Structure and dynamic properties of the twisted magnetic domain wall in an electric field

The structure of the domain wall in a magnetically uniaxial ferromagnetic film placed in an external electric field has been studied. It has been shown that the domain wall has a complex twisted structure whose characteristics (thickness, profile, and limit velocity of steady motion) depend on the film thickness, quality factor, and external electric field. The effect of the electric field on the domain wall is caused by inhomogeneous magnetoelectric coupling taking place in domain walls with a twisted structure.     

Pb(Zr0.52Ti0.48)O3陶瓷畴界粘滞运动的介电损耗模拟

对不同频率下(1—10kHz)Pb(Zr_0.52Ti_0.48)O₃多晶陶瓷的介电性能的测量表明：在接近铁电相变温度T_c以下存在一介电损耗峰,该峰具有弛豫特征但不满足Arrhenius关系．这一损耗峰被认为是由于畴界与晶格、缺陷钉扎的互作用引起的．用畴界粘滞运动的动力学方程,考虑陶瓷样品中T_c离散分布的情况,模拟了该介电损耗峰在不同频率下的行为,得到了与实验数据一致的结果．并由拟合参数计算了畴界运动     

Pb(Zr0.52Ti0.48)O3陶瓷畴界粘滞运动的介电损耗模拟

对不同频率下（１ —１０ ｋ Ｈｚ） Ｐｂ（ Ｚｒ０５２ Ｔｉ０４８） Ｏ３ 多晶陶瓷的介电性能的测量表明：在接近铁电相变温度 Ｔｃ 以下存在一介电损耗峰,该峰具有弛豫特征但不满足 Ａｒｒｈｅｎｉｕｓ 关系．这一损耗峰被认为是由于畴界与晶格、缺陷钉扎的互作用引起的．用畴界粘滞运动的动力学方程,考虑陶瓷样品中 Ｔｃ 离散分布的情况,模拟了该介电损耗峰在不同频率下的行为,得到了与实验数据一致的结果．并由拟合参数计算了畴界运动的粘滞系数和缺陷钉扎引起的回复力常量．     

Dynamics of domain walls in magnetically multiaxial films in the thickness range corresponding to the Bloch-Néel transformations of the structure

The numerical minimization of the total energy functional and the solution of the nonlinear Landau-Lifshitz equation have been performed exactly taking into account the fundamental (including dipole-dipole) interactions in terms of the two-dimensional magnetization distribution. The equilibrium structure, energy, mobility, and scenario of the dynamic transformation of the domain walls (in their non- steady-state motion) have been determined as a function of the film thickness b and external magnetic field H for two different ((010) and (110)) orientations of the surfaces of magnetically triaxial films. The range of film thicknesses, including the thickness b = b _N, for which the Néel domain walls can be transformed into the Bloch domain walls, has been investigated. The phenomena of anisotropy of the domain-wall energy, the domain-wall mobility, and the period of dynamic transformations of the domain walls have been analyzed as a function of the film thickness b and external magnetic field H. The range of film thicknesses has been determined, in which the non-steady-state motion of the Néel domain walls is accompanied by the creation and annihilation of vortex-like structures despite the one-dimensional character of the magnetization distribution in these walls.     

Effect of the electron energy on the entry blockage interval during electron scattering by a magnetic film with a strip domain structure

The trajectory of electrons in the stray field of a uniaxial magnetic film containing a strip domain structure (SDS) with a magnetization perpendicular to the sample surface are determined by numerical solution of the equations of motion. The interval of angles between the electron velocity projection onto the film surface and domain walls is determined, in which entry blockage takes place (electron scattering occurs without collisions with the sample surface). It is found that an increase in the electron energy leads to a decrease in this angular interval. The results are analyzed for multiple interactions of an electron moving in the gradient field of an SDS with attracting and repelling domain walls.     

Dielectric properties of thin films of partially deuterated betaine phosphite with large- and small-block structures

Ferroelectric thin films of partially deuterated betaine phosphite (DBPI) have been grown by evaporation on NdGaO₃ substrates with a preliminarily deposited structure of interdigitated electrodes. The block structure of the films is a texture in which the polar axis b is oriented in the plane of the film and the a* axis is perpendicular to this plane. Typical dimensions of the single-crystal blocks in DBPI films substantially exceeds the distance between the interdigitated electrodes (d = 50 μm). However, DBPI films in which the block structure has characteristic dimensions of the order of d have also been grown. Investigations of the dielectric properties of the films have demonstrated that the dimensions of the block structure have little effect on the behavior of a small-signal dielectric response, which, in the phase transition region, is characterized by a strong anomaly of the capacitance of the structure at T = T _c and by a glass-like behavior of the capacitance C and dielectric loss tangent tanδ in the temperature range of 120–200 K. By contrast, the low-frequency strong-signal dielectric response (dielectric hysteresis loops) in the structures with small blocks differs significantly from that observed for large-block structures. The difference in the frequency behavior of the hysteresis loops in the large-block and small-block structures is associated with the limitation of motion of domain walls in the case of small blocks.     

