Influence of magnetic dipole and magnetoelastic interactions on the phase states of 2D non-Heisenberg ferromagnetic with complex exchange interactions

The phase states of the 2D non-Heisenberg ferromagnetic with anisotropic bilinear and biquadratic exchange interactions are investigated. The limiting cases of the system under consideration are the two-dimensional XY-model with biquadratic exchange interaction and the isotropic Heisenberg ferromagnetic. The account of the magnetic dipole interaction leads to the realization of spatially inhomogeneous quadrupolar phase. The stability regions of various phase transitions for different values of the material parameters are studied. The phase diagram is built. Besides, the temperature phase transitions are investigated. The influence of the magnetoelastic interaction on the formation of the long-range quadrupolar order is determined.     

Mixed spin-1/2 and spin-1 Ising model with uniaxial and biaxial single-ion anisotropy on the Bethe lattice

The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.      

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.     

Co-thickness and oxidation states effect on magnetic anisotropy in Co/MgO heterostructure

Interfacial magnetism and magnetic anisotropy constant ($K_i$) in Co/MgO heterostructure have been studied using ab-initio density functional calculations. It is found that interfacial Co spin magnetic moment shows a strong interdependence on Co-O bond lengths and a reasonable spin-polarization of ～80% is established as a function of Co layers. Our results revealed a saturated positive (out-of-plane) $K_i$ of +2.80 mJ/m² at ≥12 Co layers (～1.6 nm Co thickness), which is associated with orbital magnetic moment difference in [100] and [001] direction along with a strong hybridization between $d_{xy}$ and $d_{x^2?y^2}$ orbitals through orbital angular momentum operator $\stackrel{?}{L_z}$. Furthermore, it is shown that the $K_i$ magnitude almost remains constant and weakens in the case of under- and over-oxidations in the interfacial MgO and Co layers, respectively. Interestingly, $K_i$ improved for oxygen migrated interface due to enhanced $d_{xy}$ and $d_{x^2?y^2}$ orbitals coupling. The disordered interfaces stability is checked by analyzing the formation energy. Hence, the present findings disclose that the higher Co thickness in ordered Co/MgO structure supports to out-of-plane [001] (positive) $K_i$, which could be useful for its technological implementation in high-density magnetic data storage devices with high thermal stability.     

Enhancement of magnetic anisotropy in mechanically attrited Cr2O3 nanoparticles

Cr₂O₃ nanoparticles of sizes from 24 to 12 nm were synthesized by mechanical grinding. Magnetic hysteresis loops were observed in the temperature range 5-300 K. Zero-field magnetization measurements showed two peaks, at low temperature in the range 36-52 K and at high temperature in the range 255-290 K. They were found to shift to higher temperatures as the particle size was reduced. This was ascribed due to the enhancement of the effective anisotropy constant with a decrease in particle size. The exchange bias was found to increase as the particle size became smaller. This is believed to arise due to an increase in uncompensated spins as a result of large surface area created.     

NdFeB纳米复合永磁材料的交换耦合相互作用和有效各向异性

以Nd₂Fe₁₄B/αFe为例，采用立方体晶粒结构模型，研究了纳米复合永磁材料中不同磁性晶粒间的交换耦合相互作用和有效各向异性.纳米复合永磁材料的有效各向异性Keff等于软、硬磁性相各向异性的统计平均值，每个晶粒的各向异性由晶粒表面交换耦合部分和晶粒内部未交换耦合部分的各向异性共同确定.计算结果表明，软、硬磁性相晶粒尺寸分布显著地影响有效各向异性Keff的值.当软、硬磁性晶粒尺寸D相同时，Keff随晶粒尺寸和硬磁性相体积分数的降低而减小, 当D<20nm 时，K 关键词： 纳米复合永磁材料 交换耦合相互作用 有效各向异性 晶粒尺寸     

Magnetic anisotropy,exchange coupling and Dzyaloshinskii–Moriya interaction of two-dimensional magnets

