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The ferromagnetic resonance frequencies are obtained for a thin ferromagnetic film with surface anisotropy for the cases when the external magnetic field is applied perpendicularly or parallel to the film surface, and for various combinations of boundary conditions on the film surface. It is shown that in the presence of surface anisotropy the ferromagnetic resonance frequency essentially depends both on the film thickness and on the value of the surface anisotropy constant. The results obtained provide a basis for the correct interpretation of experimental data obtained by means of broadband ferromagnetic resonance in thin film structures., 7 pages, 1 figure

The specific absorption rate (SAR) of a dilute assembly of spherical iron nanoparticles with cubic anisotropy distributed in a viscous liquid is calculated using the solution of stochastic Landau - Lifshitz equation for unit magnetization vector and stochastic equations for multiple particle directors that specify the spatial orientation of the nanoparticle in a liquid. The viscous and magnetic magnetization reversal modes of particles are revealed at low and sufficiently high amplitudes of alternating magnetic field, respectively. The SAR of iron nanoparticle assembly is shown to exceed significantly that of iron oxide nanoparticles with uniaxial anisotropy at the same amplitudes and frequencies of applied magnetic field. The linear response theory is shown to be valid only at small magnetic field amplitudes, H0 < 50 - 70 Oe., 11 pages, 5 figures

The magnetic properties of amorphous glass coated microwires are determined mainly by the distribution of residual quenching stresses over the microwire cross section. In this paper a control of the residual quenching stresses in amorphous ferromagnetic microwires is achieved by changing the microwire glass shell thickness by etching. To this end, a special gel is synthesized for precision glass shell etching of series of Co-rich microwires. The use of the gel provides a possibility of uniform etching of the microwire glass coating at a rate of 0.2–3.2 μm/h depending on the amount of glass already removed, a surface roughness being about 40–100 nm. It is also possible to completely remove the glass shell of the microwire without damage its metallic nucleus. The small angle magnetization rotation method has been used to determine the change in the amplitude of the residual quenching stress with a gradual decrease of the glass shell thickness of microwires of composition Co67Fe4Ni2Mo2B11Si14 and Co71Fe4Si10B15. It is found that the amplitude of the residual quenching stress deceases by 40–50% in average after removing of the layer of 1 μm thickness from the glass coating.

It is shown that surface domain structure arises in magnetic nanotube with uniaxial anisotropy if surface anisotropy constant is negative and sufficiently high in absolute value. The surface magnetic anisotropy affects also the structure and dynamics of a head-to-head domain wall propagating along the nanotube axis in applied magnetic field. The hopping mode is observed for stationary movement of a head-to-head domain wall. The average speed of the domain wall in the hopping mode is found to be several times less than the stationary velocity of the wall in the absence of surface anisotropy. This effect is important for various applications where fast propagation of the domain wall along the sample is essential.

The whole set of geometrical, mechanical and magnetic parameters of Co-rich amorphous ferromagnetic microwires very promising for the development of sensitive stress and Giant Magneto-Impedance sensors have been determined by means of scanning electron microscopy, selective nanoindentation and small angle magnetization rotation method. The magnetostriction constants obtained are sensitive to the true microwire compositions. The experimentally estimated amplitudes of the residual quenching stress are mainly determined by the ratio of the inner and outer wire diameters. They are found to be in good correspondence with the theoretical values calculated based on the theory of viscoelasticity.

The spatial period of magnetization perturbations that occur near the surface of magnetic nanotube or nanowire under the influence of surface magnetic anisotropy is determined by means of numerical simulation as a function of the sample geometry and material parameters. The surface magnetization distribution obtained is then used to estimate the period of the surface magnetic texture in amorphous microwire of several micrometers in diameter by means of appropriate variational procedure. The period of the surface magnetic texture in amorphous microwire is found to be significantly smaller than the wire diameter.

Weak magnetic fields of pitting corrosion currents in AISI 304 stainless steel have been measured by means of giant magneto-impedance magnetometer. Corrosion current density of a single pit has been calculated by magnetic fields mathematical modelling. The current density was also estimated by alloy mass loss in the pit that had been evaluated through optical measurement. The difference between obtained results was 16%. Moreover, pitting repassivation has been detected experimentally.

