Statistical theory of the pinning of Bloch walls by randomly distributed defects

The coercive force is calculated for a rigid and a one- or two-dimensionally vaulted Bloch wall on the basis of a statistical theory. It is shown that the validity of the various pinning models developed previously depends on the defect density, the interaction force, and the area and flexibility of the domain wall. Our theoretical results are confirmed by a computer simulation of the pinning problem. The study of the temperature dependence of the coercive force proves to be a sensitive test to decide which pinning model applies.     

Nd2(Fe1-xMnx)14B的低温内禀矫顽力

当x<0.5时,Nd₂(Fe_1-xMn_x)₁₄B可形成四方晶体结构,空间群为P4₂/mnm。在低温下,该赝三元化合物的大块铸态样品具有高矫顽力。此矫顽力不依赖于热处理等工艺过程,因此具有内禀性质。内禀矫顽力 _iH_c与样品的成分有关。Nd₂(Fe_1-xMn_x)₁₄B的起始磁化曲线具有传播场H_p,并且H_p的数值与 _iH_c接近。这表明内禀矫顽力是由畴壁钉扎造成的。研究了 _iH_c与温度的变化关系,并估算了钉扎位垒的强度。测量了Nd₂(Fe_1-xMn_x)₁₄B的居里温度和饱和磁化强度。在此赝三元化合物中,交换作用随Mn对Fe的替换而急剧降低。这使得畴壁厚度变窄。Nd₂(Fe_1-xMn_x)₁₄B的磁化和反磁化行为可用窄畴壁的特征来解释。 关键词：     

Magnetization reversal mechanism of anisotropic HDDR Nd2Fe14B-based magnet powder

The coercivity mechanism of anisotropic Nd₂Fe₁₄B-based magnetic powders prepared by hydrogenation–decomposition–esorption–recombination process was studied. Polarization and corresponding differential susceptibility curves of the powders in its thermally demagnetized state were measured. Microstructure and constituents of the powders were investigated by means of transmission electron microscope and scanning electron microscope with energy dispersive X-ray detector. In addition, theoretical calculation of the intrinsic coercive force of the magnetic powders was performed. It is concluded that the magnetic hardening mechanism of the powders is the pinning of domain walls at grain boundaries of the Nd₂Fe₁₄B main phase and Nd-rich phase that distributes homogeneously around some conglomerations composed of fine Nd₂Fe₁₄B grains. The coercive force of the powders is mainly determined by the pinning of domain walls by Nd-rich boundary phase.     

Rayleigh curve and coercive force of thin MnBi films

Statistical Rayleigh-curve theory is applied to thin evaporated MnBi films in order to obtain information concerning the density of wall pinning centra. The treatment results in a prediction of the coercive forceH _c and the average distance between adjacent wall pinning centra, 2L ₀. The coercive forceH _cis also measured experimentally. The results of the two methods are in good agreement with each other. The influence of dislocations on the coercive force is discussed briefly.     

The influence of planar defects on the coercive field of hard magnetic materials

Planar defects are found to act as strong pinning centres in hard magnetic materials. The interaction of the domain wall with planar defects is assumed to originate in a local perturbation of exchange coupling and crystalline anisotropy. The coercive field is calculated within the framework of micromagnetic continuum theory as well as with a discrete lattice theory which accounts for the interaction between the individual atomic spins. The theory has been applied to discuss the influence of grain boundaries and antiphase boundaries in the intermetallic compound Co₅Sm.     

A comparative analysis of the mechanisms of pinning of a domain wall in a nanowire

A comparative analysis of the influence of random fluctuations of the crystallographic anisotropy and surface roughnesses on the pinning of a domain wall in a nanowire has been performed in the framework of the model of a polycrystalline nanowire. The initial magnetization curve and the coercive force for these mechanisms of pinning have been calculated. A criterion has been formulated according to which surface inhomogeneities of the nanowire play the key role in the process of pinning of a domain wall. The analytical results obtained have been verified using computer simulation.     

Tb1-xGdxFe2的磁矩和矫顽力

测量了赝二元立方Laves相化合物TbGdFe₂(0≤x≤1)的磁化曲线、居里温度和矫顽力随温度的变化。发现化合物由TbFe₂向GdFe₂过渡时,样品的饱和磁化强度几乎直线下降。在所有成分下,Fe原子的磁矩都是常数(μ_Fe=1.60±0.04μ_B),但Tb原子的磁矩,由于受晶场影响,却小于自由离子的值(gJ=9.Oμ_B)。矫顽力由两部分组成:一为畴壁受Peierls势垒和稀土 关键词：     

Magnetization reversal in (0 0 1)Fe thin films studied by combining domain images and MOKE hysteresis loops

The magnetization reversal of epitaxial single-crystal Fe films has been studied by combining domain images and hysteresis loops. The reversal is quantitatively described by combining the coherent rotation model and the domain wall displacement model. The pinning energy exerted on the domain walls and the domain wall angle at the switching fields are obtained by fitting this model to experimental hysteresis loops. The field-dependent pinning energy and the domain wall angle in the reversal process, and the contributions of second-order magneto-optic effect to hysteresis loops, are revealed to be two important features of single-crystal Fe films.     