The two-dimensional (2D) magnets provide novel opportunities for understanding magnetism and investigating spin related phenomena in several atomic thickness. Multiple features of 2D magnets, such as critical temperatures, magnetoelectric/magneto-optic responses, and spin configurations, depend on the basic magnetic terms that describe various spins interactions and cooperatively determine the spin Hamiltonian of studied systems. In this review, we present a comprehensive survey of three types of basic terms, including magnetic anisotropy that is intimately related with long-range magnetic order, exchange coupling that normally dominates the spin interactions, and Dzyaloshinskii−Moriya interaction (DMI) that favors the noncollinear spin configurations, from the theoretical aspect. We introduce not only the physical features and origin of these crucial terms in 2D magnets but also many correlated phenomena, which may lead to the advance of 2D spintronics.     

Influence of steady background gradients on the accuracy of molecular diffusion anisotropy measurements

Spatial susceptibility variations of body components lead to local gradients of the static magnetic field. Effects of such background gradients on fractional diffusion anisotropy (FA) measurements on whole-body magnetic resonance units operating at 1.5, 3.0 and 7.0 T were analyzed theoretically and experimentally. Analytical expressions were derived for the cases of diffusion occurring in isotropic media and in tissues with cylindrical symmetry (e.g., white matter tracts or skeletal musculature). Typical magnitudes of background gradient strengths were estimated from in vivo and in vitro measurements with B0 field mapping sequences. Additionally, numerical simulations of magnetic field distributions and resulting field gradients were performed considering tissue-air interfaces in simplified geometrical arrangements. For media with isotropic diffusion, both measurements and analytical calculations showed increasing FA inaccuracy with stronger coupling between diffusion-encoding and background gradients. For cylindrical symmetry, FA values were estimated for a standard diffusion tensor imaging protocol in a realistic scenario. At 1 mm distance from a water-air interface, susceptibility-related background gradients amount to approximately 9 mT/m at 7 T and lead to a relative error of the measured FA of up to 48%. The error in the anisotropy assessment rises considerably with increasing field strength and must be taken into account especially for experimental and clinical studies on modern high-field systems.     

Double-Q magnetic structures and strong planar anisotropy in tetragonal ErRu2Ge2and ErRu2Si2

Single crystal magnetization measurements and powder neutron diffraction on tetragonal ErRu₂Ge₂ as well as anisotropy of the paramagnetic susceptibility and specific heat measurements on ErRu₂Si₂ are presented. Besides the huge crystal field contribution to the uniaxial anisotropy, which favors the basal plane, a strong in-plane anisotropy is evidenced. From these features and neutron diffraction experiments it is shown that magnetic structures of these materials are double-Q and accordingly non-colinear below their Néel temperature (5.2 and 6.0 K for Ge and Si based compounds, respectively). The magnetic structures induced during the metamagnetic processes are discussed. Received 24 December 1999     

Influence of quenching rate on the structural, soft magnetic and magnetoimpedance properties of melt-spun Co69Fe7Si14B10 alloy

Melt-spun ribbons of Co₆₉Fe₇Si₁₄B₁₀ alloy have been prepared at different wheel speeds viz. 47, 34 and 17 m/s and investigated for structural and magnetic properties. Degree of amorphicity in the as-spun ribbons is found to increase with wheel speed. Amorphous phase crystallizes in two stages producing Co₂Si, Co₂B and CoSi phases on annealing. Increase in wheel speed improves soft magnetic and magnetoimpedance properties due to decrease in perpendicular anisotropy which is associated with stripe domain formation. On annealing soft magnetic properties and magnetoimpedance deteriorate due to the formation of crystalline phases.     

