Magnetic Domain Structures in Wires

Introduction

Complex domain structure and stress sensitivity are those unique behaviours of amorphous wires which have attracted various researchers to identify their relationship with magnetic field and stress. Now, magnetic domain structure has an inner domain structure and an outer shell which is magnetised radically in the case of positive magnetostrictive wires, and for negative magnetostrictive wires, it is magnetised circumferentially. This domain structure will be determined by coupling stress internally with magnetorestriction. In this research, a various magnetic effect like Barkhausen effect and Matteucci effect will be discussed. These magnetic effects arise due to the appearance of microscopic magnetic properties with high magnetorestriction due to non-existential crystalline properties (Zhukov, 2016). The special focus of this study will be on Matteucci effect which has been found in amorphous structures and is most dominant in those metals with high Co content. In this research, this effect studies to find the negative magnetostrction in amorphous wires. Moreover, a pulse voltage with Barkhausen effect would also be taken into consideration. The Matteucci voltages will be elaborated in a subtle manner. The research also focussed on how Matteucci voltage is increased by treatment with heat and its application on quenched wires (Zhang, 2015). Bi-stable amorphous wires lead to sharp pulses when excited by ac magnetic field. This has been observed from either pickup coil wire around the wire or from wire’s end. The former is caused by large Barkhausen effect whereas; latter is due to Matteucci effect. When the current scene change, the AC magnetic field is inverted, and magnetisation occurs, thus inducing a voltage between ends of the wire. These induced voltages also known as pulse elements are used widely in sensors like rotational, security, magnetic field at all. These are altered by factors such as current annealing and parameters like stress, torsion and can found use in sensor applications (Kane et al., 2001). Amorphous metallic alloys like CoP have a special magnetic property which has major applications in technical and magnetisation process. The Matteucci effect has been subjected to torque, and it has been revealed that magnetic domain structures change their direction by rotating gradually form longitudinal position and thus torque is increased (Meydan, 2002).

The aim of the current study is to find the effect of axial AC magnetic field and stress on pulse generator characteristics of Matteucci effect in as-cast and current annealed amorphous wires. The focus of this project is to design a measurement system for determining the characteristics of domain wall dynamics. Essentially, the method will consist of magnetising a ferromagnetic wire placed at the centre of a long solenoid. Pick-up coils wrapped around the wire at regular intervals will detect the passage of domain wall boundaries under magnetisation conditions. Time delays of the pick-up signals, captured using an oscilloscope, will be analysed to explain the dynamic behaviour of the magnetic domains.

The major task of this research on amorphous alloy wires is to:

Assemble measurement system (i.e. solenoid, power supply and oscilloscope). • Design and construct pick-up coil assembly (including compensation coils). • Plot magnetisation - field (hysteresis) loops for each material investigated. • Perform measurements on a range of materials at different frequencies. • Analyse output data in terms of domain wall dynamics. • Study of Amphorious wire characteristics. • Study of Domain speed characteristics and measuring method. • Study of Matucci effect causes and characteristics and how to generate. • Study equations for Matucci effect and measuring method. • Implement of the excitation coil, Matucci coils, and Amphorious wire. • Measurements of Matucci voltages between two coils for domain speed calculation at different flux and stress values. • Analysing and assessment of the obtained results. • Documenting the project activities in the form of project thesis.

Matteucci Effect

It is one of the magneto-mechanical effects and is observed in amorphous wire with helical domain structure which could be obtained by either twisting the wire or annealing it under twist. It is most distinct in “dwarven alloys” where cobalt is the main substituent. In the Matteucci effect long, the thin magnetic sample is excited by an alternating magnetic field applied in the sample length direction; a voltage will be induced across the ends of the sample if the magnetisation vector is at an angle from the length direction (Takamure et al., 1990). Matteucci effect finds its application in pen-inputting personal computer tablet where an AC magnetic field is applied vertically at a point where a double AC voltage passes between both the ends (Mohri, 2009).

