Evidence for non-cubic magnetostriction in epitaxial bubble garnets

Epitaxial bubble garnet films grown on non-magnetic garnet substrates exhibit a dominant growth or stress induced uniaxial anisotropy, which is responsible for the stripe and bubble domain structures, and the intrinsic cubic magnetocrystalline anisotropy which can affect bubble device performance. The anisotropy constants have been deduced from measurements of stripe domain nucleation in the garnet films. We extend this measurement technique and its interpretation so that it also yields values of the magnetoelastic interactions.The measurement is based on observing the details of the topography of the nucleating domain structure, specifically the orientation of the nucleating stripe domains as a function of the orientation and magnitude of the applied magnetic field.The interpretation is based on a micromagnetic analysis of the conditions for homogeneous second order stripe domain nucleation. The contributions to the phenomena of the cubic anisotropy and of the magnetostriction are included in the analysis as perturbations.The theory produces predictions which are compatible with qualitative earlier experiments reported in the literature. It provides a satisfactory quantitative account of systematic new observations we have made on a GdTmY bubble garnet film with the specific objective of measuring magnetostriction.Analysis of the experimental data yields strong evidence for a non-cubic component of the magnetostriction possibly associated with the same growth-kinetic mechanism that gives rise to the non-cubic anisotropy. The sign and magnitude of the macroscopic non-cubic magnetoelastic constant is estimated from the experimental results.     

Influence of three-dimensional inhomogeneities of the magnetic parameters on the dynamics of vortex-like domain walls

The interaction of a vortex-like domain wall moving in an external magnetic field with a three-dimensional periodic chain of cubic volumes with high values of the saturation magnetization and magnetic anisotropy constant has been investigated theoretically. It has been found that the result of the interaction depends on the initial distance between the wall and the region of inhomogeneity of magnetic parameters at the moment of turning on the external magnetic field. The pinning of domain walls near the regions with high values of the saturation magnetization and magnetic anisotropy constant has been investigated, and the anisotropy of the corresponding depinning fields has been revealed. The method of investigation is the numerical micromagnetic simulation.     

Stripe domain statics in garnet films

Magnetic garnet films grown epitaxially on nonmagnetic garnet substrates exhibit a growth or stress-induced uniaxial anisotropy in addition to the cubic magnetocrystalline anisotropy associated with their crystal symmetry. When the uniaxial anisotropy is dominant over the cubic, such films exhibit stripe or bubble domain structures; even a small cubic anisotropy component can have a decisive effect on the behavior of the domains in applied fields. We report an experimental study of the quadistatic behavior of domains in fields applied to a (111) film in the film plane along (11$\text{2}$) and ($\text{1}$10). The experimental results are interpreted by a new theory that gives good agreement with the observed behavior, and yields an accurate measurement of the cubic and uniaxial anisotropy constants.The main qualitative features of the results are: In a ($\text{1}$10) field, the walls are Neél walls perpendicular to the field. In a (11$\text{2}$) field the walls are Bloch walls parallel to the field, the domain magnetization in adjacent stripes is not symmetrical about the film plane, and adjacent stripes are not of equal width; the domain period first shrinks and then expands with increasing field; and even though the applied field has no component perpendicular to the film plane, the film develops a net perpendicular magnetic moment.     

Domain wall dynamics near the limit velocity in a cubic ferromagnet with induced magnetic anisotropy

A research has been conducted into the dynamics of the 180° domain wall in a cubic ferromagnet with induced magnetic anisotropy, this domain wall moving at a velocity close to the limit one. The Landau–Lifshits equation has been reduced to a modified double Sine–Gordon equation with the highest dispersion. A solution has been found which corresponds to the moving 180° domain wall. This paper has determined the dependencies of the velocity of the domain wall's stationary movement on the quality factor and on the ratio of the induced and the cubic magnetic anisotropy constants in slabs with the developed (0 0 1) and (0 1 1) surfaces.     

Specific Features in the Spectrum of Nonlinear Magnetoelastic Waves Propagating in a (111) Plate with Combined Anisotropy

Nonlinear magnetoelastic waves with stationary profiles propagating in a cubic ferromagnetic with [111] uniaxial induced anisotropy are investigated theoretically. It is demonstrated that a new type of nonlinear waves engendered by the resonant motion of the 60-degree domain wall propagates along the [111] axis without magnetization escape from the plane of spin rotation. Some other cases of nonlinear magnetoelastic wave propagation in the examined magnetic are also studied.     