Kinetics of magnetization reversal in a thin La<Subscript>0.7</Subscript>Sr<Subscript>0.3</Subscript>MnO<Subscript>3</Subscript> manganite film

The kinetics of magnetization reversal of a thin LSMO film has been studied for the first time. It is shown that the magnetic domain structure critically depends on the conditions of structure formation. In the demagnetized state (after zero-field cooling from T _c ), a maze-like domain microstructure with perpendicular magnetization is formed in the film. However, after field cooling and/or saturating magnetization by a field of arbitrary orientation, the [110] direction of spontaneous magnetization in the film plane is stabilized; this pattern corresponds to macrodomains with in-plane magnetization. Further film magnetization reversal (both quasi-static and pulsed) from this state is implemented via nucleation and motion of 180° “head-to-head” domain walls. Upon pulse magnetization reversal, the walls “jump” at a distance proportional to the applied field strength and then undergo thermally activated drift. All dynamic characterisitcs critically depend on the temperature when the latter varies around the room temperature.     

Influence of the film thickness and additional elements (Al,O, and N) on the properties of FeCo film structures

The magnetic properties and domain structure of FeCoAlON thin films with thicknesses varying from 55 to 550 nm have been studied, and conditions favoring preparation of FeCoAlON films with uniaxial anisotropy in the direction normal to the film plane, which is required for designing “perpendicular” super-high-density information recording, have been established. In FeCoAlON films with a thickness up to 300 nm, the domain structure consists of cross-linked domain walls, because strong demagnetizing field suppresses formation of stripe domains. After the film thickness has reached 320 nm, cross-linked domain walls transform into stripe domains, with uniaxial anisotropy in the film plane disappearing, to become replaced by uniaxial anisotropy in the direction normal to the film plane, which can be assigned to magnetoelastic stresses induced by nitrogen atoms filling up interstitial space in the (110) plane. A further increase in the film thickness (up to 550 nm) leads to a rotational anisotropy due to the increase of nitrogen concentration in interstitials and the increase of magnetoelastic stresses.     

Generation of mesoscopic magnetic structures by local laser action

New effects are observed wherein the internal structure of the domain walls in a thin magnetic iron garnet film are modified by the action of focused laser radiation. A single laser pulse with increasing power gives rise to the following: 1) displacement of vertical Bloch lines in a domain wall; 2) generation of a pair of vertical Bloch lines on initially line-free walls; and, 3) an irreversible change in shape of a domain wall and the domain structure as a whole. The mechanism leading to the generation and displacement of Bloch lines is connected with the motion of domain walls which is induced by a local change in the distribution of demagnetizing fields as a result of a heating-induced decrease of the magnetization in the focal spot of the laser radiation. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 6, 398–402 (25 September 1997)     

Nonlinear dielectric properties of planar structures based on ferroelectric betaine phosphite films

Ferroelectric films of partly deuterated betaine phosphite are grown on NdGaO₃(001) substrates with an interdigitated system of electrodes on their surfaces by evaporation at room temperature. These films have a high capacitance in the ferroelectric phase transition range. The dielectric nonlinearity of the grown structures is studied in small-signal and strong-signal response modes and in the intermediate region between these two modes by measuring the capacitance in a dc bias field, dielectric hysteresis loops, and the Fourier spectra of an output signal in the Sawyer-Tower circuit. In the phase transition range, the capacitance control ratio at a bias voltage U _bias = 40 V is K ? 7. The dielectric nonlinearity of the structures in the paraelectric phase is described by the Landau theory of second-order phase transitions. The additional contribution to the nonlinearity in the ferroelectric phase is related to the motion of domain walls and manifests itself when the input signal amplitude is higher than U _st ～ 0.7–1.0 V. The relaxation times of domain walls are determined from an analysis of the frequency dependences of the dielectric hysteresis.     

Remanence due to wall magnetization and counterintuitive magnetometry data in 200-nm films of Ni

200-nm-thick Ni films in an epitaxial Cu/Ni/Cu/Si(001) structure are expected to have an in-plane effective magnetic anisotropy. However, the in-plane remanence is only 42%, and magnetic force microscopy domain images suggest perpendicular magnetization. Quantitative magnetic force microscopy analysis can resolve the inconsistencies and show that (i) the films have perpendicular domains capped by closure domains with magnetization canted at 51 degrees from the film normal, (ii) the magnetization in the Bloch domain walls between the perpendicular domains accounts for the low in-plane remanence, and (iii) the perpendicular magnetization process requires a short-range domain wall motion prior to wall-magnetization rotation and is nonhysteretic, whereas the in-plane magnetization requires long-range motion before domain-magnetization rotation and is hysteretic.     

