Magnetic and Elastic Vibrations in Manganese–Zinc Spinel Crystals as the Functions of Anisotropy Constant

The amplitudes of magnetic and elastic vibrations for Mn_0.61Zn_0.35Fe_2.04O₄ spinel crystalline slab are calculated by solving the equations describing the magnetic and elastic dynamics. The anisotropy constants, magnetization, second-order elastic constants and magnetoelastic coupling constants for a studied crystal are expressed as the functions of temperature. The magnetization vector and elastic shear components are found as the functions of the first magnetic anisotropy constant at different values of an external constant magnetic field greater than a saturation field. The procession patterns for normally and tangentially magnetized slabs are displayed for two values of the first anisotropy constant. High absolute values of the first anisotropy constant are shown to refer to reorientation of the magnetization vector.     

Gyroscopic force acting on the magnetic vortex in a weak ferromagnet

The gyroscopic (Magnus) force in weak ferromagnets acting on magnetic vortices when the domain walls move in the external magnetic field has been investigated. The general expressions for the gyroscopic force in weak ferromagnets are obtained. The particular calculation of the gyroscopic force in rhombic weak ferromagnets is performed using the method that allows one to calculate it neglecting the internal structure of a vortex in the domain wall. It is shown that the gyroscopic force for most types of domain walls is nonzero and is determined by the mean sublattice magnetization, the Dzyaloshinsky interaction constant, and the constant of the exchange interaction between the sublattices.     

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.     

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.     

Domain structure and magnetization processes in permalloy propagation elements

A review of domain structures and magnetization processes in permalloy overlays is given, together with some new results. The simplest domain structure for a given element consists of a loop of magnetic flux, but in elements with irregular geometry the circulating flux is not constant. More complex structures arise when an element contains internal closure domains. In-plane anisotropy in permalloy affects the distribution of closure domains but with decreasing bar width the influence of anisotropy is reduced. Reversible wall motion in weak fields gives way to hysteresis effects when the applied field exceeds a certain level, H_s. In particular magnetization buckling may occur. Some details of buckling in asymmetric chevrons and half-discs are given and compared with the behaviour in an I-bar. The proximity of a bubble medium containing stripe domains is shown to reduce considerably the applied fields needed for buckling in overlay components. Following saturation, changes in the demagnetized state are usually apparent. On a simple level, the spin structure and polarity of Bloch walls is altered. More noticeably the wall pattern itself can change when closure domains are created or annihilated in pairs. The significance of these fluctuations for bubble propagation is assessed by considering the intrinsic stray field profile of a Bloch wall segment. A simple wall model is employed. It is demonstrated that a curved domain wall provides a reasonable basis for modelling the field of a magnetized bar up to saturation. Calculated values of H_s agree qualitatively with experiment. The external field of the bar is rather insensitive to the exact distribution of free-pole density. Together with the observed complexities of domain behabiour this reaffirms the validity of the continuum approach to modelling.     

The magnetic properties across the martensitic transition in the Co38Ni34Al28 alloy

The magnetic properties of the Co₃₈Ni₃₄Al₂₈ alloy have been studied. The alloy exhibits a first order austenite-martensite phase transition in the temperature region between 155 and 247 K. A strain of 0.07% is produced across this phase transition. The Arrott plots obtained from the isothermal magnetic field dependence of magnetization indicate the presence of spontaneous magnetization both in the austenite and martensite phases, confirming the ferromagnetic character of the alloy up to room temperature. The temperature dependence of the high field magnetization indicates the presence of spin wave excitations, spin wave excitation gap and spin wave-spin wave interactions in the martensite phase. The magnetic anisotropy energy constant for the Co₃₈Ni₃₄Al₂₈ alloy is estimated both with the help of the standard law of approach to saturation of magnetization, and also from the field dependence of magnetization using the field for technical saturation of magnetization. The temperature dependences of these energy terms are compared. The estimated values of the magnetic anisotropy constant seem to be in agreement with the magnitude of the spin wave excitation gap estimated from the temperature dependence of high field magnetization.     

Spontaneous transformations of the magnetic structure of a film nanocontact

The magnetization distributions in a symmetric magnetic film nanocontact for oppositely magnetized ferromagnetic electrodes are analyzed based on numerically solving the Landau-Lifshitz and magnetostatic equations as a function of magnetic and geometrical factors. It is found that a symmetric magnetic configuration is unstable when the head-to-head domain wall dividing the regions with opposite orientations of magnetization is located at the center of the nanocontact. The instability arises when the uniaxial magnetic anisotropy constant reaches a certain critical value K _c below which it spontaneously leaves the center of the nanocontact. The transition from the symmetric state (wall at the center) to an asymmetric one can be continuous (second order) or discrete (first order), depending on the geometrical and physical parameters of the nanocontact (length to width ratio, anisotropy constant, and saturation magnetization). The phase diagram is constructed in terms of the variable’s nanocontact length vs. anisotropy constant. This diagram divides the symmetric and asymmetric magnetic configurations of the system. The occurrence of a tricritical point in the phase diagram is its characteristic feature.     

