The spin wave excitations and the temperature dependence of the magnetization in iron,cobalt, nickel and their alloys

A critical review is given on the literature concerning spin waves in the ferromagnetic transition metals and their alloys. It is shown that spin waves can account for the low temperature behaviour of the magnetization in metallic glasses as well as in nickel(-alloys). A systematic correlation between Curie-temperature and spin wave stiffness is worked out, holding for crystalline and amorphous alloys of iron, cobalt and nickel. The reduced magnetization versus temperature curves of (amorphous) alloys are interpreted without referring to disorder effects.     

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.     

Magnetic skyrmion dynamics in thin cylindrical dots

We calculate high‐frequency spin excitations of the skyrmion ground state cylindrical magnetic dots. The skyrmion is assumed to be stabilized at room temperature due to interplay of the isotropic and Dzyaloshinskii–Moriya exchange interactions, perpendicular magnetic anisotropy and magnetostatic interaction. The Skyrmion ground state is represented as combination of two radially symmetric bubble domains. To consider the Bloch‐ and Néel‐type magnetic skyrmion dynamics we apply an approximation of ultrathin domain wall between the circular domains and assume that the magnetic dot is thin enough (magnetization does not depend on the thickness coordinate). The eigenfunctions/eigenfrequencies of spin wave excitations over the skyrmion background are calculated as a function of the skyrmion radius. The developed approach allows predicting spin wave eigenfrequencies in the skyrmion ground state magnetic dots. Recent experiments on magnetic skyrmion dynamics are discussed. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

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.     

A study of the stripe domain phase at the spin reorientation transition of two-dimensional magnetic system

Stripe domain phase in a two-dimensional magnetic system was studied using model calculation and Monte-Carlo simulation in the spin reorientation transition (SRT) region. We find that near the SRT point the stripe domains evolve into a static spin wave structure with a fractional in-plane magnetization along the stripe direction and a fractional out-of-plane magnetization in a sinusoidal form. With increase in the uniaxial perpendicular anisotropy, both the wavelength and the height of the static spin wave increase slowly until the saturation of the wave height, after which the stripe width increases exponentially with the magnetic anisotropy. Our theoretical result is in good agreement with experimental observations.     

非均匀交换各向异性铁磁介质的非线性表面自旋波

利用Landau-Lifshitz 方程，研究了具有非均匀交换各向异性的半无限大铁磁体的非线性表 面自旋波理论。导出了部分钉扎纯交换铁磁介质的磁化强度所满足的边界条件和非线性表面 自旋波的色散关系，并获得了自旋波振幅沿z方向驻波的一维非线性Schrdinger方程和包 络振幅沿平面传播的二维非线性Schrdinger方程，结果表明铁磁体磁化强度的包络振幅随时空变化的性质是由二维非线性Schrdinger方程决定的。因此预言铁磁介质的表面非线性激发应是二维孤波的形式。对于弱非线性表面自旋波，对非线性Schrdinger方程存在孤子形式解的可能性作了讨论. 关键词： 表面自旋波 Landau-Lifshitz方程 非线性Schrdinger方程 孤子     

Finite-sized Heisenberg chains and magnetism of one-dimensional metal systems

We present a combined experimental and theoretical study of the magnetization of one-dimensional atomic cobalt chains deposited on a platinum surface. We discuss the intrinsic magnetization parameters derived by X-ray magnetic circular dichroism measurements and the observation of ferromagnetic order in one dimension in connection with the presence of strong, dimensionality-dependent anisotropy energy barriers of magnetocrystalline origin. An explicit transfer matrix formalism is developed to treat atomic chains of finite length within the anisotropic Heisenberg model. This model allows us to fit the experimental magnetization curves of cobalt monatomic chains, measured parallel to the easy and hard axes, and provides values of the exchange coupling parameter and the magnetic anisotropy energy consistent with those reported in the literature. The analysis of the spin–spin correlation as a function of temperature provides further insight into the tendency to magnetic order in finite-sized one-dimensional systems. PACS 57.10.Pq; 75.30.-m; 75.30.Gw; 78.70.Dm     

Electron correlations, spontaneous magnetization and momentum density in quantum dots

The magnetization of quantum dots (QDs) is discussed in terms of a relatively simple but exactly solvable model Hamiltonian. The model predicts oscillations in spin polarization as a function of dot radius for a fixed electron density. These oscillations in magnetization are shown to yield distinct signature in the momentum density of the electron gas, suggesting the usefulness of momentum resolved spectroscopies for investigating the magnetization of dot systems. We also present variational quantum Monte Carlo calculations on a square dot containing 12 electrons in order to gain insight into correlation effects on the interactions between like and unlike spins in a QD.     

