Influence of induced uniaxial anisotropy on the domain structure and phase transitions of yttrium-iron garnet films

The effect of induced uniaxial anisotropy on the properties and parameters of the domain structure and phase transitions in yttrium-iron garnet (YIG) films is investigated. Based on the measurements and the derived formulas we determine the difference between the magnetization and the uniaxial anisotropy field for each of the films. We have also measured the parameters of the domain structures and phase transitions of the films for the magnetization parallel and perpendicular to the projections of the [111] crystallographic axes onto the plane of the film. We find that films of pure YIG films grown in (111) are characterized by the existence of some critical value of the uniaxial anisotropy field. It is found that for films in which the uniaxial anisotropy field is larger than this critical value and films in which it is less than this critical value, such parameters of the domain structures as the ratio of the width of the domains to the film thickness, the orientation of the magnetization of the domains, the orientation of the domain boundaries, and the magnitudes of the phase transition fields differ substantially. Fiz. Tverd. Tela (St. Petersburg) 41, 2034–2041 (November 1999)     

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.     

Motion of domain walls under the action of spin-polarized current in a magnetic junction

The effect of spin-polarized current on a domain structure in a magnetic junction consisting of two ferromagnetic metallic layers separated by an ultrathin nonmagnetic layer is studied within a phenomenological theory. The magnetization of one ferromagnetic layer (layer 1) is assumed to be fixed, while that of the other ferromagnetic layer (layer 2) can be freely oriented both parallel and antiparallel to the magnetization of layer 1. Layer 2 can be split into domains. Charge transfer from layer 1 to layer 2 is not attended with spin scattering by the interface but results in spin injection. Due to s-d exchange interaction, injected spins tend to orient the magnetization in the domains parallel to layer 1. This causes the domain walls to move and “favorable” domains to grow. The average magnetization current injected into layer 2 and its contribution to the s-d exchange energy are found by solving the continuity equation for carriers with spins pointing up and down. From the minimum condition for the total magnetic energy of the junction, the parameters of the periodic domain structure in layer 2 are determined as functions of current through the junction and magnetic field. It is shown that the spin-polarized current can magnetize layer 2 up to saturation even in the absence of an external magnetic field. The associated current densities are on the order of 10⁵ A/cm². In the presence of the field, its effect can be compensated by such a high current. Current-induced magnetization reversal in the layer is also possible.     

Effective temperature, thermodynamical functions, and equilibrium properties of excited domain structure

The theory of the equilibrium properties of stripe domain structure (DS) of nonhomogeneous magnets, induced by a variable magnetic field, is developed. It is shown that an induced DS is a thermodynamic system characterized by an effective temperature which may be many orders of magnitude higher than the room temperature. For a DS of this kind, the thermodynamic functions are derived and the equilibrium conditions are determined. It is found that the entropy term in the free energy function is responsible for DS fragmentation under the variable field action, for the hysteretic dependence of the DS period on the frequency and the amplitude of the variable field, and for phase transitions attended with a jump in the number of domains.     

正交各向异性双层交换弹簧薄膜的磁矩分布

本文以Pt_(84)Co_(16)/TbFeCo双层交换弹簧体系为研究对象,利用微磁学连续模型,研究了软/硬磁层易轴方向相互垂直的新型体系中磁矩的分布特征.研究结果表明,磁矩偏离薄膜法线方向的角度在软磁层中沿膜厚方向的变化速率比硬磁层中的快.通过调节软磁层参数来增加软/硬磁的各向异性常数比、交换能常数比、饱和磁化强度比或外磁场强度,都可有效改变磁矩偏角在软/硬磁层中的变化速率.特别是当软/硬磁各向异性常数比值和交换能常数比值同时增大时,可以使得磁矩在硬磁层中的变化速率快于软磁层中的.而饱和磁化强度比值对磁矩变化速率的影响源于饱和磁化强度的变化会相应地改变各向异性常数,进而改变磁矩在软/硬磁层中磁矩方向变化速率的比值.此体系的磁滞回线显示磁性参数的改变可以显著改变体系的剩磁及饱和磁场.软磁层中的退磁场能及体系的正交各向异性可导致负的成核场.     