Role of anisotropy on the domain wall properties of ferromagnetic nanotubes

In this paper we investigate the role of magneto-crystalline anisotropy on the domain wall (DW) properties of tubular magnetic nanostructures. Based on a theoretical model and micromagnetic simulations, we show that either cubic or uniaxial magneto-crystalline anisotropies have some influence on the domain wall properties (wall size, propagation velocity and energy barrier) and then on the overall magnetization reversal mechanism. Besides the characterization of the transverse and vortex domain wall sizes for different anisotropies, we predict an anisotropy dependent transition between the occurrence of transverse and vortex domain walls in tubular nanowires. We also discuss the dynamics of the vortex DW propagation gradually increasing the uniaxial anisotropy constant and we found that the average velocity is considerably reduced. Our results show that different anisotropies can be considered in real samples in order to manipulate the domain wall behavior and the magnetization reversal process.     

High-frequency excitations of stripe-domain lattices in magnetic garnet films

Magnetic garnet films of composition (Y,Bi)₃(Fe,Al)₅O₁₂ have been grown by liquid phase epitaxy on [111] and [110] oriented substrates of gadolinium gallium garnet. The domain wall resonance and the two branches of the domain resonance of periodic stripe domains are measured as function of the bias induction applied in the film plane parallel to the stripes. Resonance frequencies up to 7.5 GHz are observed. An improved version of the hybridization model is developed to describe these resonances. It turns out that hybridization of the domain resonance branches is determined by the cubic anisotropy for [111] oriented films, while for [110] oriented films coupling of the domain resonances is mainly caused by the orthorhombic anisotropy. The theoretical model is in excellent agreement with experiments, no fitting parameters are used. It is also used to derive the phase relation between the precessing magnetizations of neighbouring domains.     

Sense anisotropy of the kink dynamics in an evolutionary equation with broken space symmetry

A nonlinear diffusion-type evolutionary equation that describes the effect of sense anisotropy of velocity when the front of a solitary wave (kink) moves with unequal velocities in the forward and (when an external field reverses sign) backward directions is suggested. A prerequisite for such behavior is space symmetry breaking in the system. The equation is applied to describing the dynamics of 180° domain walls in ferromagnets with negative cubic crystalline anisotropy. The amount of the sense anisotropy effect in YIG may reach 20%.     

Negative Poisson’s ratio for cubic crystals and nano/microtubes

The paper systemizes numerous cubic crystals which can have both positive and negative Poisson’s ratios (the so-called partial auxetics) depending on the specimen orientation in tension. Several complete cubic auxetics whose Poisson’s ratio is always negative are indicated. The partial cubic auxetics are classified with the use of two dimensionless elastic parameters. For one of the parameters, a critical value is found at which the orientation behavior of the crystals changes qualitatively. The behavior of mesotubes obtained by rolling up plates of cubic crystals (crystals with rectilinear anisotropy) is considered in detail. Such mesotubes with curvilinear cubic anisotropy can have micron and nanometer lateral dimensions. It is shown that uniform tension of nano/microtubes of cubic crystals is possible only in the particular case of zero chirality angle (the angle between the crystallographic axis and the axis of a stretched tube). It is demonstrated by the semi-inverse Saint-Venant method that solution of the axial tension problem for cylindrically anisotropic nano/microtubes of cubic crystals with a non-zero chirality angle is possible with radially inhomogeneous fields of three normal stresses and one shear stress. In the examples considered, the cylindrically anisotropic nano/microtubes of cubic crystals are auxetics even if they are initially non-auxetics with rectilinear anisotropy.     

Topology and properties of the 0-degree domain wall in a transverse magnetic field

The conditions of formation, the structure, and the stability of 0-degree domain walls with noncircular trajectories of the magnetization vector in cubic ferromagnets with induced uniaxial anisotropy along the [011] direction have been investigated. It has been found that magnetic inhomogeneities with such topology can appear only in an external magnetic field perpendicular to the domain wall plane. It has been shown that the Euler-Lagrange equations in the low-field limit can be reduced to second-order linear differential equations, whose solutions describe the structure of the above inhomogeneities, while the eigenvalues of the corresponding differential operators specify their stability conditions.     