磁畴壁手性和磁斯格明子的拓扑性表征及其调控

磁性斯格明子由于拓扑的保护性,具有很高的稳定性和较小的临界驱动电流,有望应用于未来的赛道存储器件中.而在中心对称体系,由于偶极作用的各向同性,磁泡的拓扑性和螺旋度都呈现出多样性的特征.其中非平庸的磁泡即等同于磁性斯格明子.我们通过近期实验结果,结合微磁学模拟的方法,发现在中心对称体系中磁斯格明子的拓扑性会受到体系垂直各向异性的调控.另外在加磁场的演变过程中,会很大程度上依赖于基态畴的畴壁特性.磁场的倾斜或者一定的面内各向异性也会改变磁斯格明子的形态.通过对材料的基态磁结构及磁各向异性的调节,辅助以面内分量的控制,可以对基态磁畴、进而对磁斯格明子的拓扑性实现调控.这对磁斯格明子在电流驱动存储器件中的应用具有重要意义.     

Two-dimensional micromagnetic simulation of domain structures in films with combined anisotropy

The transformation of the domain structure of micrometer-thick films with variations in the induced uniaxial anisotropy constant with the easy magnetization axis perpendicular to the film surface has been investigated using numerical micromagnetic simulation in the framework of a two-dimensional model of the magnetization distribution. The case where the tetra-axial crystallographic anisotropy exists in the film with uniaxial magnetic anisotropy has been considered. The transformation of the open domain structure into the structure with a magnetic flux closed inside the sample has been investigated in detail, and new types of 109-degree and 90-degree vortex-like domain walls and periodic domain structures have been obtained.     

Co纳米线磁矩反转动态过程的有限元微磁学模拟

采用有限元微磁学模拟方法研究了Co纳米线在不同外加恒磁场下磁矩的翻转过程.研究结果表明在直径为10 nm的Co纳米线内,经过一定的形核时间将在其一端形成一个反向磁畴.磁畴壁的类型为横向畴壁,该畴壁将在一外加恒定磁场的驱动下匀速地从一端运动到另一端.畴壁的运动速度与外加磁场大小呈线性关系.在H为1000 kA/m时,发现在纳米线的两端均会形成一个“头对头”的反向磁畴.计算结果表明,畴壁内磁矩的方向旋转一个周期所导致的畴壁运动的距离相同,与外加磁场强度无关. 关键词： 磁性纳米线 微磁学模拟 磁畴 横向畴壁     

铁磁/非磁金属异质结中的拓扑霍尔效应

在铁磁/非磁金属异质结中,界面处的Dzyaloshinskii-Moriya相互作用会诱导诸如磁性斯格明子等手性磁畴壁结构的形成.当巡游电子通过手性磁畴壁结构时,会获得一个贝里相位,而相应的贝里曲率则等效于一个外磁场,它将诱导额外的霍尔效应,即拓扑霍尔效应.拓扑霍尔效应是当前磁性斯格明子和自旋电子学研究领域的热点之一.本文由实空间贝里相位出发,简要介绍了拓扑霍尔效应的物理机制;然后着重讨论了铁磁/非磁金属异质结中的拓扑霍尔效应,包括磁性多层膜中和MnGa/重金属双层膜中的拓扑霍尔效应.这两种结构都可以通过改变材料的厚度、种类、生长方式等调控界面Dzyaloshinskii-Moriya相互作用,从而有效地调控磁性斯格明子和拓扑霍尔效应.     

铁磁/反铁磁双层薄膜中应力各向异性研究

采用铁磁共振方法,研究了铁磁/反铁磁双层薄膜中交换各向异性和应力各向异性对其物理性质的影响.结果表明,单向各向异性来源于界面交换作用,应力各向异性对材料的磁化难易程度有较大影响.当外磁场方向与应力场方向平行时,应力场的存在将促进该方向的磁化.反之,应力场将会阻碍该方向的磁化.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

Magnetostatic energy and stripe domain structure in a ferromagnetic plate of finite width with in-plane anisotropy

The magnetostatic energy and domain structure (DS) in a long ferromagnetic plate of a finite width with in-plane anisotropy are calculated for the case of the domain magnetization vectors lying in the plane of the plate. The situation where the DS period is much shorter than the width but is considerably larger than the thickness of the plate is analyzed in detail. The equilibrium DS period and the width ratio of two adjacent domains are determined as functions of an external magnetic field parallel to the plane of the plate by minimizing the energy. The DS period is found to be proportional to the plate width and the domain wall energy and inversely proportional to the squared saturation magnetization. While the width of the favorable domains (with the magnetization parallel to the field) grows with increasing field, the unfavorable domains, rather than disappearing completely, form relatively narrow transition regions between the favorable domains, i.e., 360° domain walls.     