Switching of vortex polarization in 2D easy-plane magnets by magnetic fields

We investigate the dynamics of out-of-plane (OP) vortices, in a 2-dimensional (2D) classical Heisenberg magnet with a weak anisotropy in the coupling of z-components of spins (easy plane anisotropy), on square lattices, under the influence of a rotating in-plane (IP) magnetic field. Switching of the z-component of magnetization of the vortex is studied in computer simulations as a function of the magnetic field's amplitude and frequency. The effects of the size and the anisotropy of the system on the switching process are shown. An approximate dynamical equivalence of the system, in the bulk limit, to another system with both IP and OP static fields in the rotating reference frame is demonstrated, and qualitatively the same switching and critical behavior is obtained in computer simulations for both systems. We briefly discuss the interplay between finite size effects (image vortices) and the applied field in the dynamics of OP vortices. In the framework of a discrete reduced model of the vortex core we propose a mechanism for switching the vortex polarization, which can account qualitatively for all our results. A coupling between the IP movement (trajectories) of the vortex center and the OP core structure oscillations, due to the discreteness of the underlying lattice, is shown. A connection between this coupling and our reduced model is made clear, through an analogy with a generalized Thiele equation. Received 6 June 2002 / Received in final form 4 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: juan.zagorodny@uni-bayreuth.de     

Theoretical study of enhanced ferromagnetism and tunable magnetic anisotropy of monolayer CrI3 by surface adsorption

Magnetic anisotropy energy (MAE) plays a key role for 2D magnetic materials, which have attracted significant attention for their promising applications in spintronic devices. Based on first-principles calculations, we have investigated the influence of surface adsorption on the ferromagnetism and MAE of monolayer CrI₃. We find that Li adsorption can dramatically enhance its ferromagnetism, and tune its easy magnetization axis to the in-plane direction from original out-of-plane at certain coverage of Li. The monotonic enhancement of in-plane magnetism in CrI₃ as the coverage of Li increases are attributed to electrostatic doping induced by charge transfer between Li atoms and I atoms, as supported by the charge doping simulation. The tunable robust magnetic anisotropy may open new promising applications of CrI₃–based materials in spintronic devices.     

Influence of Tb on easy magnetization direction and magnetostriction of ferromagnetic Laves phase GdFe_2 compounds

The crystal structure,magnetization,and spontaneous magnetostriction of ferromagnetic Laves phase Gd Fe2 compound have been investigated.High resolution synchrotron x-ray diffraction(XRD) analysis shows that Gd Fe2 has a lower cubic symmetry with easy magnetization direction(EMD) along [100] below Curie temperature TC.The replacement of Gd with a small amount of Tb changes the EMD to [111].The Curie temperature decreases while the field dependence of the saturation magnetization(Ms) measured in temperature range 5–300 K varies with increasing Tb concentration.Coercivity Hc increases with increasing Tb concentration and decays exponentially as temperature increases.The anisotropy in Gd Fe2 is so weak that some of the rare-earth substitution plays an important role in determining the easy direction of magnetization in GdFe_2.The calculated magnetostrictive constant λ100 shows a small value of 37×10~(-6).This value agrees well with experimental data 30×10~(-6).Under a relatively small magnetic field,GdFe_2 exhibits a V-shaped positive magnetostriction curve.When the field is further increased,the crystal exhibits a negative magnetostriction curve.This phenomenon has been discussed in term of magnetic domain switching.Furthermore,magnetostriction increases with increasing Tb concentration.Our work leads to a simple and unified mesoscopic explanation for magnetostriction in ferromagnets.It may also provide insight for developing novel functional materials.     

Magnetic anisotropy and domain patterns in electrodeposited cobalt nanowires

The magnetic anisotropy and domain structure of electrodeposited cylindrical Co nanowires with length of 10 or 20 μm and diameters ranging from 30 to 450 nm are studied by means of magnetization and magnetic torque measurements, as well as magnetic force microscopy. Experimental results reveal that crystal anisotropy either concurs with shape anisotropy in maintaining the Co magnetization aligned along the wire or favours an orientation of the magnetization perpendicular to the wire, hence competing with shape anisotropy, depending on whether the diameter of the wires is smaller or larger than a critical diameter of 50 nm. This change of crystal anisotropy, originating in changes in the crystallographic structure of Co, is naturally found to strongly modify the zero (or small) field magnetic domain structure in the nanowires. Except for nanowires with parallel-to-wire crystal anisotropy (very small diameters) where single-domain behaviour may occur, the formation of magnetic domains is required to explain the experimental observations. The geometrical restriction imposed on the magnetization by the small lateral size of the wires proves to play an important role in the domain structures formed. Received 14 September 2000     

