We presented an analytical solution to the magnetostatic problem of finding the magnetic field strength of a film with a harmonic surface profile, as well as a relation for the scalar magnetic potential of this magnetic field. The energies and interaction forces of a pair of such films in the case of their location under each other and at displacement of the upper film relative to the lower one are calculated, and the vertical component of the force is analyzed as a function of the shear parameter.

A method is proposed to significantly reduce the influence of the magnetostatic magnetic field of the fixed magnetic layer on the free layer of a spin-tunnel element. The method is based on the use of a free layer the size of which exceeds that of the fixed layer, due to which a significant reduction in the influence of the magnetostatic field is achieved.

A solution is presented for a non-standard boundary value problem using Laplace’s equation with mixed Dirichlet–Neumann boundary conditions in a two-dimensional element with periodically alternating media that have different conductivities. The distribution of current lines and equipotentials is found for different ratios of media conductivities in the barber-pole structure used in anisotropic magnetoresistive magnetic field sensors.

Results are presented from an experimental and theoretical analysis of the quasi-stationary magnetization reversal of ferrite–garnet films with complex anisotropy. A magneto-optical setup based on the Faraday effect is used to determine conditions that allow reduction of the area of a domain structure. Destruction of the homogeneous magnetization of the magnetic film in four narrow regions relative to one another at right angles is also established. A theory in good agreement with the experimental results is proposed.

The paper presents the findings of a study investigating the dependence of the magnetoresistance of a magnetic straintronics element comprising a multilayer film nanostructure of Ta (5 nm)/FeNiCo (20 nm)/CoFe (10 nm)/Ta (5 nm) layers, successively sputtered on a silicon substrate, on the strength of the external remagnetization magnetic field and compression stress. It has been established that the experimental value of the maximum change in the magnetoresistance of the nano-structure at remagnetization of layers is less than the theoretical value. This discrepancy can be attributed to the random character of the orientational phase transition of the bistable magnetic system in proximity of the critical value of the external magnetic field. A variational method of theoretical approximation of magnetoresistance dependences has been developed, which enables determining unknown parameters of magnetic nanolayers from experimental data, for example, the Han anisotropy field and Hσ magnetostriction field. The developed theory is shown to be in quantitative agreement with experimental results.

The authors discuss the problem of calculating the force of magnetic ponderomotive interaction between two micromagnetic films with a corrugated semi-cylindrical surface presented as a lattice of half-magnets in the form of long cylindrical rods. It is established that the force of lattice interaction is determined largely by the distance between the semi-cylinders. Depending on this parameter, the force can be either attractive or repulsive.

An exact expression is found for the magnetostatic energy of interaction of a synthetic antiferromagnet with a free layer of a spin-tunnel element and ferromagnetic layers in the shape of strongly oblate ellipsoids of revolution. It is established that the exact value of this energy of interaction can differ considerably from the usual value calculated with the expression for a demagnetizing field. The parameters at which the magnetic interaction of a synthetic antiferromagnet is completely compensated are calculated.

A theoretical and experimental study of the dependence of the magnetoresistance for two spin-tunnel junctions (STJs) of ellipsoidal shape has been made. The one-sided homogeneous magnetization reversal mode of an ellipsoidal STJ with different aspect ratios has been experimentally selected. Despite the reverse inhomogeneous remagnetization, this selection has allowed for the calculation of the magnetic parameters of these elements by developing the Stoner-Wohlfarth theory.

A theoretical model of the magnetization distribution is proposed on the basis of an experimentally discovered domain structure and its evolution in an external magnetic field in thin films of FeNiCo composition with uniaxial anisotropy. The analytical dependence of the domain size on the magnitude of the magnetic field is obtained. The change in magnetoresistance because of the evolution of the magnetic domain structure is calculated.

The ponderomotive force of the adhesion of two permanent magnets depends on their shape. We present the results of determining the optimal shape of ellipsoidal magnets providing maximum magnetic adhesion between them. The interaction of two halves of a magnet, which is an ellipsoid of revolution, and a magnet in the form of a long rod with an elliptical cross section, is analyzed. Analytical formulas for the cohesion forces in these cases are obtained. For a fixed mass or volume of magnets, the problem of optimizing the adhesion force is solved and a geometric shape which provide the maximum adhesion force is determined. It is shown that in the case of a magnet in the form of an ellipsoid of revolution, the maximum adhesion force of its halves (ignoring the magnetic tension on the side surfaces) is achieved at an eccentricity of 0.625958. The magnitude of the maximum adhesion force exceeds the adhesion force of the halves of a uniformly magnetized spherical magnet of the same volume by 1.7%. In this case, the adhesion area of the ellipsoidal magnet will be less than the adhesion area of the spherical magnet by 28%. The optimal form of a bar magnet with an elliptical section with the maximum force of adhesion of its halves at a fixed volume of the magnet is determined. A formula is derived for the ponderomotive magnetostatic force of the interaction between the halves of a bar magnet with an elliptical section and the maximum force of interaction. Numerical estimates for a sintered NdFeB bar magnet showed that the ponderomotive force of interaction with a cross-sectional radius of 5 cm can reach 2 tons per 1 m of length. The results obtained can be used to improve the efficiency of devices based on permanent magnets.