In this paper highly oriented magneto-polymer composites have been obtained by means of Co and Fe-rich glass-coated amorphous microwires with various metal nucleus and outer diameters. The microwire segments with length L ~ 0.5–0.6 cm were oriented in the magnesium alloy matrix and were poured with a liquid polymer whose composition was a mixture of methyl methacrylate methacrylic acid and methacrylate copolymers in a ratio of 37/63% by mass. The magneto-polymer composites obtained possess high electric resistance, chemical stability and mechanical strength. The high average saturation magnetizations, = 20–30 emu/cm3, have been obtained for Co and Fe based composites with the volume fraction of the magnetic material in the polymer matrix within the range 0.02–0.05. Both Co and Fe based composites show highly anisotropic magnetic properties. The magneto-polymer samples can be cut into pieces of arbitrary size and shape. This facilitates their use in various technical applications.

A scanning giant magneto-impedance (GMI) magnetometer has been used to measure small magnetic fields of corrosion currents in zinc-copper cells. In situ magnetic images of the copper plates with one or two small anode (zinc) inclusions of different sizes located at various distances at the sample surface have been obtained. To interpret the magnetic images of the corrosion currents a numerical simulation program has been developed. A good qualitative agreement between experimental and theoretical results proves that the scanning GMI magnetometry is a promising tool for in situ investigation of some of local corrosion processes.

The ultrasonic oscillation of a macroscopic sample in a viscous liquid is used to create magnetic particles of FeCo alloy with an average diameter D ~100 nm. The FeCo particles obtained have a high specific saturation magnetization, Ms = 1960 emu/cm3, close to that of a bulk sample. The hysteresis loop of a magneto-polymer composite prepared from FeCo particles shows low coercive force and a remanent magnetization close to zero. The magnetic saturation of the magnetic composite samples is achieved in a sufficiently strong magnetic field, H = 6.5 kOe. The hysteresis loop features of the magnetic composite have been explained by means of the numerical simulation of the quasistatic hysteresis loops of non-oriented dilute assemblies of spheroidal FeCo particles with various aspect ratios.

Quasistatic hysteresis loops of a single-domain magnetic nanoparticle with uniaxial anisotropy in a rotating magnetic field have been calculated. Magnetic hysteresis is shown to exist only in a limited range of reduced magnetic field amplitudes, 0.5 1 the total energy of the nanoparticle has a single energy minimum, so that there is no magnetic hysteresis. Quasistatic hysteresis loops of a randomly oriented assembly of non interacting nanoparticles in a rotating magnetic field are also obtained.

The amplitude of the second harmonic of the electro-motive force occurring in the receiving pick-up coil when alternating electrical current is flowing through the microwire is measured as a function of applied external magnetic field, at different mechanical tensile stresses. In addition, an analytical expression for the amplitude of the second harmonic of the electro-motive force is derived. Comparing the experimental and theoretical data the saturation magnetization, the magnetostriction constant and the amplitude of the residual quenching stress have been determined for a family of Co-rich glass-coated microwires.

A set of equations describing the motion of a free magnetic nanoparticle in an external magnetic field in a vacuum, or in a medium with negligibly small friction forces is postulated. The conservation of the total particle momentum, i.e. the sum of the mechanical and the total spin momentum of the nanoparticle is taken into account explicitly. It is shown that for the motion of a nanoparticle in uniform magnetic field there are three different modes of precession of the unit magnetization vector and the director that is parallel the particle easy anisotropy axis. These modes differ significantly in the precession frequency. For the high-frequency mode the director points approximately along the external magnetic field, whereas the frequency and the characteristic relaxation time of the precession of the unit magnetization vector are close to the corresponding values for conventional ferromagnetic resonance. On the other hand, for the low-frequency modes the unit magnetization vector and the director are nearly parallel and rotate in unison around the external magnetic field. The characteristic relaxation time for the low-frequency modes is remarkably long. This means that in a rare assembly of magnetic nanoparticles there is a possibility of additional resonant absorption of the energy of alternating magnetic field at a frequency that is much smaller compared to conventional ferromagnetic resonance frequency. The scattering of a beam of magnetic nanoparticles in a vacuum in a non-uniform external magnetic field is also considered taking into account the precession of the unit magnetization vector and director.

