Chaotic dynamics of interacting domain walls in uniaxial ferromagnetic films

The nonlinear dynamics of a periodic system of interacting domain walls in a thin ferromagnetic uniaxial film with transverse anisotropy is examined. The interaction between the domain walls takes place through the magnetostatic demagnifying fields of the domains. The equations of motion derived for such a system of walls are solved numerically by a 4–5th-order Runge-Kutta scheme, while the uniformity of the distributions of the phase trajectory, the form of the Poincaré cross section, and the spectral density of the vibrations serve as indicators of the type of oscillations. All the known types of oscillations are observed in a computer simulation of this nonlinear system: periodic, quasiperiodic, and chaotic. The computational results have a universal character for uniaxial, highly-anisotropic ferromagnetic films having a strip domain structure, since the results can be easily scaled for materials with different magnetic characteristics. Fiz. Tverd. Tela (St. Petersburg) 39, 2036–2039 (November 1997)     

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

Oscillations of Andreev states in clean ferromagnetic films

We investigate the influence of the exchange field on the Andreev bound states in a ferromagnetic ( F) film backed on one side by a superconductor ( S). Our model accounts for diffusive reflection at the outer surface and possible backscattering at the FS interface. Phase shifting of the Andreev level by the exchange field results in an oscillatory behavior of the density of states of F as a function of the layer thickness. We show that our results agree quantitatively with recent experiments.     

铁磁金属量子阱态的共振隧穿

非铁磁金属层中的量子阱态在磁输运过程中的重要性已被广泛认识．铁磁金属层中自旋极化的量子阱态以前并没有详尽的理论研究；实验上也没有清晰地观测到自旋极化量子阱态的隧穿．文章介绍了最近由卢仲毅、张晓光和Pantelides预言的Fe／MgO／FeO／Fe／Cr和其他铁磁量子阱隧道结中的共振隧穿，并解释铁、钴、铬的△1能带的对称性在这种共振隧穿中的作用．     

铁磁金属量子阱态的共振隧穿

非铁磁金属层中的量子阱态在磁输运过程中的重要性已被广泛认识.铁磁金属层中自旋极化的量子阱态以前并没有详尽的理论研究;实验上也没有清晰地观测到自旋极化量子阱态的隧穿.文章介绍了最近由卢仲毅、张晓光和Pantelides［1］预言的Fe/MgO/FeO/Fe/Cr和其他铁磁量子阱隧道结中的共振隧穿,并解释铁、钴、铬的Δ1能带的对称性在这种共振隧穿中的作用.     

Suppression of the domain structure in uniaxial ferromagnetic films with a superconducting coating

Specific models of domain walls are used to investigate conditions for the single-domain state and quasi-single-domain states in structures with magnetic materials having a quality factor higher than one. It is shown that the critical thickness of the magnetic film in a tangentially magnetized system decreases monotonically as the magnetizing field increases from zero to the transition from the collinear to the homogeneous angular phase and then increases monotonically with increasing external field. In a thin isolated magnetic film, the size of the domains increases exponentially with decreasing thickness. This dependence is logarithmic near the transition to the single-domain state for a film coated on two sides and obeys a power law for a film coated on one side. The establishment of a single-domain state and characteristic features in the asymptotic behavior of the domain structure in magnetic films with and without coatings can be attributed to differences in the asymptotic behavior of the field of a single domain wall. Fiz. Tverd. Tela (St. Petersburg) 40, 1068–1074 (June 1998)     

Shape effect in the magnetostriction of ferromagnetic composite

The magnetostriction of composite consisting of a soft matrix, non-magnetic, randomly filled by ferromagnetic particles is measured. The measured elongation on cylinder-shaped samples displays shape dependence. A model based on the demagnetizing field and the effective Young’s modulus is provided. Both calculation and measurement show a positive magnetostriction with larger values as the samples are flatter. The model is derived to have the behavior of the elongation as a function of the filling factor. An expression of the optimal filling factor, providing a maximal strain, is also expressed.     

Theory of shear magnetostriction in amorphous and crystalline ferromagnetic metals

The theory of shear magnetostriction (SMS) in ferromagnetic metallic systems is formulated in terms of Green functions in real space for a tight binding model. This is general enough to include amorphous (“glassy”) alloys, as well as crystalline materials. It is shown that the SMS coefficient λ_s(E_F) must have at least four zeros as a function of band filling E_F through the d-band, which explains the change in sign between Fe alloys and Co, Ni alloys. A method is presented for computing the indefinite integral of the imaginary part of the product of two Green functions expressed as continued fractions, not necessarily over the same band width, and some preliminary calculations explore the importance of various terms.     

Volume and shape magnetostriction of ferromagnetic invar type alloys

The volume and shape magnetostriction ω_V(H) and ω_S(H) of an Invar alloy and a technical constant-modulus alloy were measured with a strain gauge technique at room temperature. The considerable shape magnetostriction amounts to 0.1 of the volume effect. The itinerant model of ferromagnetism and Kanamori's formula for correlation effects is applied. The observed magnetostriction implies a deformation potential of about 0.3 eV.     

Magnetization vector field in a uniaxial ferromagnetic film

Technical Physics - Analytical models for the magnetization vector field B m in a uniaxial ferromagnetic film are studied. Some of them are found to closely approximate B m even if the quality...     

Tunneling states in ferromagnetic glasses

We study the interaction between structural defects, represented by two level systems, and spin waves in a ferromagnetic glass. The damping and energy shift of the spin wave due to this interaction have a “resonant” and a “relaxation” contribution in analogy with the case of phonons. Ferromagnetic resonance in amorphous ferromagnets can provide useful information on structural relaxation in these materials.     