Matteucci Voltage

In the amorphous wire, the component of the magnetisation vector, in the inner core of the wire where large Barkhausen jumps occur, is at an angle from the wire axis, produce the Matteucci voltage (Meydan, 2002). The structure is of ‘inner core’ domain and outer shell. The domain structure is defined by the internal stresses that arise from quenching, and the magnetic moment orientation in the outer shell depends on the sign of the magnetostriction (Takamure et al., 1990). This voltage can be derived with the help of given diagram:

It is considered that Matteucci Voltage is induced in inner core domain walls. Here, the domain wall is modelled as the cone-shaped wall where the z-axis is in the wire axis and a cone-shaped domain wall of length l within a core of radius R to propagate with velocity, v. Then no current flows in the wire radially. Hence, if Bq is the induction component in the circumferential direction, then from the Maxwell equation:

(rot E)Ө =-∂BӨ/∂t

We obtain the following:

∂Ez/∂r=∂BӨ/∂t

Then the Matteucci voltage epm generated by this cone-shaped domain wall may be obtained by integrating above equation along the z-axis over the length of the wall I:

epm = ∫Ez dz and thus

epm= BӨ vRl

Thus the Matteucci voltage epm is proportional to the domain wall velocity v, the inner core radius R and the wall length 1. The voltage epm induced in a pickup coil by large Barkhausen jumps is proportional to the time rate of change of the magnetic flux in the axis direction, and the shorter the domain wall length I, the greater is epm. Conversely, the Matteucci voltage is proportional to the wall length (Meydan, 2002).

Weidmann Effect

It is special kind of magneto-mechanical effect and a special case of magnetostriction where a field is twisting of the ferromagnetic rod due to the joint action of longitudinal current and magnetic field present in the rod, when there is a flow of electric current. It is used in ultrasonic pulse and magnetostrictive wires (Heng et al., 2012).

Large Barkhausen Effect

It is the production of noise in the magnetic input of ferromagnet when a magnetised force is applied on it. It is caused due to a sudden change in size and orientation of magnetic domains that occurs during the continuous process of magnetisation, as well as, demagnetisation. It finds its application in evaluation of degradation of mechanical properties in magnetic materials and high energy particles. It is also used to find damage in a thin film structure (Zhukov et al., 2015).

Magnetic Flux

It is a measurement of the total magnetic field which passes through a given area. It is helpful in areas where there is a magnetic force in a given area. The measurement of magnetic flux is tied to the particular area chosen. It is measured by magnetometer which is also used to measure magnetic field (Patrick and Fardo, 2008).

Assembling of measurement system

This figure illustrates influence on Matteucci effect from dc magnetic field. The measurement was done effectively. So when the axial dc field was laid, there was a decrease in Matteucci voltage. This would happen only when there exists a circular component of magnetisation. This can be achieved if torsional stress is applied on each axis having non-helical component. The strength of this axis increases by applying ac axial field which alters its orientation and changes circular, as well as, axial component (Zhukov, 2016). When the twist in the structure is increased, the Matteucci voltage and stress also increases. By applying magnetic field perpendicular to the given axis, the improved pattern resolution could be achieved.

Design and construct pick-up coil assembly

In the above figure, a cylindrical coil with pick-up is used to measure magnetic flux using Matteucci effect which is derived from longitudinal component after compensating the flux produced by the applied field in the second coil in series but is connected opposite to the pickup coil. An electric flux meter then integrates induced voltage in it. Then, electrodeposition process was applied where the wire was rotated along its cylindrical symmetry axis at a constant speed. Then the wires were heated to reduce internal stress, and they were polished electrolytically to avoid possible surface irregularities. Magnetic domain structure was studied, and the magnetic domain was analysed to achieve clear domain pictures scenario (Kane et al., 2001).

Cause and characteristics of Matteucci effect

The Matteucci effect in amorphous wires is represented as:

The amorphous alloy wires are magnetised circumferentially which shows that they are negative magnetostrictive in nature (Atalay et al., 2015)

The tensile stress could be applied to them due to negative magnetostriction which would further improve its magnetic properties (Zhukov, 2016)

Due to increased flux density, annealing under torsional stress, the inner radius is enlarged and which increases Matteucci voltage (Kane et al., 2001)

Therefore, when an alternate magnetic field is applied in the same direction, a voltage would be produced with thin magnetic strain. Here, Matteucci effect involves sharp voltage pulse across both the ends of the wire due to the coherent magnetic rotation with coupling accompanied by large Barkhausen jump (Atalay et al., 2015). Matteucci effect shows a long, thin magnetic strain excited by an alternating magnetic field applied in the sample length direction; a voltage will be induced across the ends of the wire if the magnetisation vector is at an angle from the length direction. In the amorphous wire, Matteucci effect involves generation of the sharp voltage pulse at the end of wires due to coupling with the coherent magnetisation rotation accompanying the large jumps in the wire. The advantage is that there is no requirement of detection of pulses via a coil. Still, there is room for further improvement before making these types of wires functional as a pulse generating elements in sensors, and there is more to be discovered regarding the mechanism of pulse generation (Sakurai, Y. et al. 2013). In this study, the researcher is providing an explanation of the mechanism of voltage pulse generation by the Matteucci effect, and experimentally confirmed the factors contributing to the Matteucci voltage. Furthermore, Co-base negative magnetostriction wire was annealed under mechanical stress and subjected to obtain results from magnetic properties under even larger magnetic effect.