The electrodynamic method is used to measure the hysteresis losses of a dense assembly of magnetite nanoparticles with an average diameter D =25 nm in the frequency range f =10–150 kHz and for magnetic field amplitudes H 0 =100–300 Oe. It is found that the specific loss power is determined by a demagnetizing factor of a whole sample. It diminishes approximately 4.5 times when the sample aspect ratio decreases from L / d =11.4 to L / d ≈1, where L and d are the sample length and diameter, respectively. For H 0 ≤300 Oe the maximal specific loss power 120 W/g is obtained for the sample with L / d =11.4 at f =120 kHz. For comparison, the assembly specific absorption rate has been determined also by means of direct measurement of the temperature difference between the inner and outer surfaces of a flat cuvette containing magnetic nanoparticles. For both methods of measurement close values for the specific absorption rate are obtained for samples with similar demagnetizing factors.

The micromagnetic structure of static and moving head to head domain walls (DW) in soft magnetic nanotube is calculated by means of 2D numerical simulation. Approximate formula is obtained for stationary DW velocity in external magnetic field. The numerical results for the DW width and stationary velocity are in agreement with the analytical estimations. Also the structure of vortex and transverse types of head to head DWs in soft magnetic nanowires is calculated by means of 3D numerical simulations. The vortex propagation mode is found to be similar to that of head to head DW in nanotube. The propagation of the transverse DW is accompanied by a procession of wall magnetization. For a thin nanowire this propagation mode can be successfully described based on the Walker's 1D solution.

A scanning high-temperature superconducting quantum interference device microscope with spatial resolution of about 50mm andsensitivity of 2mOe/Hz 1/2 has been used to study stray magnetic fields of glass-coated microwires with compositions Fe 74 B 13 Si 11 C 2 andCo 74 B 13 Si 11 C 2 at T ¼ 77K. The stray field images have been obtained within a soft magnetic shield (residual magnetic field, H r o1mOe),as well as with applied magnetic field within the range of 750Oe. For a Fe-rich microwire, a simple two-pole structure has been observedin the ground state, whereas for a Co-rich microwire the ground state corresponds, probably, to a domain structure with alternatingmagnetic poles along the wire length.r 2007 Elsevier B.V. All rights reserved. PACS: 85.25.Dq; 75.75.+a; 75.40.MgKeywords: Scanning squid magnetometry; Stray magnetic field; Magnetic domain 1. IntroductionThe glass-coated amorphous ferromagnetic microwiresare very promising for application in magnetic sensors, fordeveloping of new types of stress-tunable compositematerials, for magnetic codification, etc. [1,2]. For theseapplications it is important to control the magnetizationdistribution within the wire in the remanent state and itsresponse to a weakly applied magnetic field. However, anexperimental investigation of the domain structures inwires with diameters from 5 to 30mm turns out to be arather complicated technical problem. Recently, themagneto-optical Kerr effect has been successfully used tovisualize the domain structures existing at the surface ofCo-rich microwires and wires [3,4]. However, using Kerreffect one can obtain only information about magnetiza-tion distribution within a thin surface layer of the wire,with a thickness of the order of the light penetration depth.On the other hand, bamboo-type domain walls (DWs) inCo-rich wires, or head-to-head DWs in Fe-rich wires havevery complicated structures. They spread out through thetotal wire diameter. These DWs are usually charged. Dueto a large value of the wire saturation magnetization themagnetic charges located within the DW can create straymagnetic fields of appreciable value. Therefore, one candetermine the DW positions measuring the distribution ofthe stray magnetic field along the wire length. The strayfield image may help one also to recognize the type of theDW observed, as well as to detect the presence of internalor surface defects in the wire. In principle, one can usemagnetic force microscope (MFM) to measure the wire

The angular dependence of the hysteresis loops of ferromagnetic/antiferromagnetic (FM/AF) bilayer with a compensated interface is investigated by means of numerical simulation for a perfect single-crystalline AF layer having no AF domains at the FM/AF interface, as well as for a twinned AF layer. For applied magnetic field direction nearly parallel to the AF easy axis the completely reversible loops with finite exchange bias field have been obtained for the uniform case, while a large exchange bias has been found for the twinned case, in agreement with experimental results.

High- T C scanning SQUID magnetometer is applied for measuring the magnetization relaxation of the ensembles of spherical colloidal Fe 3 O 4 nanoparticles dispersed in the rigid polymer matrix preventing nanoparticles from agglomeration. According to the transmission electron microscopy data, the size distribution of nanoparticles is well described by the Gaussian profile with the mean size and the dispersion of about 7.5 and 2.3 nm, respectively. High sensitivity of SQUID magnetometer allows us to study samples at low contents of the magnetic component (0.1–1.0 vol%) magnetized in low magnetic field (∼10 –4 T) produced by a low-inductance coil with short switching time (12 μs). A low content of the magnetic component provides the absence of interparticle dipolar interactions, thus simplifying significantly the theoretical description of the magnetization relaxation process. The measured magnetization relaxation curves are found to be in reasonable agreement with the numerical simulation data.