Statistics of irreversible displacements of domain walls in nanowires

The process of quasistatic displacement of domain walls is considered in a nanowire represented as a one-dimensional chain of ferromagnet crystallites. The domain wall pinning due to spatial fluctuations of the anisotropy axes is analyzed. Based on the theory of overshoots of random processes, we have calculated the distribution functions of the initial susceptibility and of the maximal force of interaction of the domain wall with inhomogeneities. These functions are found to be non-Gaussian. We have derived expressions for the magnetization curve and the coercive force, which depend on the length of the chain.     

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．     

Size effects and magnetoelastic couplings: a link between Hall–Petch behaviour and coercive field in soft ferromagnetic metals

Size effects regarding Hall–Petch (HP) relation are studied in this work for cobalt, nickel and Fe–3wt.%Si (FeSi), from polycrystalline to multicrystalline states. The materials show a breakdown in HP plot for thickness (t) to grain size (d) ratio less than a critical value. This appears in the beginning of plasticity for cobalt and FeSi whereas a plastic strain threshold must be overcome for nickel. Measurements of the coercive field on strained samples are able to depict such modification for low t/d ratio. Values of the coercive field in the polycrystalline domain allow an estimation of the magnetocrystalline anisotropy energy, related to the grain volume fraction concerned by reversal mechanisms for magnetic domains. Multicrystalline samples of cobalt and FeSi becomes magnetically softer at the yield stress. This is linked to a delay of the maximum intergranular stress towards higher strains for FeSi. For cobalt, non-linear elasticity and strong basal texture modify the magnetoelastic effects in coarse grain samples. For nickel, size effect on the coercive field appears after a few per cent of plastic strain as for HP relationship. A mean internal stress can be captured by magnetic measurements on polycrystals, related to the intragranular part of the kinematic stress. The softening of the magnetic properties for strained nickel multicrystals is due to a competition between the apparition of dislocation cells, which increases the coercive field by mechanisms of magnetic domain wall pinning, and surface softening of multicrystals, which tends to decrease the value of H_c.     

Three-and two-dimensional calculations for the interface anisotropy dependence of magnetic properties of exchange-spring Nd2Fe(14)B/α-Fe multilayers with out-of-plane easy axes

Hysteresis loops,energy products and magnetic moment distributions of perpendicularly oriented Nd2Fe(14)B/α-Fe exchange-spring multilayers are studied systematically based on both three-dimensional(3D)and one-dimensional(1D)micromagnetic methods,focused on the influence of the interface anisotropy.The calculated results are carefully compared with each other.The interface anisotropy effect is very palpable on the nucleation,pinning and coercive fields when the soft layer is very thin.However,as the soft layer thickness increases,the pinning and coercive fields are almost unchanged with the increment of interface anisotropy though the nucleation field still monotonically rises.Negative interface anisotropy decreases the maximum energy products and increases slightly the angles between the magnetization and applied field.The magnetic moment distributions in the thickness direction at various applied fields demonstrate a progress of three-step magnetic reversal,i.e.,nucleation,evolution and irreversible motion of the domain wall.The above results calculated by two models are in good agreement with each other.Moreover,the in-plane magnetic moment orientations based on two models are different.The 3D calculation shows a progress of generation and disappearance of vortex state,however,the magnetization orientations within the film plane calculated by the 1D model are coherent.Simulation results suggest that negative interface anisotropy is necessarily avoided experimentally.     

Coercivity mechanism of Sm(Co, Cu)5

The mechanism of the high intrinsic coercivity of the Sm(Co_1−xCu_x)₅ (0≦x<1) system was studied by relating the coherency between the lattice constants of hexagonal Sm(Co, Cu)₅ and hcp Co to the coercive force. It was found analytically that the intrinsic coercive force reaches a maximum in the composition range from x=0.6 to 0.8, where the lattice mismatch approaches zero, so that there is a strong correlation between lattice matching and coercive force. When a Sm ion was located within a Sm(Co, Cu)₅ grain and in the outmost edge of the a and c planes of its grain surrounded or not surrounded by the coherent Co phase, the crystal field parameter at each Sm³⁺ site was calculated using a point charge model under the assumption that the Co and Cu atoms located in a grain and the hcp Co atoms situated at the interface uniformly have a charge of 3/5−. The results indicated that the Co phase precipitated coherently along the grain boundaries effectively enhances the magnetocrystalline anisotropy of Sm ions located in the outmost edges of the a and c planes of a Sm(Co, Cu)₅ grain.     