Characteristics of Matteucci Voltage

The Matteucci voltage has the important feature of being proportional to the length of the propagating domain wall, in contrast with the voltage pulse due to Barkhausen jumps. The experiment was conducted to verify this behaviour. In practice it is difficult to control the length of the domain wall; therefore Matteucci voltage, epm was measured while varying the distance I between electrodes. When I is longer than the wall length, epm is shown by epm= BӨvRl; but when I is shorter than the wall length, epm can be found by integrating over I rather than over I, so that epm is proportional to I.

The above figure shows the changes in epm when one electrode is fixed to left end of the wire due to the generation of the reverse domain from the left side and are then measured along with other electrodes moved along the wire in 1 cm intervals. It shows that epm increases as 1 is increased, but does not vary in proportion to I. This happened because for electrode distances I of up to 2 cm, the effect of the demagnetising field bring about a decrease in the inner core diameter so that epm is reduced. In measurements for distances greater than 2 cm, epm increased at a faster rate than I. The reason for this is an increase in the velocity of propagation of domain walls due to changes in the external magnetic field. The diagram also illustrates that pulses, epm are measured at each individual intervals of the wire. As the segment id shifted from the left end towards the centre, the pulse also starts shifting to the right side of time axis which shows that pulse propagates from the left end towards right within the wall (Kane et al., 2001).

Measurement of Matteucci Voltage

The table demonstrates and compares Matteucci voltages obtained from various wires. The maximum Matteucci voltage was obtained from a Co-base wire which is ten times greater than the value of as-prepared Co-base wire and 100 times greater than Fe-base wire. An important feature of Matteucci voltage is that it is proportional to the length of the propagating domain wall while inversely proportional to voltage pulse due to jumps. As it is practically impossible to control the length of the domain wall, therefore Matteucci voltage is measured while varying the distance between electrodes.

Figure 5 shows a change in epm which is got by fixing one electrode to left end of a wire which generate and propagate reverse domains, and measurements are performed with the other electrode moved along the wire in 1 cm intervals. It has been found that epm at faster rate from line 2 than to line 1 as there is an increase in velocity of propagation of domain walls due to changes in the external magnetic field. The figure displays pulses epm measured over each of the individual intervals of the wire as the measurement segment is shifted from the left end towards wire’s centre which shows that walls generated shifting of pulse towards the right. The figure also shows same wire domain lengths, which were measured at different saw-tooth-wave exciting field frequencies (Stefanescu, 2011). When length, l was increased, epm also increased, and l was saturated it becomes greater than domain wall length. When a frequency ten times higher was employed, the domain length did not change, but epm doubled in magnitude. The reason behind this phenomenon is that when the velocity of wall propagation increases, there is an increase in frequency which also results in an increase in epm.

Measurement of Matteucci Voltage under magnetic field

Above figure exhibits a dependence of epm on the amplitude in which shows that frequency id varied and epm increases with amplitude as shown in the figure where Co-base wire’s epm increases when the amplitude increases (Buschow, 2003).

The given figure shows that the epm id not dependent on frequency, f. This proves that the core diameter of the Matteucci voltage id forming a rectangular waveform in the given magnetic field. On the basis of these results, it can be said that the measured domain length contributes considerably to the epm which was detected in the amorphous wire and that the increased velocity of domain wall propagation resulting from increased exciting field strength during propagation which greatly affected the epm (Vázquez, 2015).

Magnetic Field

It is the magnetic effect of electric current and magnetic materials. It is a vector field as it is specified in both directions, as well as, magnitude. It is produced by moving electric charges and the intrinsic magnetic moments of elementary particles which are usually associated with a fundamental quantum property and their spin movement (Mohri, 2009).

Stress

Stress is a physical quantity which expresses internal forces that neighbouring particles of a continuous material exert on each other. The computation of the mechanical stresses in cylindrical magnetic field coils requires knowledge of the distribution of forces acting upon the conductor, and a theory whereby this force pattern may be converted into a stress pattern (Kane et al., 2001).