Quantum mechanical Hartree–Fock approximation is used to calculate a magnetic state of a nanoparticle. The cases of ferromagnetic (FM), antiferromagnetic (AFM) and composite particles having an FM core surrounded by an AFM shell are considered in a unified manner. It is shown that effective interaction at the boundary between FM and AFM areas rotates FM and AFM spins perpendicular to each other. The coercive force of a composite particle increases as a function of the AFM shell thickness.

Reversible and irreversible magnetization processes of the single-domain elliptical permalloy dot are studied by simulation. The magnetization curve of the reversible process obtained by applying the field along the hard axis of the elliptical dot is almost linear, as is the case in the single-domain ellipsoidal particle. Due to the occurrence of the non uniform reversal, the switching field is reduced significantly compared to that predicted by the Stoner–Wohlfarth model. The nucleation fields of elliptical dots are calculated as a function of ellipse's aspect ratio, and the function reveals a step-like behavior.

Micromagnetic states are strongly related to sizes of nano-dots. The quasiuniform state becomes unstable and transforms to a new nonuniform state as the diameter of the permalloy circular dot exceeds some critical size. The magnetization curvature increases gradually as the diameter increases. Finally, when the diameter is larger than another critical size, the new nonuniform state becomes unstable and a vortex enters the particle. Hence the new nonuniform state plays an intermediate role in the evolution from the quasiuniform state to the vortex state as the diameter increases.

The effect of the length sample and applied tensile stress on the hysteresis loop of a Co 72.5 Si 12.5 B 15 amorphous wire has been investigated at the amplitude of applied field just above the switching field. The character of the hysteresis loop changes with the length as well as with the applied stress. Measurements of the magnetic remanence were made by displaying the hysteresis loop of the center of the wire as well as the local hysteresis loop in different points along the wire. Experimental results can be satisfactorily explained by the generalization of the outer-shell model developed for a Co-rich amorphous wire of finite length exhibiting negative magnetostriction, where the outer-shell magnetization configuration is a consequence of a radial dependence of the residual tensile stress.

The results of numerical simulation of equilibrium magnetization patterns and magnetization reversal in flat cylindrical and elliptical particles of the soft magnetic type are discussed. It is found that the bending state originates in these particles due to instability of quasi-uniform magnetization at large enough in-plane sizes. Similar states exist also in certain intervals of an external magnetic field. It is shown that the magnetization reversal in an elliptical particle depends considerably on the particle thickness and aspect ratio. The nucleation field of an elliptical particle saturates as a function of particle aspect ratio. The effect of a mutual magnetostatic interaction on the magnetic properties of an array of soft magnetic particles is discussed briefly.

Illustrative two-dimensional micromagnetic simulations are carried out for amorphous ferromagnetic wires with diameter D⩽5 μm and aspect ratios up to Lz/D=20. A radial domain structure is obtained for a wire with λs>0 in case an effective anisotropy constant Ke is high enough, Ke/2πMs2⩾0.3, where Ms is the saturation magnetization. A structure of the bamboo type domain wall has been calculated for the first time for a wire with λs

Equation of motion is stated for effective variables describing a vortex motion in thin cylindrical platelet of soft magnetic type. It is shown that the motion of the vortex centre resembles a precession of a charged particle in a uniform external magnetic field. A resonant absorption of energy is possible in a weak in-plane alternating magnetic field.

Local nucleation fields of Fe-rich amorphous glass-coated microwires with composition Fe 74 Si 11 B 13 C 2 have been measured along the wire length at different applied tension stresses. From these measurements the ratio λ s / M s , where λ s is the magnetostriction constant and M s is the saturation magnetization, as well as the amplitude of the residual quenching stresses have been determined for wires with different metal core radius and glass shell thickness. The method enables one to determine also the positions of strong localized defects that reduce considerably the wire nucleation field from its average value.

