Magnetization of an elastic ferromagnet

At the macroscopic level, ferromagnetism is a quantum mechanical phenomenon. To describe magnetic materials, it is necessary to create a heuristic model that in terms of continuum mechanics describes the interaction between the lattice continuum, which is a carrier of deformations, and the magnetization field, which is associated with the spin continuum through the gyromagnetic effect. According to the laws of quantum mechanics, each individual particle is associated with a magnetic moment and an internal angular momentum – spin. Electrons mainly contribute to the magnetic moment of the atom. Therefore, the continuum is continuously associated with the discrete distribution of individual spins in a real ferromagnetic body known as the electron spin continuum. In addition, it is necessary to formulate field equations that, together with Maxwell’s equations, describe the electron spin continuum. After that, it is necessary to consider the interaction between the lattice continuum and the electron spin continuum. Elastic ferromagnets should be described with due regard to the spin density and couple stresses. The spin system is a carrier of the magnetic properties, and the mechanical properties are associated with the lattice. Thus, spin–lattice interactions indicate the relationship between magnetic and mechanical properties.

Dielectric Spectroscopy of Hybrid Magnetoactive Elastomers

Dielectric properties of two series of magnetoactive elastomers (MAEs) based on a soft silicone matrix containing 35 vol% of magnetic particles were studied experimentally in a wide temperature range. In the first series, a hybrid filler representing a mixture of magnetically hard NdFeB particles of irregular shape and an average size of 50 μm and magnetically soft carbonyl iron (CI) of 4.5 μm in diameter was used for MAE fabrication. MAEs of the second series contained only NdFeB particles. The presence of magnetically hard NdFeB filler made it possible to passively control MAE dielectric response by magnetizing the samples. It was shown that although the hopping mechanism of MAEs conductivity did not change upon magnetization, a significant component of DC conductivity appeared in the magnetized MAEs presumably due to denser clustering of interacting particles resulting in decreasing interparticle distances. The transition from a non-conducting to a conducting state was more pronounced for hybrid MAEs containing both NdFeB and Fe particles with a tenfold size mismatch. Hybrid MAEs also demonstrated a considerable increase in the real part of the complex relative permittivity upon magnetization and its asymmetric behavior in external magnetic fields of various directions. The effects of magnetic filler composition and magnetization field on the dielectric properties of MAEs are important for practical applications of MAEs as elements with a tunable dielectric response.

A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers

We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions (O(r−3) in d=3 dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka’s toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.

Asymptotic Behavior of Magnetostrictive Elasticity for Microstructured Materials

According to the classical theory of Weiss, Landau, and Lifshitz, in a ferromagnetic body there is a spontaneous magnetization field m, such that ∥m∥ = τ0 = const in all points of this material Ω. In any stationary configuration, this ferromagnetic body consists of areas (Weiss domains) in which the magnetization is uniform (i.e. m = const) separated by thin transition layers (Bloch walls). Such stationary configuration corresponds to the minimum point of the magnetostrictive free energy E. We are considering an elastic magnetostrictive body in our paper. The elastic magnetostrictive free energy Eδ depends on a small parameter δ such that δ → 0. As usual, the displacement field is denoted by u. We will show that each sequence of minimizers (ui, mi) contains a subsequence that converges to a couple of fields (u0, m0). By means of a Γ-limit procedure we will show that this couple (u0, m0) is a minimizer of the new functional E0. This new functional E0 describes the magnetic-elastic properties of the body with microstructure.

Self-Excited Codirectionally Magnetically Compensated Rotating Ranging Method

During the Steam-Assisted Gravity Drainage (SAGD) technology-based dual horizontal well drilling process, it is necessary to accurately monitor the well spacing in real time to ensure safe and parallel drilling. In this paper, a self-excited codirectionally magnetically compensated rotating ranging method and device is proposed. In the numerical calculation and simulation, both parallel and nonparallel drilling models are established. Based on the models and the magnetic dipole theory, the relation between the magnetization field and the well spacing is analyzed. Furthermore, the one-to-one correspondence between the peak-to-peak value of the magnetization field and the well spacing is revealed. Well spacing is then determined according to the measured peak-to-peak value. To achieve better results, the influence of magnetic source (the magnetic moment) and casing characteristics (magnetic susceptibility, dynamic magnetization length) on measured peak-to-peak value is analyzed. Finally, field tests are carried out, and the feasibility and effectiveness of the theory and device are proved. This study provides innovation for a new approach of magnetic guidance while drilling and has a great significance in the development, testing, and calibration of well-ranging instruments.

Одноионный механизм слабого антиферромагнетизма и спин-флоп-переход в двухподрешеточном ферромагнетике

The ground state of a Heisenberg ferromagnet with noncollinear single-ion anisotropy axes of two sublattices is investigated in the external magnetic field applied in the anisotropy axes plane. The noncollinearity of local anisotropy axes leads to new effect - the first order spin reorientation phase transition of the spin-flop type. The transition field depends on the value of anisotropy and orientation of the sublattice axes. Stability analysis of magnetic states shown that the field induced transition is accompanied by the magnetization hysteresis. The dependencies of the spin-flop transition field, the magnetization jump value and the susceptibility on the anisotropy parameters are determined. The obtained results are used for explanation of the magnetization field dependence in the ferromagnetic crystal PbMnBO_4.

On the field-induced transport of magnetic nanoparticles in incompressible flow: Modeling and numerics

By methods from non-equilibrium thermodynamics, we derive a class of nonlinear pde-models to describe the motion of magnetizable nanoparticles suspended in incompressible carrier fluids under the influence of external magnetic fields. Our system of partial differential equations couples Navier–Stokes and magnetostatic equations to evolution equations for the magnetization field and the particle number density. In the second part of the paper, a fully discrete mixed finite-element scheme is introduced which is rigorously shown to be energy-stable. Finally, we present numerical simulations in the 2D-case which provide first information about the interaction of particle density, magnetization and magnetic field.