Derivation of magnetostriction constants for ferrite single crystals by ferromagnetic resonance

Anisotropic elastic stresses are used with discs. Formulas are derived for the saturation magnetostriction constants in terms of the observed shifts in the resonance field. Results are reported for manganese, lithium, and yttrium ferrites.     

Extracting uniaxial anisotropy of ferromagnetic layer in exchange-biased system

Effective anisotropy of the ferromagnetic pinned layer of ferro(FM)-antiferromagnetic (AF)-coupled NiFe(FM)/FeMn(AF) exchange-biased system was investigated in a broad frequency range (100 MHz-5 GHz) using a complex permeability spectrum. The exchange bias and effective uniaxial anisotropy fields of the thin film have been computed theoretically using the Landau-Lifschitz-Gilbert (LLG) equation. From the measurements, uniaxial anisotropy of the pinned FM layer has been extracted to understand the nature of the exchange bias in the system. It is found that the uniaxial anisotropy field of NiFe layer when exchange biased with the AF layer increases from 5 to 15 Oe at different external magnetic fields.     

The effect of stripe domain structure on dynamic permeability of thin ferromagnetic films with out-of-plane uniaxial anisotropy

The permeability is calculated for a thin ferromagnetic film with the stripe domain structure and out-of-plane uniaxial magnetic anisotropy. Analytical expressions for the frequency dependence of components of permeability tensor are derived with the use of the Smit–Beljers method, with the thickness of domain walls and the domain wall motion being neglected. The effect of the domain width and the angle between the anisotropy axis and the film plane on the frequency dependence of the permeability is analyzed. General equations relating the static permeability components and the ferromagnetic resonance frequencies are found. The results of the approach are applied to the derivation of the constraint for the microwave permeability of thin ferromagnetic films. The analysis of the constraint as a function of the axis deviation angle, the domain aspect ratio and the damping parameter allows the conditions to be found for maximal microwave permeability. The results obtained may be useful in connection with the problem of developing high-permeable microwave magnetic materials.     

From dipolar interactions of a random distribution of ferromagnetic particles to magnetostriction

The magnetostriction of a soft matrix, nonmagnetic, randomly filled by ferromagnetic particles is measured and calculated. Dipolar forces between particles have been calculated using a simple model of particles with the same permanent magnetic moment. Forces are injected in an FEM software to evaluate the strain of the composite. The longitudinal strain calculated for a cylinder-shape distribution is positive. A sample with the same shape has been prepared and shows the same strain.     

Tunneling between ferromagnetic films

FeGeCo junctions conductance G(V) is studied when mean magnetizations of the two ferromagnetic film are parrallel or antiparallel. Conductance measurement, in these two cases, is related to the spin polarizations of the conduction electrons.     

Phase transitions in uniaxial ferromagnetic film covered by superconducting layers

The phase diagram and the single-domain uniform state for a uniaxial ferromagnetic film with the superconducting layers covering one or both sides of a ferromagnet are investigated. The superconductor is supposed to be a second-order one and the interaction between the magnetic sub-system and with the conductivity electrons in a superconductor is purely electromagnetic and the vortices in a superconductor are pinned. The critical thickness of the magnetic film for which the uniform state becomes absolutely stable is calculated when the external magnetic field is supposed to be in-plane of the film. It is shown that the critical thickness of the film from the magnetic material with the quality factor Q>1 monotonically decreases as the magnetic field increases in the range from zero value to the value of the transition field where the collinear phase transforms into the angular (canted) phase. Further the critical thickness increases with the increase of the field. The quasi-single-domain magnetic film states were considered when the film thickness was close to the critical one. It is shown that for a thin isolated magnetic film the domain period exponentially increases with the decrease of the film thickness. Such dependence, however for the film with double-side superconducting cover and close to the transition into the single domain state becomes logarithmic and for the film covered by superconductor only on the one side varies as the power series. The single-domain state existence and the asymptotic behaviour of the domain structure is explained by the features of the asymptotic behaviour of the domain walls within the system. As for isolated magnetic film and for a film with the superconductor cover layers the transition from the collinear phase to the inhomogeneous state is the second-order phase transition and the transition from the uniform angular phase to the inhomogeneous phase is the first-order transition.     

Surface magnetization in semi-infinite ferromagnetic semiconductors with single-ion uniaxial anisotropy

A Green's function technique combined with the transfer-matrix method is used to calculate the surface localized-spin and the conduction-electron magnetization in semi-infinite ferromagnetic semiconductors (FMSs) in the ferromagnetic phase taking into account a single-ion uniaxial anisotropy. The theoretical results were applied to narrow-band as well as to wide-band FMSs.     

Nernst-Ettingshausen effect in thin ferromagnetic films

A new thermomagnetic effect in a ferromagnetic film is discussed. When a temperature gradient is established along the x axis in a ferromagnetic sample, a transverse electric field arises in the same plane as the spontaneous-magnetization vector (in the case H = 0, where H is the external magnetic field). A phenomenological expression is given for the transverse electric field as a function of the square of the magnetization. Theory is given for the Nernst-Ettingshausen effect due to the spin-orbit interaction in a ferromagnetic film in the effectivemass approximation, and the Nernst-Ettingshausen constant is derived. The calculation is carried out by the density-matrix method derived by Kohn and Luttinger.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 28–32, November, 1969.     

Measurement of the magnetostriction constants,saturation magnetization,and internal stresses of ferrite thin films by the ferromagnetic resonance method

The magnetostriction constants of thin films are calculated by the Soule-Smit method, using external anisotropic stresses produced by deforming the film together with its substrate by means of two pairs of parallel blades. The ferromagnetic resonance technique is used to determine the magnetostriction constant ₁₀₀, the saturation magnetization M₀, and the internal stresses of thin films of nickel-alloyed Mg-Mn ferrite.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 91–95, November, 1976.