The equilibrium magnetization states existing in soft magnetic nanotubes and their behavior in external magnetic field are investigated by means of micromagnetic simulation. In the ground state the middle part of a sufficiently long tube is uniformly magnetized along the tube axis, however there are curling states of various circular polarities near the tube ends. The characteristic length of ending curling states, as well as switching field Hs in the external magnetic field parallel to the tube axis, have been calculated as a function of outer tube radius and tube thickness.

The results of ferromagnetic resonance (FMR) investigation of the amorphous glass-coated microwires with different internal stresses are reported. The internal stresses determine the shift of the resonance field position indicating the magnetoelastic anisotropy as the origin of the magnetic anisotropy of the wire surface region. The values of the magnetoelastic anisotropy field calculated on the basis of the theory of viscoelasticity are also presented.

Glass-coated magnetic microwires with positive magnetostriction show peculiar domain structure that consists mostly of one large domain with magnetization-oriented axially. It was shown that small closure domains appear at the end of the microwire in order to decrease the stray fields. As a result of such domain structure, the magnetization reversal in axial direction runs through the depinning of one of such closure domains and subsequent propagation of the corresponding domain wall. Quite unusual domain-wall (DW) dynamics of the DW propagation predicted previously from the theory has been found in such amorphous microwires. In this paper, we are dealing with the DW dynamics of glass-coated microwires with small positive magnetostriction. The DW damping coming from the structural relaxation dominates at low temperatures as a result of the decrease of the mobility of the structural atomic-level defects. Negative critical propagation field points to the possible DW propagation without applied magnetic field. Probable explanation could be in terms of the effective mass of the DW.

An approach is developed to calculate effective anisotropy constants for 2D and 3D clusters of single-domain grains with arbitrary distributions of the easy anisotropy axes and grain volumes. The method enables one to consider both uniaxial and cubic types of magnetic anisotropy of single-domain grains, as well as a shape anisotropy contribution.

The effect of various types of magnetic anisotropy on the giant magneto-impedance spectra of amorphous wires with low magnetostriction is studied theoretically. For the first of the model considered the easy anisotropy axis is supposed to be parallel to the wire axis, whereas for the second model it has circumferential direction. In case of a wire with axial type of magnetic anisotropy the transverse magnetic permeability is obtained as a function of external magnetic field amplitude H 0 and other magnetic parameters of the wire. A strong dependence of this quantity on H 0 is shown to explain the giant magneto-impedance (GMI) effect in this type of amorphous wire. Besides, the amplitude of the GMI effect depends substantially on the value of a phenomenological damping parameter. In case of a wire with circumferential anisotropy the classical expression [Landau and Lifshitz, Electrodynamics of Continuous Media, 2nd ed, Pergamon, New York, 1984] for the wire impedance is not valid in the range of external magnetic field 0⩽ H 0 ⩽ H a , where H a is the anisotropy field. In this range of external magnetic field the wire impedance becomes a tensor. It has both longitudinal and transverse components that can be measured experimentally [Antonov et al., IEEE Trans. Magn. 33 (1997) 3367]. In case of a wire with circumferential anisotropy the peak of the longitudinal component of wire impedance as the function of H 0 corresponds to the anisotropy field, whereas in case of axial anisotropy it is found at zero magnetic field. The results obtained show that the good magnetic softness of amorphous wire is one of the most important conditions to observe the GMI effect; neither any domain structure nor circumferential anisotropy are strictly necessary.

It is shown that the bamboo domain structure in the outer shell of the Co-rich amorphous wire may arise due to small disturbances in the axial symmetry of the wire. As an example, an elliptical deformation of the wire cross-section is considered. If the anisotropy constant has sufficient value near the wire surface, even small elliptical deformation may lead to a finite period of the domain structure of the order of wire radius.

We present the results of experimental and theoretical investigations of giant magneto-impedance (GMI) in the thin-film multilayer structure of F/SiO2/Ti/Cu/Ti/SiO2/F, where F stands for the ferromagnetic alloy having a composition of Fe73.5Cu1Nb3Si16.5B6. The layers were deposited under a transversemagnetic field Hp = 200 Oe applied in the plane of the sample perpendicular to its long side and were annealed at 280°C under Hp = 420 Oe for 2h. The GMI effect was measured at frequencies ranging from 0.5 to 1250 MHz using a waveguide methhod. An external magnetic field with a strength of up to 130 Oe was applied along the direction of the alternating current. The GMI is shown to exist in the multilayer structure even if the skin depth in the ferromagnetic layers is of the order of their thickness. Both real and imaginary parts of the impedance vary significantly under external magnetic field. A maximum GMI sensitivity of 10–35%/Oe was achieved at high frequencies.

