R. A. Doroshenko

High-frequency properties of two-layer exchange-coupled ferromagnetic structures

A numerical study of peculiarities of ferromagnetic resonance (FMR) in a two-layer exchange-coupled ferromagnetic structure has been performed at various magnitudes and directions of an external magnetic field. The layers have a finite thickness and are characterized by an anisotropy of the easy-plane or easy-axis type. The FMR frequencies have been found to decrease relative to the frequencies calculated in the model of an infinitely thin film. It has been demonstrated that with an increase in the layer thickness the direction of the displacement of the lower FMR mode depends on the magnitude and direction of the external magnetic field and that the frequency of the higher mode decreases at any direction of the external field. The amplitudes of the resonance curves decrease with increasing magnetic field, with the ratio of the half-width of the resonance curve to the resonance frequency decreasing up to the saturation point, after which this parameter varies only slightly. The FMR frequencies have been studied as a function of the constant of the interlayer exchange interaction for fields located in the saturation region.

Ferromagnetic resonance in a plate with a stripe domain structure with allowance for the inhomogeneity of the demagnetizing field

A numerical simulation of ferromagnetic resonance (FMR) in the absence of an external magnetic field has been performed for a plate with a high quality factor. A domain structure with Bloch domain walls (DWs) has been studied. It has been shown that the allowance for the inhomogeneity of the intrinsic demagnetizing field leads to the appearance of additional peaks in the FMR spectrum. With decreasing plate thickness, there occurs a displacement of the resonance-curve peaks into the region the low frequencies. An increase in the size of one of the domains at the expense of another in the periodic domain structure leads to an increase in the amplitude of the susceptibility of the low-frequency FMR mode and its shift into the region of low frequencies. Accordingly, the amplitude of the susceptibility of the high-frequency mode decreases and is shifted into the region of high frequencies. Furthermore, in the presence of resonance, in the plate with unequal domains the peak of the resonance curve that corresponds to the high-frequency mode is observed also upon the excitation of oscillations by an external ac field perpendicular to the DW, and the peak corresponding to the low-frequency mode, upon the excitation by an ac field parallel to the DW. These features of the FMR are explained by the corresponding changes in the inhomogeneous demagnetizing field.

Magnetostatic field in a thin plate with a stripe-domain structure

Magnetostatic fields inside and outside of a plate with a stripe-domain structure have been calculated based on the formulas derived depending on the domain and domain-wall parameters and the plate thickness. In a plate with equal-size domains, the induction Bz perpendicular to the plate surface nearly repeats the magnetization (without extremes) in thick samples, while in a thin plate, the maximum Bz values correspond to domain-wall edges. It has been shown that the maximum value of the field component Hx perpendicular to the domain-wall plane is, on the order of magnitude, close to the logarithm of the ratio of the wall thickness to the period of the domain structure; for thin domain walls, it can exceed the saturation magnetization by several times.

Resonance modes of two-layer exchange-coupled ferromagnetic film

Ferromagnetic and spin-wave resonances in two-layer exchange-coupled ferromagnetic films have been investigated numerically at different intensities of a magnetic field when it is directed in parallel or perpendicular to the film plane. Layers of the film have finite thicknesses and possess anisotropy of the easy-plane and easyaxis types. It has been shown that at a nonzero parameter of interlayer exchange coupling the dynamic component of magnetization upon ferromagnetic resonance is distributed nonuniformly across the film thickness. Its change has been described when the external magnetic field decreases from the saturating field to zero.

Thickness shear modes in structures with alternating magnetic and nonmagnetic layers

Frequencies of dimensional resonances of elastic and magnetoelastic waves in bilayer and trilayer structures of the magnetic layer-nonmagnetic substrate type have been studied. It has been shown that the existence and position of an interface between the media leads to the appearance of specific features in the behavior of resonance frequencies. Plots of the dependences of resonance frequencies on the thickness of the nonmagnetic layer have been constructed and studied at various material parameters of the system. A comparative analysis of the results obtained for bilayer and trilayer structures has been performed. It has been shown that in a layered medium the equidistant disposition of harmonics of resonance frequencies characteristic of monolayer samples is violated in the low-frequency region of the spectrum. The theoretical calculations for trilayer structures agree with the experimental data obtained.

Resonance modes of a two-layer exchange-coupled ferromagnetic film upon oblique magnetizing

A numerical investigation of the ferromagnetic and spin-wave resonances in a two-layer exchange-coupled ferromagnetic film with an easy-plane and easy-axis anisotropies of the layers has been performed at different directions of an external magnetic field and different film thicknesses. The profiles of the dynamic component of the magnetization over the film thickness have been studied upon the ferromagnetic and spin-wave resonances. The dependences of the frequencies of the ferromagnetic and spin-wave resonances on the direction of an external field have been constructed and the process of their transformation upon the change in the film thickness has been described.

Magnetization reversal of a double-layer exchange-coupled ferromagnetic film

A theoretical investigation of magnetization reversal of a double-layer magnetic film with an easy-plane and easy-axis anisotropy has been performed. An analytical expression for the magnetization distribution in the layers in the presence of a magnetic field has been obtained. The calculations performed on the basis of the analytical relationships obtained show that when the thickness of the layers is close to the width of a magnetic inhomogeneity, it substantially affects the magnitude of the critical field for the magnetization reversal of the sample and the shape of the magnetization curve. It is also shown that a decrease in the exchange coupling between the layers leads to an increase in the magnitude of the critical field of magnetization reversal.

Ferromagnetic resonance in a two-layer exchange-coupled ferromagnetic film with a combined uniaxial and cubic anisotropy in the layers

Dynamic properties of ferromagnetic two-layer exchange-coupled (100) films with a combined cubic and uniaxial magnetic anisotropy of layers have been studied numerously upon the magnetization along the [100], [010], and [011] directions. The allowance for cubic anisotropy substantially affects the dependence of the frequencies of the ferromagnetic resonance on the field strength. Repeated changes in the localization of the ferromagnetic-resonance modes between the layers of the film have been found to occur with an increase in the strength of the magnetic field. At a certain relationship between the constants of the combined anisotropy for the directions [010] and [011], an increase in the field leads to a shift of the maximum of the dynamic-susceptibility distribution toward the interlayer boundary without a change in the localization of the modes.

On the magnetoelectric effect in a two-layered film with a ferromagnetic Spin-Spin interaction

Inhomogeneous magnetoelectric effect in a two-layered exchange-coupled film has been investigated theoretically. Smooth and jumplike changes (increases and decreases) in the polarization have been observed in accordance with changes in the inhomogeneities of the magnetization in the magnetic field. The specific features of polarization depending on the changes in the magnitude and direction of the magnetic field, magnitude of magnetic anisotropy, and thickness of the layers have been considered.

NMR frequencies of domain walls in a (110) plate of yttrium iron garnet upon the magnetization in the \([\bar 110]\) direction

AbstractNumerical methods have been used to study the shapes of NMR absorption lines of domain walls (DWs) in a (110) plate of yttrium iron garnet upon the magnetization along the