Analytic expression for the magnetization curve and hysteresis loop

In a real ferromagnet there are a large number of domains differing greatly in energy, so that a domain energy distribution can be introduced. The nonvanishing initial permeability and saturation on the magnetization curve allow an analytic expression to be found for this function and thus for the magnetization curve. Taking the domain interaction into account by introducing a starting field allows the B(H) dependence found to be generalized to weak fields. Analysis of ideal magnetization curves shows that the superposition on a constant field of varying fields having nonvanishing amplitudes reduces the starting field to zero, i.e., removes the magnetic interaction. The B, H plane can be thought of as a complex plane, each point of which is associated with some state of the ferromagnet. A transformation is made from the magnetization curve to the remagnetization curve by a linear transformation of this complex point. In this manner, a transformation can be made from the B(H) dependence found for weak fields to an analytic expression for the hysteresis loop in the same field range.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 11, pp. 59–62, November, 1970.     

Modeling of domain wall displacement in crystals with dislocations

The domain wall displacement in ferromagnetic crystals with dislocations that produce a continuous potential field with wavelength greater than the domain wall width is investigated by the machine modeling method. It is established that the domain wall shape and the start field are determined during magnetization by the potential field characteristics that depend on the specific location of the dislocations. It is shown that the start field is proportional to the ratio between the mean stress and the variance of the potential field stress at the site of domain wall fastening. The results of the modeling agree with values of the start field obtained experimentally and the behavior of the domain wall during magnetization of iron microcrystals.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 77–83, December, 1990.     

Formation of phase domain structures in thin films under conditions of a first-order magnetic phase transition

This paper reports on the results of a theoretical investigation into the magnetic and resonance properties of thin films in the range of the transition from a paramagnetic state to a ferromagnetic state in the case where the magnetic transition is a first-order phase transformation. It is demonstrated that, in an external magnetic field directed perpendicular to the film plane, the formation of a specific domain structure consisting of domains of the coexisting paramagnetic and ferromagnetic phases can appear to be energetically favorable. The parameters of the equilibrium system of stripe phase domains and their dependences on the temperature, the magnetic field, and the characteristics of the material are calculated. The specific features of the magnetic resonance spectra under the conditions of formed stripe phase domains are considered. A relationship is derived for the dependence of the resonance field of the system of ferromagnetic domains on the magnetization and temperature. It is shown that the alternating external field can fulfill an orientation function in the formation of stripe phase domains.     

Effect of nonuniform mechanical stresses on the domain structure of iron borate

A magnetooptic method is used to study the effect of nonuniform radial mechanical stresses on the domain structure, magnetic susceptibility, and magnetic hysteresis loops of a FeBO₃ single crystal. When a magnetic field is applied in the basal plane of FeBO₃ along the stress vector, a system of tapered domains appears in the crystal during magnetization. These domains exist in a certain temperature-dependent field range H₀ ≤ H ≤ H _c . The appearance of a system of tapered domains is found to substantially affect the technical magnetization of a stressed crystal. The results obtained are discussed within the thermodynamic theory of a domain structure. A theoretical model used is shown to adequately describe the experimental temperature and field dependences of the ratio \({D \mathord{\left/ {\vphantom {D {\sqrt L }}} \right. \kern-\nulldelimiterspace} {\sqrt L }}\) (where D and L are the average width and length of a tapered domain, respectively). The calculated value of D is approximately 1.3 times smaller than the experimentally observed domain width.     

Domain and wall structures in films with helical magnetization profile

We study soft magnetic bilayers having orthogonal, in-plane easy axes. The layers are thicker than the Bloch wall width linked to the anisotropy, so that a helical magnetization with a large angle exists across the sample thickness. The magnetic domains structure has been investigated at both sample surfaces, using magneto-optical microscopy. The domain structure is found to be similar to that of double films with biquadratic coupling. Two kinds of domain walls are identified, namely with a 90° and 180° rotation of the average magnetization. The detailed structure and energy of these walls are studied by micromagnetic calculations.     