Amorphous Alloy Wires

They consist of those amorphous metals which do not have any crystalline structure. They exhibit several mechanical properties like hardness with fractured stress and have high elasticity and rigidity than crystalline metals. They are generally used in making metal glasses, knives, sporting equipment of golf and baseball and in springs for high-speed relay (Zhang, 2015). Amorphous allow wires have various advantages in various electric, chemical and magnetic properties which are connected with various technologies. Some of these are explained as:

Mechanical Strength

High residual stress High tensile strength High elasticity (up to 95%) (Atalay et al., 2015)

Magnetic Strength

High stress anneal High domain wall energy density Effective current anneal High rotation permeability (Kane et al., 2001)

Electrical Strength

High Resistivity High impedance Low current losses (especially eddy current) (Favieres, 2000)

Chemical Strength

High anti-corrosiveness (Atalay et al., 2015)

Magnetisation in Amorphous Alloy wires

Amorphous wires were earlier developed for their hardness and strength characters but after some extensive research; it was found they have shown some unique behaviour in the as-quenched state. The general composition of alloy wire is in the form (Fe, Co, Ni)SiB. This alloy shows positive, near-zero and negative magnetostriction, thus allowing the researcher to study the impact of magnetostriction on their magnetic property vigorously. The low magnetic field has also been observed (Favieres, 2000). The magnetisation occurred through the large Barkhausen jump which switched approximately one-half of the magnetisation of the wire and led to bi-stable magnetic behaviour at low fields. The generation of a voltage pulse between the ends of the wire, known as Matteucci effect, is associated with this magnetisation switching. This effect can be observed as a series of voltage spikes when the magnetisation is excited with an alternating magnetic field (Atalay et al., 2015). The magnetoelastic effects of amorphous materials are relatively large, because of the magnitude of the magnetostriction and the low anisotropy associated with the lack of crystalline order. These are used in sensors in security, magnetic or rotational speed sensors (Meydan, 2002).

Characteristics of Amorphous Wires

Exhibits Positive magnetostriction Shows magnetically bi-stable behaviour Excellent magnetic softness Large magneto and stress impedance (Zhukov, 2015)

Magnetic Coil

Also known as an electromagnetic coil, a magnetic coil is a piece of wire in the form of coil, helix and spiral, through which electricity passes and creates a magnetic field. Its application is in electrical engineering where electric current interacts with magnetic fields. It is used in the manufacturing of inductors, transformers and electromagnets (Savini and Turowski, 2012).

Setup of the magnetic pickup coil

Figure 5 shows a magnetic coil with reduced inductivity providing a magnetic field which detects propagation of magnetic waves in the coil. The stored information is manipulated through motion along the wires. The speed of electrodes in domain wall while travelling in the wire impacts the viability of many technological applications in logical, sensing and storage operations. However, the DW can be introduced by nanowires at low field density injected magnetically at the soft region connected to the wire.

Longitudinal Magnetisation

It is magnetisation of any material made up of metal in which a current is passed through coils with more than one turn in such a manner that magnetic flux is in parallel to long axis of the given magnetic field, thus establishing a magnetic field. It is used for detection of discontinuities in the circumference of the wire. One of its important techniques which would be discussed in this topic is a longitudinal magnetic field (Campbell, 2013).

Longitudinal Magnetic Field

When the length of material is several times larger than its diameter, then there is an establishment of a longitudinal magnetic field. This is one of the magnetisation techniques which is also referred as coil shot (Campbell, 2013).

The above figure shows the hysteresis loop, Mz-Hz. With a longitudinal direction running parallel to the given axis. The data was obtained using a pulsed electrical current. Due to pulsed electric current, the growth was broken. Each pulse consist of a positive electric current with density= j151500 mA/cm2 for t1565 ms and negative current whose density= j252100 mA/cm2 for t2560 ms. The total number of the pulse was 8000. Now, every pulse depends on the electric current, so each layer has different concentration of Co and P atoms and produces a multilayered compositional material. Sample thickness was estimated by analysing the cross section of the samples through a microscope. The analysis showed both the copper core and the CoP shell. The estimated thickness of the sample was 25 mm (Atalay et al., 2015). In this experiment, magnetic pickup coil was studied, and the processes of magnetic domain structures and the magnetisation were discussed. The technique was applied in analysing magnetic domain configurations. In order to polarise the colloidal suspension, a magnetic field was applied which was perpendicular to the axis which led to the achievement of getting the improved contrast and pattern resolution. Thus magnetic domain pictures are obtained for both the as-obtained samples, as well as, for the samples that were subjected to angular deformation, where a controlled torque was applied to the copper core. Figure 6 shows a switched twisted curve, when the torque on the wire was applied, and which produces 90° angular deformations in the negative direction after torque is removed. This behaviour exhibits zero applied torque which happens due to angular deformation and residual helical stress in the sample. The figure displays increase in circular magnetisation initially to reverse magnetic wall displacement until the maximum value is reached (Campbell, 2013).