Spin wave excitations in Fe films grown on GaAs(1 1 3)A substrates

The spin wave excitation and its size effect has been studied in Al-capped Fe films grown on low-symmetry GaAs(1 1 3)A substrates. The temperature dependence of saturation magnetization follows an effective Bloch's law as long as magnetization remains larger than about 70% of its saturation value. A significant increase of the spin wave parameter B is found in Al-capped ultrathin Fe films grown on GaAs(1 1 3)A compared to bulk Fe, Fe films on GaAs(0 0 1) and other systems. This is explained as a result of the reduction in uniaxial magnetic anisotropy observed in this orientation for the same thickness range. However, this observed uniaxial magnetic anisotropy is found to be a likely reason for stabilizing the ferromagnetism.     

Influence of induced anisotropy on the processes of magnetization reversal of cobalt circular nanodots

The magnetic structure and the processes of magnetization reversal of individual cobalt nanodots and arrays of cobalt nanodots have been studied using the magneto-optical Kerr effect and magnetic force microscopy. Arrays of nanodots have been prepared by ion etching from a continuous cobalt film. Magnetic anisotropy is induced during deposition of the cobalt films. The nanodots have the diameter d = 600 nm and the period varying from 1.5d to 3.0d. Magnetic force microscopy images have shown that the induced magnetic anisotropy affects the orientation of magnetization of noninteracting nanodots and the direction of displacement of the magnetic vortex center in the nanodots coupled by the dipole-dipole interaction.     

Field-induced magnetic reorientation and effective anisotropy of a ferromagnetic monolayer within spin wave theory

The reorientation of the magnetization of a ferromagnetic monolayer is calculated with the help of many-body Green's function theory. This allows, in contrast to other spin wave theories, a satisfactory calculation of magnetic properties over the entire temperature range of interest since interactions between spin waves are taken into account. A Heisenberg Hamiltonian plus a second-order uniaxial single-ion anisotropy and an external magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson-Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the spin components (), which are calculated with the help of the spectral theorem. The knowledge of the orientation angle allows a non-perturbative determination of the temperature dependence of the effective second-order anisotropy coefficient. Results for the Green's function theory are compared with those obtained with mean-field theory (MFT). We find significant differences between these approaches. Received 6 April 1999 and Received in final form 9 July 1999     

Anisotropy and dynamic properties of Co2MnGe Heusler thin films

Co₂MnGe films of 30 and 50 nm in thickness were grown by RF-sputtering. Their magnetic anisotropies, dynamic properties and the different excited spin wave modes have been studied using conventional ferromagnetic resonance (FMR) and Microstrip line FMR (MS-FMR). From the in-plane and the out-of-plane resonance field values, the effective magnetization (4πM_eff) and the g-factor are deduced. These values are then used to fit the in-plane angular-dependence of the uniform precession mode and the field-dependence of the resonance frequency of the uniform mode and the first perpendicular standing spin wave to determine the in-plane uniaxial, the four-fold anisotropy fields, the exchange stiffness constant and the magnetization at saturation. The samples exhibit a clear predominant four-fold magnetic anisotropy besides a smaller uniaxial anisotropy. This uniaxial anisotropy is most probably induced by the growth conditions.     

Magnetic excitations in ferromagnetic semiconductors

Magnetic excitations in a series of GaMnAs ferromagnetic semiconductor films were studied by ferromagnetic resonance (FMR). Using the FMR approach, multi-mode spin wave resonance spectra have been observed, whose analysis provides information on magnetic anisotropy (including surface anisotropy), distribution of magnetization precession within the GaMnAs film, dynamic surface spin pinning (derived from surface anisotropy), and the value of exchange stiffness constant D. These studies illustrate a combination of magnetism and semiconductor physics that is unique to magnetic semiconductors.     

Spin kinetic Monte Carlo method for nanoferromagnetism and magnetization dynamics of nanomagnets with large magnetic anisotropy

The Kinetic Monte Carlo (KMC) method based on the transition-state theory, powerful and famous for simulating atomic epitaxial growth of thin films and nanostructures, was used recently to simulate the nanoferromagnetism and magnetization dynamics of nanomagnets with giant magnetic anisotropy. We present a brief introduction to the KMC method and show how to reformulate it for nanoscale spin systems. Large enough magnetic anisotropy, observed experimentally and shown theoretically in terms of first-principle calculation, is not only essential to stabilize spin orientation but also necessary in making the transition-state barriers during spin reversals for spin KMC simulation. We show two applications of the spin KMC method to monatomic spin chains and spin-polarized-current controlled composite nanomagnets with giant magnetic anisotropy. This spin KMC method can be applied to other anisotropic nanomagnets and composite nanomagnets as long as their magnetic anisotropy energies are large enough.      