TiO2电子结构与其双折射性、各向异性 关联的理论研究

采用基于密度泛函理论的第一性原理平面波超软赝势方法对锐钛矿相TiO₂的晶体结构、能带结构、态密度等电子结构进行了理论分析, 在此基础上对介电函数、能量损失函数、光电导率等光学性质进行系统的理论计算, 分析了TiO₂双折射现象、各向异性与电子结构之间的关联, 其结果与文献报道的相关实验结果相符合, 从理论上探讨了TiO₂电子结构和其双折射现象、各向异性的特征.     

Composition dependence of magnetic anisotropy and quadratic magnetooptical effect in epitaxial films of the Heusler alloy Co2MnGe

Magnetic anisotropy and magnetooptic Kerr effect for epitaxial films of Co_xMn_yGe_1−x−y grown on Ge (1 1 1) substrates have been studied systematically in the compositional vicinity of the Heusler alloy Co₂MnGe. A large quadratic magnetooptic Kerr effect has been observed within a narrow region of composition centered around the Co to Mn atomic ratio of 2. The effect has been used to probe and quantify the magnetic anisotropy of the system, which is shown to have a strong sixfold in-plane component accompanied by a weak uniaxial component at room temperature. These properties are shown to depend sensitively on atomic ratio between Co and Mn, indicating the presence of an intrinsic composition-driven phenomenon.     

Tuning stress-induced magnetic anisotropy and high frequency properties of FeCo films deposited on different curvature substrates

It is important to control magnetic anisotropy of ferromagnetic materials. In this work, FeCo thin films are deposited on the curving substrates by electrochemical deposition to adjust the stress-induced magnetic anisotropy. The compressive stress is produced in the as-deposited films after the substrates are flattened. A simplified theoretical model of ferromagnetic resonance is utilized to measure the intrinsic magnetic anisotropy field and saturation magnetization. The results show that the stress-induced magnetic anisotropy and the resonance frequency increase with the increase of substrate curvature. The induced easy axis is perpendicular to the compressive stress direction.     

Magnetic and optical response of tuning the magnetocrystalline anisotropy in Fe3O4 nanoparticle ferrofluids by Co doping

Co_xFe_3−xO₄ (0?x?0.10) nanoparticles coated with tetramethyl ammonium hydroxide as a surfactant were synthesized by a co-precipitation technique. The Fe:Co ratio was tuned up to x=0.10 by controlling the Co²⁺ concentration during synthesis. The mean particle size, determined by transmission electron microscopy, ranged between 15±4 and 18±4 nm. The superparamagnetic blocking temperature and the magnetocrystalline anisotropy constant of the ferrofluids, determined using ac and dc magnetic measurements, scale approximately linearly with cobalt concentration. We also find distinct differences in the optical response of different samples under an applied magnetic field. We attribute changes in field-induced optical relaxation for the x=0 and 0.05 samples to differences in the anisotropic microstructure under an applied magnetic field.     

晶粒间界相对纳米Nd_2Fe_(14)B各向异性和矫顽力的影响

本文采用立方晶粒结构模型研究了晶粒间界相对纳米硬磁材料各向异性和矫顽力的影响.结果表明:晶粒间界相减弱了交换耦合作用.当晶粒尺寸D为定值时,随着晶粒间界相厚度d的增加,晶粒平均各向异性单调增加,而材料的有效各向异性Keff、矫顽力单调减小.我们计算的矫顽力随晶粒尺寸的变化与相关理论和实验结果基本一致.