The first figure shows switching curves when torque was applied while producing 90° angular deformations in the negative direction. When the torque is removed, it exhibits zero applied torque. The figure displays residual helical stress in the magnetic sample and increases in circular magnetisation initially to reverse magnetic wall displacement until the maximum value is reached. Afterwards, there is a decrease in signal due to reversible magnetisation rotation towards the magnetic field direction. Following this, a new torque is applied creating a 180° angular deformation in the negative direction. From this experiment, the result obtained is that the torque increases in successive steps gradually. Now if external torque is applied in the opposite direction, there is an angular variation which induced voltage nearly to zero. Therefore, all curves corresponded to zero applied torque (Campbell, 2013).

Torsional Stress

Torsional stress is the shear stress produced when twisting the part of any application in equal and opposite torques at the end of shaft produce stress (Pilkey and Pilkey, 2008).

Perform measurements with torsional stress

The first figure presents magnetisation curves of Co based wire when torsional stress is applied; magnetisation curve was transformed into a constant square curve, showing a bi-stable behaviour. The second diagram shows that when torsional stress is increased further, the annealing occurs leading to increasing in inner core diameter. The third figure displays that when the wire id annealed further under the influence of torsional stress, the internal stress remains but the large effect produced due to rapid quenching disappears. This leads to a reduction of epm which is dropped to 1/10th of wire. The figure also indicates that epm varies with annealing temperature and time duration and slack is formed. To remove slack, torsion stress is to be effectively applied in the wire axis direction. Because of the negative magnetostriction of Co-base wire, the tension applied in the axis direction also contributes to the magnetisation component in the circumferential direction in the figure. Therefore, holding the applied tension constant lead to obtaining of mateucci voltage, epm with good production (Savini and Turowski, 2012).

The above figure displays magnetic fluid domain observations which reveal the magnetic anisotropy induced in the wire when torsional stress was applied. When Fe-base wire was subjected to torsional annealing, the following things happened:

A magnetic axis was induced in the direction same as that of applied stress in the domain wall and exhibits a "bamboo" like striated domain pattern (Pilkey and Pilkey, 2008)

However, subjecting to torsional annealing in the same direction leads to distortion figure inducing at 90° to the direction of torsional stress due to negative magnetostriction (Pilkey and Pilkey, 2008)

When the axis was at 90° to the direction of torsional stress, there is increase in epm in Co based wire and torsional stress had occurred in the direction of torsion so that the circumferential component of the flux density within the wire core is increased, and also because the inner core diameter is increased (Blanco, Zhukov and Gonzalez, 2000)

References

Atalay, S. et al. 2015. Magnetic and Magnetoelastic Properties of Annealed Cold-Drawn CoSiB AmorphousWires. J Supercond Nov Magn. 28. pp.1621–1628.

Blanco, M. J. Zhukov, A. and Gonzalez, J. 2000. Asymmetric torsion stress giant magneto impedance in nearly zero magnetostrictive amorphous wires. Journal of Applied Physics. 87(9). pp.4813-4815.

Favieres, C. 2000. Matteucci effect as exhibited by cylindrical CoP amorphous multilayers. Journal of Applied Physics. 87(1889).

Kane, N. S. et al. 2001. Influence of current annealing, stress, torsion and dc magnetic field on Matteucci effect in amorphous wires. Materials Science and Engineering. 306. pp.1055-1057.

Meydan, T. 2002. Influence of stress on Matteucci and search coil voltages in amorphous wires. Journal of Magnetism and Magnetic Materials. 249. pp.382-386.

Savini, A. and Turowski, J. 2012. Electromagnetic Fields in Electrical Engineering. Springer Science & Business Media.

Stefanescu, M. D. 2011. Handbook of Force Transducers: Principles and Components. Springer Science & Business Media.

Takamure, H. et al. 1990. Matteucci Effect in Amorphous Wires with Negative Magnetostriction. IEEE Translation Journal on Magnetics in Japan. 5(7).

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Zhang, B. 2015. Amorphous and Nano Alloys Electroless Depositions: Technology, Composition, Structure and Theory. Elsevier.

Zhukov, A. 2016. Novel Functional Magnetic Materials: Fundamentals and Applications. Springer.

Zhukov, A. et al. 2015. Tailoring of Magnetic Properties and Magneto impedance Effect in Thin Amorphous Wires. 5th International Science Congress & Exhibition. 129.