Mobility of domain walls in low-loss garnet films

The dependence of the domain wall mobility on the strength of a static magnetic field applied in the plane of the sample is investigated in single-crystal garnet films of the system YBiFeGa with perpendicular magnetic anisotropy and a narrow ferromagnetic resonance line. It is shown that, as in the case of YIG single crystals with cubic magnetic anisotropy, wall motion gives rise to an additional energy loss contribution far greater than the relativistic contribution also present in the case of homogeneous magnetization. It is established that a mechanism recently proposed in theory does not give a correct explanation for this additional contribution, because qualitative as well as quantitative discrepancies exist between the theoretical conclusions and measurement data. Fiz. Tverd. Tela (St. Petersburg) 39, 1253–1256 (July 1997)     

Structure of a Bloch domain wall in a cubic crystal

Planar Bloch domain walls with different senses and paths of rotation of the magnetization vector are studied in a cubic crystal with a negative first constant of magnetic anisotropy.     

Temperature variation of bubble domains in Dy0.3Tm0.7FeO3 mixed orthoferrite

Bubble domain structure in Dy_0.3Tm_0.7FeO₃ mixed orthoferrite was studied between room temperature and 480 K using the Faraday effect. Temperature dependence of the magnetization and domain wall energy density has been determined. Starting from the molecular field theory and one-ion theory of magnetocrystalline anisotropy, expressions describing a temperature dependence of the domain wall energy density in orthoferrites have been derived. In the expression for magnetocrystalline energy, uniaxial as well as cubic anisotropy have been accounted for.     

Domin structure of (111) crystal plates of ferrite-garnets with uniaxial anisotropy

The influence of the magnetic field, thickness, and magnetic prehistory on the general form and quantitative parameters of domain structure (DS) of the (111) single-crystal plates of the ferrite-garnet (EuEr)₃(FeGa)₅O₁₂ is investigated. The field interval of stability of circular (conical) and annular domains is determined. It is shown that the DS of ferrite-garnet structures with induced uniaxial anisotropy reveals a series of features which may be explained by the influence of cubic anisotropy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 57–61, March, 1982.     

压应力对Fe0.81 Ga0.19单晶磁化和磁致伸缩的影响

研究了Fe_0.81Ga_0.19合金单晶沿[100]方向的磁机械效应和磁致伸缩效应.基于Stoner-Wohlfarth模型,通过数值计算获得了在压应力和外磁场联合作用下磁化强度的方向余弦.研究表明,随着压应力的增加,退磁态下合金中的磁各向异性会由三轴各向异性向双轴各向异性转变.这使得合金中 90° 畴的体积分数增加,导致磁致伸缩效应增大. 关键词： FeGa合金 磁机械效应 巨磁致伸缩效应     

Magnetic Phases and Inhomogeneous Micromagnetic Structures in a Ferrite Garnet Film with Orientation (210)

Possible magnetic states of a cubic ferromagnet with a uniaxial anisotropy induced along the [210] direction are theoretically investigated. It is demonstrated that the orientation phase diagram of a magnet is nontrivial and admits the existence of three types of magnetic phases that differ in transformational properties and the presence of quintuple points, isostructural phase transitions, etc. It is found that magnetic inhomogeneities, regardless of the values of parameters of the matter, have a common structure: they correspond to 180-degree domain boundaries with a noncircular trajectory of the magnetization vector. The features of homogeneous and inhomogeneous magnetic states, found in these materials, make it possible to explain the manifestation of a flexomagnetoelectric effect in them.     

Uniaxial magnetocrystalline anisotropy of metal/semiconductor interfaces: Fe/ZnSe(001)

A theoretical study of the magnetic moments and the in-plane magnetic anisotropy of an interface between a cubic ferromagnet and a cubic semiconductor, Fe/ZnSe(001), is presented. Theory confirms the observed, much debated, uniaxial anisotropy of the iron film. This result is important since the calculations are for perfect interfaces with squarelike environments, proving that the fourfolded symmetry of the interface Fe atoms is broken beyond the nearest neighboring semiconducting layer, effects that are usually assumed small. It is demonstrated how the uniaxial anisotropy is produced by the directional covalent bonds at the interface, even without atomic relaxations.     

Hydrostatic pressure and hexagonal magnetic anisotropy of hematite

The effect of hydrostatic pressure on the hexagonal basal magnetic anisotropy of a rhombohedral easy-plane weak ferromagnet is investigated in terms of the thermodynamic theory. It is shown that the contribution to the hexagonal anisotropy is determined by the effective constants of the uniaxial and cubic anisotropy, which include the additions proportional to the hydrostatic pressure. The hydrostatic pressure, which leads to the basal anisotropy observed in experiments for stressed samples, is determined for hematite.