Small- and strong-signal dielectric response in a single-crystal film of partially deuterated betaine phosphite

Poly- and single-crystal films of betaine phosphite deuterated to ∼20% have been grown by evaporation on NdGaO₃ (001) substrates with a preliminarily deposited planar interdigital structure of electrodes. The small-signal dielectric response in the 0.1–100.0-kHz frequency range has revealed a strong anomaly in capacitance upon the transition of the films to the ferroelectric state. Application of a bias field brings about suppression and a slight shift of the dielectric anomaly toward higher temperatures. The strong-signal dielectric response has been studied by the Sawyer-Tower method over the frequency range 0.06–3.00 kHz both in the para- and ferroelectric phases. In contrast to the case of a plane-parallel capacitor, in the planar structure studied, the dielectric hysteresis loops exhibit a very small coercivity at low frequencies, which grows with increasing frequency. This difference should be assigned to different domain structures formed in a planeparallel capacitor and in a planar structure in a saturating field. The growth of hysteresis with increasing frequency in a planar structure is considered to be associated with the domain wall motion.     

Substrate clamping effects on irreversible domain wall dynamics in lead zirconate titanate thin films

The role of long-range strain interactions on domain wall dynamics is explored through macroscopic and local measurements of nonlinear behavior in mechanically clamped and released polycrystalline lead zirconate-titanate (PZT) films. Released films show a dramatic change in the global dielectric nonlinearity and its frequency dependence as a function of mechanical clamping. Furthermore, we observe a transition from strong clustering of the nonlinear response for the clamped case to almost uniform nonlinearity for the released film. This behavior is ascribed to increased mobility of domain walls. These results suggest the dominant role of collective strain interactions mediated by the local and global mechanical boundary conditions on the domain wall dynamics. The work presented in this Letter demonstrates that measurements on clamped films may considerably underestimate the piezoelectric coefficients and coupling constants of released structures used in microelectromechanical systems, energy harvesting systems, and microrobots.     

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)     

Damping of the domain walls motion in Co-based amorphous ribbons with helical magnetic anisotropy: Part III

The damping of the motion of domain walls of a sandwich domain structure by the eddy currents magnetic fields, the stray fields and the hysteresis friction fields is investigated. The blocking of the motion of domain walls by the eddy currents magnetic fields is discovered.     

Modelling of structural domains and elastic strain calculation in rhombohedral La1−x Sr x MnO3 films on (110) SrTiO3

As reported in the literature, structural domains in (110) oriented rhombohedral La_{1? x} Sr _x MnO₃ (LSMO) films on (110) SrTiO₃ show a pattern with alternating domain widths and inclined domain walls. An appropriate one-dimensional periodic domain model was developed and the non-uniform strain field in a coherently grown film was calculated by applying the coherency-defect approach. The strain is sharply peaked at the junction of the domain walls and the film/substrate interface. The dependence of the equilibrium domain-width ratio and domain-pattern period on film thickness was determined by minimizing the sum of elastic and domain-wall energies. The proposed domain structure can be formed only in a certain range of the film's crystal-structure data compared to the substrate. Corresponding composition-dependent structure data of LSMO are compiled.     

Effect of 90° domain walls on the low-field permittivity of PbZr(0.2)Ti(0.8)O3 thin films

We report on the contribution of 90° ferroelastic domain walls in strain-engineered PbZr(0.2)Ti(0.8)O(3) thin films to the room-temperature permittivity. Using a combination of phenomenological Ginzburg-Landau-Devonshire polydomain thin-film models and epitaxial thin-film growth and characterization, the extrinsic or domain wall contribution to the low-field, reversible dielectric response is evaluated as a function of increasing domain wall density. Using epitaxial thin-film strain we have engineered a set of samples that possess a known quantity of 90° domain walls that act as a model system with which to probe the contribution from these ferroelastic domain walls. We observe a strong enhancement of the permittivity with increasing domain wall density that matches the predictions of the phenomenological models. Additionally, we report experimentally measured bounds to domain wall stiffness in such PbZr(0.2)Ti(0.8)O(3) thin films as a function of domain wall density and frequency.     

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.     

Influence of isomorphous substitution of metal ion on the low-frequency dielectric dispersion in NH2(CH3)2Al1−xCrx(SO4)2⋅6H2O ferroelectrics

This paper is devoted to the study of the influence of metal ion isomorphous substitution on the ferroelastic-ferroelectric phase transition and dispersion caused by the motion of domain walls in dimethylammonium metal sulfate hexahydrate DMAAl_1?xCr_xS ferroelectric crystals (x = 0, 0.065, 0.2). It is shown that such a substitution significantly changes the phase transition temperature and parameters of the dielectric dispersion. These changes are explained in terms of interaction between the metal-hydrate complexes and DMA groups that carry the dipole moment and due to this they are responsible for the phase transitions and motion of the domain walls.     

Dynamics of interphase domain walls during a Morin-type phase transition

The dynamics of 90-degree interphase domain walls during a first-order Morin-type spin-reorientation phase transition is studied theoretically. It is shown that an oscillatory motion of the walls with an amplitude that depends linearly on the field amplitude, as well as a drift motion of the wall at a velocity proportional to the square of the field amplitude, are driven by an external oscillating magnetic field. Drift of the entire domain structure as a whole is predicted to be possible. Fiz. Tverd. Tela (St. Petersburg) 41, 274–282 (February 1999)