Influence of surface and bulk anisotropies on domain structures in a thin plate

The method of micromagnetic modeling is used to investigate the influence of the surface anisotropy of easy plane type on the domain structures in a thin uniaxial magnetic plate for different values of the bulk anisotropy constant. The easy magnetization direction is oriented perpendicularly to the plate plane. It is established that for low and high bulk anisotropy values, the surface anisotropy has no significant effect on the magnetization field M. For some intermediate values of the bulk anisotropy constant, the surface anisotropy can influence the structure of the domain boundaries and change qualitatively the domain structure of the sample.     

Microscopic domain structures in unidirectional and isotropic exchange-coupled NiO/NiFe bilayers

The dependence on nickel oxide thickness in unidirectional and isotropic exchange-coupled NiO/NiFe bilayer films was investigated by magnetic force microscopy to better understand exchange biasing at microscopic length scales. As the NiO thickness increased, the domain structure of unidirectional biased films formed smaller and more complex in-plane domains. By contrast, for the isotropically coupled films, large domains generally formed with increasing NiO thickness including a new cross type domain with out-of-plane magnetization orientation. The density of the cross domain is proportional to exchange biasing field, and the fact that the domain mainly originated from the strongest exchange coupled region was confirmed by imaging in an applied external field during a magnetization cycle.     

Tb0.3Dy0.7Fe2合金磁畴偏转的滞回特性研究

研究了不同载荷作用下Tb_0.3Dy_0.7Fe₂合金在压磁和磁弹性效应中磁畴偏转的滞回特性. 基于Stoner-Wolhfarth模型的能量极小原理, 采用绘制自由能-磁畴偏转角度关系曲线的求解方法, 研究了压磁和磁弹性效应中载荷作用下的磁畴角度偏转和磁化过程, 计算分析了不同载荷作用下磁畴偏转的滞回特性. 研究表明, 压磁和磁弹性效应中磁畴偏转均存在明显的滞回、跃迁效应, 其中磁化强度的滞回效应来源于磁畴偏转的角度跃迁; 压磁效应中预加磁场的施加将增大磁化强度的滞回, 同时使滞回曲线向大压应力方向偏移; 磁弹性效应中磁畴偏转的滞回存在两个临界磁场强度, 不同磁场强度下合金具有不同的磁畴偏转路径和磁化滞回曲线, 临界磁场强度的大小取决于预压应力的施加. 理论分析对类磁致伸缩材料磁畴偏转模型的完善和材料器件的设计应用非常有意义.     

Modeling of irreversible switching and viscosity phenomena in perpendicular thin films

We have developed a simple numerical model for simulating domains as well as remanence and viscosity curves in the slow dynamics regime, for thin films characterized by perpendicular magnetization and irregular domain configurations due to strong disorder. The physical system is represented as constituted of identical switching units, described by proper switching field distributions and energy barrier laws for pinning and nucleation processes. The model also includes an effective field which accounts for magnetic forces proportional to magnetization, on average. Simulations of DCD curves show that when the reversal of magnetization is governed by pinning, the coercive field depends on the physical size of the film area on which the external field is applied. In the case of viscosity phenomena described by a linear energy barrier law associated with a single predominant reversal process (pinning or nucleation), universal viscosity curves can be generated by properly transforming the DCD curve of the system. We also demonstrate that a reduction of the maximum viscosity coefficient can coexist with a reduction of the energy barrier heights.     