Current driven magnetization dynamics in helical spin density waves

A mechanism is proposed for manipulating the magnetic state of a helical spin density wave using a current. It is shown that a current through a bulk metal with a helical spin density wave induces a spin transfer torque, which gives rise to a rotation of the order parameter. The use of spin transfer torque to manipulate the magnetization in bulk systems does not suffer from the obstacles seen for magnetization reversal using interface spin transfer torque in multilayered systems. The effect is demonstrated by a quantitative calculation of the current induced magnetization dynamics of a rare earth metal, Er. Finally, we propose a setup for experimental verification.     

束缚施主电子与Si29核超精细作用的各向异性

本文利用Si中浅能级施主的有效质量波函数,计算了束缚施主电子与Si²⁹核超精细作用的等效自旋哈密顿量。超精细作用中不同谷的Bloch函数之间,相干效应非常明显,超精细作用的各向异性主要是由谷间相干效应决定的。在强场近似下求出了Si²⁹核的核磁共振频率的表示式,定量地解释了Feher的实验结果,并且可以由实验定出谷间磁偶极相互作用矩阵元。从正交干面波的观点出发进行了计算,与实验结果比较定出了导带底布洛赫函数中2P心态波函数的组合系数的大小为0.20。指出了利用双共振方法及其压力效应有可能测定导带底的波矢及有效质量波函数的各向异性分布。     

Reflection of spin waves from a ferromagnetic multilayer with interfacial coupling of finite strength (reflection of spin waves from multilayer)

The reflection coefficient of bulk spin waves from a ferromagnetic multilayer with periodically modulated parameters of the exchange interaction, the uniaxial magnetic anisotropy and the saturation magnetization (a magnonic crystal) is calculated. The dependence of the reflection coefficient upon the spin wave frequency and the values of the bias magnetic field, the parameter of interfacial coupling, and the internal structure of the unit cell are investigated.      

Spin-wave theory for the dynamics induced by direct currents in magnetic multilayers

A spin-wave theory is presented for the magnetization dynamics in a ferromagnetic film that is traversed by spin-polarized carriers at high direct-current densities. It is shown that nonlinear effects due to four-magnon interactions arising from dipolar and surface anisotropy energies limit the growth of the driven spin wave and produce shifts in the microwave frequency oscillations. The theory explains quantitatively recent experimental results in nanometric point contacts onto magnetic multilayers showing downward frequency shifts (redshifts) with increasing current, if the external field is on the film plane, and upward shifts (blueshifts), if the field is perpendicular to the film.     

Band structure of collective modes and effective properties of binary magnonic crystals

In this paper a theoretical study of the band structure of collective modes of binary ferromagnetic systems formed by a submicrometric periodic array of cylindrical cobalt nanodots partially or completely embedded into a permalloy ferromagnetic film is performed. The binary ferromagnetic systems studied are two-dimensional periodic, but they can be regarded as three-dimensional, since the magnetization is non uniform also along the z direction due to the contrast between the saturation magnetizations of the two ferromagnetic materials along the thickness. The dynamical matrix method, a finite-difference micromagnetic approach, formulated for studying the dynamics in one-component periodic ferromagnetic systems is generalized to ferromagnetic systems composed by F ferromagnetic materials. It is then applied to investigate the spin dynamics in four periodic binary ferromagnetic systems differing each other for the volume of cobalt dots and for the relative position of cobalt dots within the primitive cell. The dispersion curves of the most representative frequency modes are calculated for each system for an in-plane applied magnetic field perpendicular to the Bloch wave vector. The dependence of the dispersion curves on the cobalt quantity and position is discussed in terms of distribution of effective “surface magnetic charges” at the interface between the two ferromagnetic materials. The metamaterial properties in the propagative regime are also studied (1) by introducing an effective magnetization and effective “surface magnetic charges” (2) by describing the metamaterial wave dispersion of the most representative mode in each system within an effective medium approximation and in the dipole-exchange regime. It is also shown that the interchange between cobalt and permalloy does not necessarily lead to an interchange of the corresponding mode dispersion. Analogously to the case of electromagnetic waves in two-dimensional photonic crystals, the degree of localization of the localized collective modes is expressed in terms of an energy concentration factor.     

微波作用下有直接隧穿量子点系统中的泵流特性

利用演化算符的方法,研究了量子点体系中的电流以及自旋流,该体系中量子点和左右磁性电极耦合并且受到微波作用,且两电极之间有直接隧穿,得到了体系电流的解析表达式.发现对于无直接隧穿和零偏压情况,无论对称结构还是非对称结构,电流和自旋流总为零.对于直接隧穿和零偏压情况,对于两边为非对称结构,微波场辐射在量子点上可以导致自旋流而非零的总电流,给出了平行和反平行磁构型下的结果并进行了讨论;对于两边为对称结构结构,平行磁构型下,量子点上加微波场时自旋流和总电流均为零;在反平行磁构型下,量子点上加微波场可以导致自旋流而 关键词： 微波场 直接隧穿 量子点 泵流