Dependence of magnetic characteristics on sputtering-power and substrate-temperature in amorphous Tb40(FeCoV)60 films

The amorphous Tb₄₀(Fe₄₉Co₄₉V₂)₆₀ films were deposited at different sputtering powers and substrate temperatures. The microstructural and magnetic characteristics were investigated by means of field emission scan electron microscope, magnetic force microscope and vibrating sample magnetometer. Our results show that with increasing sputtering power, out-of-plane coercivity decreases monotonically while saturation magnetization has a maximum value of 231 kA/m for the sample prepared at 50 W. The as-deposited alloy films are amorphous, whereas the coercivity and saturation magnetization are strongly dependent on the substrate temperature. An out-of-plane hysteresis loop with coercivity below 22 mT and saturation magnetization over 290 kA/m is obtained combining dc power and substrate temperature. The dominant mechanism of room temperature coercivity appears to be domain wall pinning, rather than nucleation under all conditions measured. The variation of saturation magnetization is similar to that of perpendicular magnetic anisotropy with either sputtering power or substrate temperature according to the difference of magnetic domain structure.     

双模随机同向晶场对spin-1和spin-1/2混合自旋纳米管中Blume-Capel模型平均磁化强度的影响

利用有效场理论研究了纳米管上双模随机同向晶场中混合自旋Blume-Capel模型格点的平均磁化强度,得到了系统格点的平均磁化强度与双模随机晶场的取值概率、外磁场、晶场参数和晶场强度比值的关系。结果表明：取值概率、外磁场、交换相互作用、晶场强度比值和晶场强度等诸多因素相互竞争,使系统表现出比恒定晶场作用的Blume-Capel模型更为丰富的磁化现象;双模随机同向晶场会抑制系统的平均磁化强度,使其基态饱和值小于5/6;外磁场导致系统的二级相变消失;一定条件下系统发生一级相变;系统的平均磁化强度呈现部分缺失和负值现象。     

Determination of the in-plane anisotropy field in hexagonal systems via rotational magnetization: Theoretical model and Monte Carlo simulations

The magnetic anisotropy field in thin films with in-plane uniaxial anisotropy can be deduced from the VSM magnetization curves measured in magnetic fields of constant magnitudes. This offers a new possibility of applying rotational magnetization curves to determine the first- and second-order anisotropy constant in these films. In this paper we report a theoretical derivation of rotational magnetization curve in hexagonal crystal system with easy-plane anisotropy based on the principle of the minimum total energy. This model is applied to calculate and analyze the rotational magnetization process for magnetic spherical particles with hexagonal easy-plane anisotropy when rotating the external magnetic field in the basal plane. The theoretical calculations are consistent with Monte Carlo simulation results. It is found that to well reproduce experimental curves, the effect of coercive force on the magnetization reversal process should be fully considered when the intensity of the external field is much weaker than that of the anisotropy field. Our research proves that the rotational magnetization curve from VSM measurement provides an effective access to analyze the in-plane anisotropy constant K ₃ in hexagonal compounds, and the suitable experimental condition to measure K ₃ is met when the ratio of the magnitude of the external field to that of the anisotropy field is around 0.2. Supported by the National Natural Science Foundation of China (Grant Nos. 90505007 and 10774061) Recommended by LI FaShen     

双模随机交错晶场对spin-1和spin-1/2混合自旋纳米管中Blume-Capel模型磁化强度的影响

利用有效场理论研究了纳米管上双模随机交错晶场中混合自旋Blume-Capel模型格点的平均磁化强度,得到了系统格点的平均磁化强度与双模随机晶场的取值概率、外磁场、晶场参数和晶场强度比值的关系.结果表明:取值概率、外磁场、交换相互作用、晶场强度比值和晶场强度等诸多因素相互竞争,使系统表现出比恒定晶场作用的Blume-Capel模型更为丰富的磁化现象;双模随机交错晶场会抑制系统的平均磁化强度,使其基态饱和值小于5/6;外磁场导致系统的二级相变消失;一定条件下系统发生一级相变;系统的平均磁化强度呈现部分缺失和负值现象.     

Magnetization of interacting electrons in anisotropic quantum dots with Rashba spin–orbit interaction

Magnetization of anisotropic quantum dots in the presence of the Rashba spin–orbit interaction has been studied for three and four interacting electrons in the dot for non-zero values of the applied magnetic field. We observe unique behaviors of magnetization that are direct reflections of the anisotropy and the spin–orbit interaction parameters independently or concurrently. In particular, there are saw-tooth structures in the magnetic field dependence of the magnetization, as caused by the electron–electron interaction, that are strongly modified in the presence of large anisotropy and high strength of the spin–orbit interactions. We also report the temperature dependence of magnetization that indicates the temperature beyond which these structures due to the interactions disappear. Additionally, we found the emergence of a weak sawtooth structure in magnetization for three electrons in the high anisotropy and large spin–orbit interaction limit that was explained as a result of merging of two low-energy curves when the level spacings evolve with increasing values of the anisotropy and the spin–orbit interaction strength.     

Computer simulation of magnetization relaxation in amorphous magnetics with random anisotropy

On the basis of Heisenberg model, the magnetic properties of amorphous terbium were studied by the Monte Carlo method. The temperature dependences of spontaneous magnetization and magnetic susceptibility were plotted as functions of the fraction of the constant of anisotropy to the exchange constant D/J ₀. The behavior of magnetization in an external magnetic field was studied, and the dependence of a coercive field and residual magnetization on the value D/J ₀ was found. The relaxation of magnetization was investigated after the external magnetic field was switched off.