Stability diagram for elastic domains in epitaxial ferroelectric thin films

The statics of isolated elastic domains (twins) in epitaxial thin tetragonal films grown on a cubic substrate is investigated theoretically. Different possible variants of the geometric shape of a domain are studied: plate, trapezoidal, and triangular. The nonuniform internal stresses, which also exist in polydomain epitaxial systems, are calculated by the effective-dislocation method. Hence the elastic energies stored in heterostructures with different domains are determined. The equilibrium width of a domain is calculated by minimizing the total internal energy of the heterostructure. Next, the stability diagram for isolated domains in epitaxial films is constructed from energy considerations. It is shown that in a large part of this diagram trapezoidal domains are energetically more advantageous than plate-shaped domains. The effect of an external electric field on the stability of 90° domains in epitaxial ferroelectric films is investigated. Fiz. Tverd. Tela (St. Petersburg) 39, 127–134 (January 1997)     

Magnetization processes in the narrow domain structures of amorphous ferromagnetic alloys

The magnetization processes within the narrow domain laminae of amorphous ferromagnetic alloys have been investigated by means of the magneto-optical Kerr effect. Changes of the domain width of the closure domains by a magnetic field applied perpendicular to the laminae have been determined for the alloys Fe₈₀B₂₀ and Fe₄₀Ni₄₀P₁₄B₆. These results are compared with theoretical calculations, assuming that wall displacements within the closure domains and rotations of the magnetization in the bulk domains take place simultaneously and a stray field free domain structure is developed. It turned out, that the closure domain structure on the surface of the sample vanishes at the same magnetic field where magnetic saturation is approached.     

Low-temperature study of the magnetization reversal and magnetic anisotropy of Fe,Ni, and Co nanowires

We present an extensive study of the magnetic reversal mechanism of Fe and Ni nanowires with diameters down to 6 nm, i.e. smaller than the domain wall width. The coercive field at 5 K is a factor of 3 lower than the prediction for rotation in unison. We also observe that the activation energy associated with the reversal process is proportional to the cross-section of the wires and nearly independent of the wire length. From the temperature dependence of the coercive field and the magnetic viscosity we can conclude that magnetization reversal takes place via a nucleation of a small magnetic domain, probably at the end of the wire, followed by the movement of the domain wall. For Co wires, we observe a different behavior that is dominated by the competition between the shape anisotropy and the temperature-dependent magnetocrystalline anisotropy.     

Diamagnetic domains and magnetostriction in beryllium

Magnetostriction was for the first time studied under the conditions of formation of diamagnetic domains (Condon domains). Transverse magnetostriction oscillations on a beryllium single crystalline plate oriented normally to magnetic field were measured in magnetic fields up to 7 T at temperatures down to 1.5 K. The relative amplitude of oscillations increased almost as the square of magnetic field and reached 10^?5. The signal had a sawtoothed shape corresponding to alternation of homogeneous and inhomogeneous (domain) states in the region of the existence of magnetic domains. The arising of domains was accompanied by singularities in the observed signals which is explained by an anomalous increase in the compressibility coefficient of the domain state: coefficient oscillations were more than 100 times larger than the value predicted by the standard theory. The observed relation between magnetization current and deformation led us to conclude that the compressibility of the metal was fully determined by conduction electrons. Magnetostriction then exactly compensated Fermi level oscillations. The position of the Fermi level therefore remained constant under magnetic field variations. In addition, the domain wall thickness had to increase as the plate grew thicker.     

Effect of the orientation of the Fe-3% Si crystal surface with respect to crystallographic axes on the dynamic behavior of the domain structure and magnetic losses in rotating magnetic fields

A domain structure and its dynamic transformation in a rotating magnetic field are experimentally studied over a wide induction range (up to 1.7 T) on a single-crystal plate whose surface deviates through angle β from a (110) crystallographic plane. The induction ranges of different dynamic behavior of the domain structure are determined. At an induction below 0.5 T, the magnetization reversal of the plate occurs via a change in the main domain structure. At inductions up to 1.4 T, the main structure undergoes strong dynamic fragmentation. At a higher induction, the magnetization reversal of the sample proceeds via the growth of the closure structure localized at the periphery of the sample in the absence of a magnetic field. The dependences obtained support the early considerations regarding the behavior of magnetic losses.