A simple upper bound for the nucleation field of a spheroidal particle in a magnetic field applied at an arbitrary angle with the particle symmetry axis has been given. The bound is supposed to be good enough for particles of a soft magnetic type with a moderate aspect ratio.

Effect of the tensile stress, σ , on hysteresis loops of Co 72.5 Si 12.5 B 15 conventional (120 μm) amorphous wires with different length, l , (2⩽ l ⩽10 cm) have been measured at the amplitude of applied field just above the switching field. The character of the hysteresis loops change drastically with the sample length, being attributed to the existence of a critical length, l c , found to be around 4 cm. Measurements performed by a short movable coil permit to obtain dependence of remanent magnetization, μ 0 M r , and coercivity, H c , on the position of this coil, L . At l > l c μ 0 M r ( σ ) dependence first shows a decrease and then increases with σ . Local hysteresis loops at l l c without stress do not show a rectangular character even in the central region. It was found that by increasing the applied stresses initially, the flat local hysteresis loop measured for L =1.5 cm (at l =3 cm) becomes rectangular. This means that the application of tensile stress reduces the penetration depth of the closure domains, which results in the decreasing of the critical length. Stress dependence of μ 0 M r and H c should be understood in terms of the competition of magnetostatic and magnetoelastic energies. The correlation of the critical length with the magnetic anisotropies (i.e. magnetoelastic and shape anisotropies) is discussed.

The magnetic properties of an assembly of very small Fe nanoparticles with an average diameter of the order of 3–5 nm are studied both experimentally and theoretically. The particles are dispersed in a polyethylene matrix with mass concentration 5%. The stray magnetic field of the samples with sizes 1×1×0.2 mm is measured by means of scanning SQUID microscope at 77 K as a function of external magnetic field. The presence of a weak remanent magnetization indicates a magnetic ordering in the samples studied at rather high temperatures. A distribution of the particle volumes or partial agglomeration of the particles within the assembly is suggested to be responsible for this unexpected behavior.

Flower state micromagnetic structures in a fine ferromagnetic parallelepiped and a rather flat cylinder with an easy axis of magnetocrystalline anisotropy perpendicular to the cylinder axis are studied by means of the perturbation theory given recently in Ref. [1]. The flower state patterns in these particles are also analyzed in detail with the help of a computer simulation. The comparison of the numerical and analytical data obtained for the wide ranges of particle sizes and aspect ratios shows that the lowest-order formulas of the perturbation theory fit quantitatively the flower state patterns in small enough particles with L ⩽ 0.3 R 0 , where L is the characteristic length of a particle and R 0 is the exchange length. It is found that due to the similar increases in particle size the amplitude of a flower state increases gradually. Nevertheless, there is no qualitative change in the magnetization pattern, so that the numerical and analytical data remain similar up to L ⋍ R 0 , where the stability of a flower state in a soft-type particle vanishes.

The flower state micromagnetic structure is analyzed in detail for soft and hard types of cylindrical ferromagnetic particles by means of computer simulation. Wide ranges of particle sizes and aspect ratios are considered. An analytical description of a flower state pattern in a fine ferromagnetic particle is also given on the basis of a perturbation theory. It is shown that for a small particle of a non-ellipsoidal external shape a flower state arises due to excitation of the Brown's stationary nucleation modes against the background of a uniform magnetization. These modes are brought about by the nonuniform components of the demagnetizing field of a particle. The comparison of the numerical and analytical data for a cylinder shows that the first-order formulas of the perturbation theory fit quantitatively the flower state pattern transformation due to changing of the particle aspect ratio l for a soft type cylinder with radius R ⩽0.3 R 0 , where R 0 is the exchange length. For a hard type cylindrical particle the same approach is approximately valid over the whole ranges of R and l which have been investigated.

The magnetic properties of amorphous ferromagnetic 30–50-μm diameter microwires produced by means of spinning process are studied both experimentally and theoretically. The magnetic images of the microwire are measured at 77 K with the high-spatial resolution scanning SQUID microscope in an axial magnetic field up to 103 A/m. The values of the local magnetic fields produced by the microwire in remnant state are typically a few μT at a distance 50–100 μm far from the sample. It is shown that the wire's domain structure calculated numerically is in a qualitative agreement with the magnetic images obtained experimentally.