The new generalized Laplace’s equation for an electric potential is presented, which in the general case, is nonlinear for media with resistance anisotropy caused by the anisotropic magnetoresistance (AMR) effect and determined by the orientation of the magnetization vector relative to the current density vector at an arbitrary point of the sample. The solution to this equation is obtained for an anisotropic medium with a non-uniform distribution of current density and magnetization in the case of an oblique-shaped plate of nanoscale thickness. In addition, the analytical solution was obtained for the current density distribution in such a medium using conformal mapping, which confirms the numerical solution in the case of an isotropic conductor. An analysis of the results showed that the presence of the AMR effect leads to a significant change in the current density distribution in the sample compared to the isotropic case, which is expressed in the deviation of the current density vector in perpendicular to the magnetization vector direction in the plate. It has been established that the presence of an external magnetic field in the film plane, which leads to the emergence of an inhomogeneous magnetization distribution, entails self-organization of the electric current distribution. The graphs of the plate resistance as a function of applied magnetic field demonstrate asymmetry for the cases of the direct and reverse directions of the external magnetic field, which cannot be obtained within the framework of simplified models of current flow in media with the AMR effect.

The change in magnetoresistance upon remagnetization by an external magnetic field is calculated using the model of coherent rotation of the magnetization vector of the free layer of a spin tunnel element subjected to homogeneous strain of tension and compression. It is shown that the conclusions of the theory coincide with the classical experimental.

Typical experimental dependences of the giant magnetoresistance of a spin tunnel element are compared to theoretical curves obtained using the classical Stoner–Wohlfarth theory of coherent magnetization reversal and a case of incoherent magnetization reversal with the formation of magnetic domains. It is established that the reversal of magnetization through the formation of a domain structure explains the difference between the experimental hysteretic curve and the Stoner–Wohlfarth theory.

An experimental study is performed using an advanced magneto-optical setup that simplifies the preparation and observation of domain structures which arise upon magnetizing ferrite-garnet films with in-plane anisotropy.

A solution is found to the problem of calculating the electrostatic field induced by a filament charged with a given linear density and located over a dielectric with a specific functional dependence of the dielectric susceptibility on the field. The limits of applying this technology to calculating such fields is investigated. The contributions from induced volumetric and surface polarization charges to the collective electric field are considered.

An analytical solution is obtained for the two-dimensional distribution of the electric potential and current density in an oblique magnetoresistive element using conjugate functions and conformal transformations. Graphs of the dependences of the element’s electrical resistance on an external magnetic field, obtained using the numerical solution to the generalized Laplace equation for an anisotropic magnetoresistive medium, are shown to be asymmetrical.

It is known that highly charged droplets formed in the course of electrospraying disintegrate into a number of smaller droplets. The criteria for the instability and disintegration of conducting liquid droplets in the course of electrospraying have been considered in this article. Some forms of the perturbation of a spherical liquid droplet have been shown for the case when the Rayleigh stability criterion is exceeded. The analysis of the development of charge instability has shown that a quasi-stable state may exist during the disintegration of a liquid droplet in the region of instability according to the Rayleigh criterion.

The influence of a magnetic field directed orthogonal to the easy magnetization axis (EMA) of an elliptical spin-tunnel junction based on the Ta/CoFe/CoFeB/MgO/CoFeB/Ru/CoFe/FeMn/Ta structure on the dependence of the spin-tunnel junction (STJ) resistance on the external magnetic field is considered. This dependence is calculated using the model of coherent rotation of the magnetization of the free layer. The calculation results are comparable with the experimental studies and can be used to simulate the design of magnetic field transducers based on spin-tunnel magnetoresistive nanostructures.

Spin-dependent tunneling structures are widely used in many spintronic devices and sensors. This paper describes the magnetic tunnel junction (MTJ) characteristics caused by the inhomogeneous magnetic field of ferromagnetic layers. The extremely oblate magnetic ellipsoids have been used to mimic these layers. The strong effect of an inhomogeneous magnetic field on the magnetoresistive layers' interaction was demonstrated. The magnetostatic coupling coefficient is also calculated.

A theory is developed for the force of interaction between a lattice of hard magnetic strips with arbitrary parameters and a massive ferromagnetic medium. The force of interaction between a magnetic lattice and a massive ferromagnetic medium is analyzed, depending on the thickness and width of a strip, and the general distance from the lattice to the ferromagnet. A general analytical formula is obtained for the considered force of interaction.