many different authors, obtaining a shift of the bistable jumps which is a function of flow intensity BIB009 . These bistable jumps can be extinguished by applying simultaneously axial tensions, torsions and electric currents. A stable magnetization direction M in a ferromagnetic sample is determined by the configuration that most minimizes the total free energy of the system. Considering that the saturation magnetization MS of a thin film forms an angle θ with the longitudinal axis of the sample, that a HR field forming an angle α with the axis is applied and that the anisotropy field forms an angle γ with the said axis, the system's magnetic energy will be defined as follows  : (1) Zeeman Magnetic Energy When applying an external magnetic field, magnetization will tend to parallel that field in order to decrease the system's energy: Anisotropy energy concerns the existence of different preferential directions, so-called easy axis, to magnetize the material. These easy axes are determined by the rate of symmetry of the crystalline pattern of the (spin-orbit coupling): It represents the magnetization energy in the demagnetization field created by magnetization itself as a consequence of the existence of pole distribution in the sample: being ND the demagnetization field opposite to MS direction: adding up the three contributions to the system's energy and differentiating with respect to θ, we can find the condition that minimizes that energy: This equation determines the relation between the applied field HR and the θ angle between the magnetization vector and the longitudinal film axis, which is also used as the current direction ( Figure 12 ). This θ angle has the following relation with the material's resistivity: being Δρ the maximum value of the resistivity change to the magnetic field (saturated magnetoresistance): Combining Equations (7) and (8), θ can be eliminated, obtaining so the relation between the relative change of magnetoresistance and the magnitude and direction of the applied field, assuming that the other constants are known. This is the operating basis of magnetostrictive sensors. Figure 12 . Magnetization, applied magnetic field and anisotropy direction. This type of sensor is based upon the mutual induction coefficient variation between two coupled circuits with a magnetic core, as a consequence of a position change of this core BIB015 . The linear variable differential transformer is commonly referred to as LVDT. This sensor consists of a primary winding alongside the core centre and of two secondary coils placed symmetrically in relation to the centre (Figure 14) . The three windings are covered with an impermeable substance to enable them to operate in highly humid environments. The core is an iron and nickel alloy, longitudinally laminated to reduce the Foucault currents. The stem that drags it should not be magnetic, and is at the other end attached to the piece of which the movements are to be measured. The whole set can be magnetically screened to make in it immune to external fields. When an alternating current is applied to the principal winding, a current is induced into the two secondary coils. Since the secondary coils are connected in series-opposition, when the ferromagnetic core is in the centre, the tensions induced in each secondary coil will be equal and the output sensor will give a zero value. When the core moves away from the centre, one of the two tensions increases and the other one reduces with in same magnitude (Figure 15) , generating a proportional linear output to the magnetic core position. The relation between input and output tension can be determined by means of basic transformer equations, as they basically function in the same way. where es is the output voltage of the secondary coils and e0 is the primary coil input voltage. The main problem with this traducer configuration is that it becomes impossible to detect the sense of movement within it. In order to solve this problem, the transducer is provided with a suitable signal fitting. For that purpose, a phase detection is carried out. In principle, the e.m.f. of the secondary coils increases with the frequency. However, according to the "skin" effect, the real response of the device gives a maximum value, because the penetration depth of the magnetic field into core decreases with the frequency. That is why usually hollow cylindrical cores are used, since with the normal operating frequencies of these devices (from 1 to 5 KHz), the magnetic field hardly penetrates in ferromagnetic conductor materials. This device can reach a 0.25% to 0.05% linearity in a millimetric range, depending on the core length and the excitation frequency. With a proper design it is possible to measure 10 mm with micron resolution. The magnetoimpedance is defined as the change in impedance of a ferromagnetic conductor, to which is applied an AC current of low intensity and constant frequency, in order to induce an alternating magnetic field in the presence of an external magnetic field. Changes in impedance are caused by the variation of the material magnetization with constant magnetic field and the alternating magnetic field induced by alternating current. Accordingly, these changes in impedance reflect changes in the magnetic structure of the material. So the increase in impedance is a function of the permeability of the material in the direction of the applied field BIB010 . Early work correctly describing the effect magnetoimpedance was published in 1930 by Harrison, based on experiments performed in Permalloy wire. However, it was in the year 1990 when this topic attracted interest due to the discovery of amorphous and nanocrystalline magnetic materials, resulting in a significant number of publications. The first published magnetoimpedance effect work in amorphous samples was developed by Makhotkin in 1991. Subsequently, the giant magnetoimpedance was defined as the response of materials at high frequencies, so that the surface effect results in large changes in impedance of 600% in some materials BIB010 . For high frequencies, the effect of giant magnetoimpedance (GMI) it has been explained by classical electrodynamics, as an interaction between the alternating magnetic field and the magnetization due to the constant magnetic field. The GMI effect is mainly caused by changes in the resistive component of the impedance, as is a skin effect. This causes current is limited to the sample surface, reducing the effect of the cross section of the material, producing an increase in the resistive component of the impedance. Therefore, at high frequencies the skin effect is determining the behavior of the magnetoimpedance.