Simulations of non-uniform micromagnetic structures for magnetically soft asymmetrical ellipsoidal particles having different aspect ratios and anisotropy constants are compared to those for prolate spheroidal particles. The single-domain size for the former, in contrast to the latter, is determined by transverse curling, although above it, the uniform magnetization can remain stable before gradually transforming to a longitudinal curling state.

It is proved that for a usual micromagnetic energy functional the total energy of a finite circular cylinder being in a nonuniform flower state is smaller than that of a uniformly magnetized cylinder for any radius and aspect ratio of the cylinder.

Micromagnetic curling configurations in finite magnetically soft cylinders are studied by means of computer simulation. A simple model based on the variational principle is suggested. The model quantitatively describes the obtained resu;ts over a wide range of particle sizes.

Equilibrium micromagnetic patterns in soft and hard type fine ferromagnetic particles are studied by means of computer simulation. Transformations of the equilibrium states due to change of sizes and aspect ratios of parallelepipeds and ranges of stability of these states are determined.

An AC voltage of double frequency with respect to that of an AC current is detected in a coil wound around a Co-rich amorphous wire when the amplitude of the AC current exceeds several mA. The amplitudes of the even harmonics depend on the value of uniform external magnetic field applied parallel to the wire axis. It is shown theoretically that for large enough amplitude of the AC current the longitudinal component of the wire’s magnetization undergoes oscillations with double frequency with respect to that of the AC current. Therefore, the experimentally observed AC voltage arises due to the Faraday effect.

Curling type magnetization distributions in soft magnetic particles with large aspect ratios are studied by means of numerical simulation. The evolution of the magnetization distribution is analyzed as a function of the particle's aspect ratio in the range from 2 to 10 for certain fixed values of particle's diameter. It is shown that the central part of the particle with a large enough aspect ratio turns out to be uniformly magnetized along its axis whereas the magnetization twisting occurs near the particle ends only. As a result, the remanent particle magnetization may approach the saturation magnetization even for particles with large average diameters. The estimation is given for a characteristic length of the magnetization twisting near the particle end. The results obtained hold qualitatively for elongated soft type ferromagnetic particles of various cross sections, for example, for elongated parallelepipeds.

The giant magneto-impedance (GMI) spectra of amorphous wires with low magnetostriction are studied theoretically, based on the model of an amorphous wire consisting of a uniformly magnetized inner core with axial anisotropy and an outer shell where the easy anisotropy axis may be circumferential or radial. It is shown that the presence of the uniformly magnetized core considerably modifies the GMI spectra of the wire with circumferential anisotropy for external magnetic field lower than the anisotropy field of the outer shell, so that at zero magnetic field real component of wire impedance may be several times larger than the corresponding DC value.

We investigate numerically the magnetization structures of the metastable states including quasiuniform state and various vortex states existing in an elliptical permalloy thin film. The typical energy curves as functions of the particle's size are obtained. It is found that the energy density of the quasiuniform state is smaller than the energy densities of these vortex states for small particles, but after a narrow transition range of size the energy density of the quasiuniform state becomes larger than the energy densities of these vortex states.

We use the micromagnetic simulation to investigate the reversible and irreversible magnetization processes of the single-domain elliptical permalloy thin films. The reversible magnetization curve without hysteresis obtained by magnetizing the single-domain elliptical permalloy thin film along the hard axis is almost linear as are single-domain ellipsoidal particles. For irreversible processes with hysteresis, the switching field of the ellliptical thin film is reduced compared with that predicted by the Stoner–Wohlfarth model due to the occurrence of non-uniform reversal.

The special case of the two magnetic subbands arising from a degenerate wavefunctions of Landau level when the electrons are subjected to a weak periodic potential as well as a strong magnetic field is studied in detail. The condition for the existence of the gap between the bands is stated. It is shown that the wavefunction of an electron regarded as function of wavevector k has the peculiar singularities, i.e. the branch points of its phase. The Kubo formula for the Hall conductance is written in the form of the new topological invariant that is a degree of Gaussian mapping of the torus into the unit sphere. The invariant is calculated for some quite general example.

The ionization probability of the bound impurity states in a semiconductor inversion layer under strong magnetic fields H is calculated as a function of temperature and electric field value E . The conditions for relatively large ionization probability are determined. The possibility of the bound state ionization must be taken into account for the interpretation of the inversion layer properties at the Shubnikov-De Haas conductivity minima.