低温固相反应法制备的NiFe2O4纳米颗粒的结构与磁性

采用低温固相反应法制备了晶粒尺寸在8—47nm之间的NiFe₂O₄纳米颗粒系列样品，用X射线衍射仪(XRD)、高分辨中子粉末衍射谱仪、振动样品磁强计和超导量子干涉仪等对样品的晶体结构、宏观磁性和纳米颗粒的表面各向异性进行了分析研究.XRD和中子衍射测量结果显示纳米颗粒的晶格常数略高于块体材料，样品的氧参量表明纳米颗粒的晶格畸变程度没有块体材料严重.相对块体材料，纳米颗粒具有较小的磁化强度、较大的矫顽力和各向异性能密度.纳米颗粒从多畴转变为单畴的临界尺寸约为40nm，超顺磁性临界尺寸约为16nm.     

Magnetic viscosity and domain wall pinning in an MnAlC permanent magnet

Magnetic viscosity in a hot extruded MnAlC permanent magnet has been measured over a temperature range from 80 to 295 K. The results are fitted to a recent theory of “strong” and “weak” domain wall pinning which allows values of the thermal activation free (“absolute zero”) coercive field to be determined from the data. If the pinning is due to strong pins, randomly distributed throughout the material, a pin density of ≈3×10¹⁵ cm^-3 is predicted. There is no obvious evidence of pin sites of this density within the grains visible in electron micrographs.If the pinning is localized (possibly at grain boundaries) then weak pinning by a similar, but localized, density of pins is predicted. Lorentz electron microscopy domain contrast in such regions might however be overwhelmed by strain contrast effects.     

Hysteresis mediated by a domain wall motion

The position of an interface (domain wall) in a medium with random pinning defects is not determined unambiguously by the instantaneous value of the driving force, even on average. Employing the general theory of the interface motion in a random medium, we study this hysteresis, different possible shapes of the hysteresis loop, and the dynamical phase transitions between them. Several principal characteristics of the hysteresis, including the coercive force and the curves of dynamical phase transitions obey scaling laws and display a critical behavior in the vicinity of the mobility threshold. At finite temperature the threshold is smeared and a new range of thermally activated hysteresis appears. At a finite frequency of the driving force there exists a range of the non-adiabatic regime in which not only the position, but also the average velocity of the domain wall, displays hysteresis.     

Angular dependence of the coercive field in sintered Fe77Nd15B8 magnets

The intrinsic nucleation and instability fields of uniaxial single domain particles are determined including the effects of the second anistropy constant and of oblique applied magnetic fields. The theoretical results for the angular dependences of the nucleation and pinning fields are compared with the angular dependence of the coercive field as measured for oriented sinter magnets of composition Fe₇₇Nd₁₅B₈. The experimental results are compatible with the assumption that at room temperature the coercive field in Fe₇₇Nd₁₅B₈ is determined by a nucleation mechanism.     

Magnetization distribution in magneto-optical medium on patterned substrate

A micromagnetic calculation of magnetization in a ferromagnetic thin film with a perpendicular magnetic anisotropy fabricated on a patterned substrate is carried out. The domain wall energy of pinning of domain walls between up and down magnetized domains is shown to be determined by geometry of substrate. Estimations of regions of stability of two different domain structures in the hexagonal lattice of circle patches are given.     

Domain wall resistance in epitaxial Fe wires

We studied the magnetoresistance behavior of epitaxial Fe wires grown on GaAs(1 1 0) with varying widths at room temperature. Single nanowires show a wire width (w) dependence of the coercive field, which increases with 1/w for decreasing wire widths. This enables the pinning of a single domain wall in the connection area of two wires with different widths. Magnetoresistance measurements of such wire structures clearly reveal resistance contributions arising from a domain wall. The presence of the domain wall is proven by photoemission electron-microscopy with synchrotron radiation. Moreover, micromagnetic simulations are performed to determine the spin orientations, especially within the domain wall. This permits us to calculate the anisotropic magnetoresistance caused by the domain wall. Taking this into account, we determine the intrinsic domain wall resistance, for which we found a positive value of 0.2%, in agreement with theoretical predictions.