Micromagnetism in a planar system with a random magnetic anisotropy and two-dimensional magnetic correlations

The hysteresis loops and the micromagnetic structure of a ferromagnetic nanolayer with a randomly oriented local easy magnetization axis and two-dimensional magnetization correlations are studied using a micromagnetic simulation. The properties and the micromagnetic structure of the nanolayer are determined by the competition between the anisotropy and exchange energies and by the dipole–dipole interaction energy. The magnetic microstructure can be described as an ensemble of stochastic magnetic domains and topological magnetization defects. Dipole–dipole interaction suppresses the formation of topological magnetization defects. The topological defects in the magnetic microstructure can cause a sharper change in the coercive force with the crystallite size than that predicted by the random magnetic anisotropy model.     

Collective oscillations of the magnetic moments of a chain of spherical magnetic nanoparticles with uniaxial magnetic anisotropy

Magnetic particles moving freely in a fluid can organize dense phases (3D clusters or linear chains). We analyze the spectrum of magnetic oscillations of a chain of spherical magnetic particles taking into account the magnetic anisotropy of an individual particle for an arbitrary relation between the anisotropy energy and the energy of the dipole interaction of particles. For any relation between these energies, the spectrum contains three branches of collective oscillations: a high-frequency branch and a weakly split doublet of low-frequency branches. The frequency of the high-frequency branch is determined by a stronger interaction, while the frequencies of the low-frequency branches are determined by the weakest interaction. Accordingly, the dispersion is maximal for oscillations formed by the dipole-dipole interaction of particles, which have high frequencies in the case of a strong dipole interaction or low frequencies in the case of a strong anisotropy.     

The anisotropy of the dipole fields at interstitial sites in ferromagnetic bcc and hcp crystals

The anisotropy of the local magnetic dipole field is calculated for interstitial lattice sites of tetragonal, trigonal, or orthorhombic symmetry in bcc and hep crystals. In addition, for interstitial sites of uniaxial symmetry the effects of lattice deformations on the magnetic dipole field are investigated. A discussion of experimental results obtained from muon spin rotation experiments on Co and Gd shows that in these metals lattice-deformation effect may influence the local dipole fields significantly.     

Nonlinear dynamic structure rearrangement of vortexlike domain walls in magnetic films with in-plane anisotropy

The nonlinear dynamic behavior of vortexlike domain walls in magnetic uniaxial films having an in-plane anisotropy was investigated within a rigorous micromagnetic approach in the framework of a two-dimensional magnetization distribution by numerically solving the Landau–Lifshitz equations (with the Gilbert damping parameter) with allowance for all the main interactions, including the dipole–dipole one. The studies were carried out on magnetic soft films with an anisotropy axis lying in their plane in a dc magnetic field parallel to an easy axis and a pulsed magnetic field normal to it. New possibilities for controlling the nonlinear dynamic rearrangement of the internal structure of domain walls and their velocities in fields both above and below the critical field are established. The wall motion in the field above the critical one is nonstationary.     

Element-specific magnetocrystalline anisotropy energy studied by transverse magnetic circular X-ray dichroism

The magnetocrystalline anisotropy energy in 3d transition metal systems is related to the spin-subband orbital moments and the magnetic dipole operator which accounts for the spin-flip excitations. Magnetic circular X-ray dichroism measurements in a transverse geometry, where the light helicity is perpendicular to the magnetization direction, make it feasible to determine the easy-axis of magnetization.     

Effect of anisotropy and dipole interaction on long-range order magnetic structures generated by Dzyaloshinskii–Moriya interaction

Self-organized long-range order structures, such as stripe domains and magnetic skyrmion lattices, are formed by the competition between ferromagnetic exchange interaction and Dzyaloshinskii–Moriya (DM) interaction. We investigated the properties of the magnetic structures generated by a DM interaction under the influence of anisotropy or magnetic dipole interaction, by performing Monte-Carlo simulated annealing. We constructed phase maps in external-field and anisotropy space to study the effect of anisotropy or dipole interaction on the phase boundaries between the magnetic structures. The simulation results show that the phase boundaries are sensitive to perpendicular anisotropy and that the skyrmion lattice region in phase space is extended under easy-plane anisotropy. The effect of the long-range dipole interaction was studied and was found to stabilize the skyrmion lattice phase and reduce the size of the magnetic structures.     

Some remarks on the diamagnetic anisotropy of C-C and C-H bonds in saturated hydrocarbons

Data on the diagmagnetic anisotropies of C-C and C-H bonds obtained by measurements of chemical shifts, crystal diamagnetic susceptibilities, and Cotton-Mouton constants are discussed. It is suggested that for both C-C and C-H bonds the absolute value of the transverse susceptibility is greater than the absolute value of the longitudinal susceptibility. A relation for the anisotropy of a straight chain paraffin in terms of the bond anisotropies is derived. It is concluded that the crystal susceptibilities and Cotton-Mouton constants can be explained if the C-H bond anisotropy is greater than about one-half of the C-C bond anisotropy. It is suggested that values for the bond anisotropies obtained from proton chemical shifts are too high, owing to other contributions to the proton shielding, and to the breakdown of the classical magnetic dipole equation. Values for the C-C and C-H bond anisotropies consistent with the available data are given.     

Dipole magnetic anisotropy fields in rhombohedral antiferromagnetic materials

Results of calculations of the contribution of magnetic dipole interactions to the effective uniaxial anisotropy fields of antiferro- and ferromagnetism vectors in rhombohedral antiferromagnetic materials with theS ions are given as functions of the ratio of the hexagonal crystal cell parameters c_H/a_H. There is a strong dependence of the calculated curves on the lattice parameters of real compounds. From the dependences obtained the effective anisotropy fields are calculated for FeF₃, FeBO₃, and MnCO₃. L. V. Kirenskii Institute of Physics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 82–86, May, 1999.     

Magnetic anisotropy of ferromagnetic metals in low-symmetry systems

We have constructed an analytic formula to treat the perpendicular magnetic anisotropy energy in ferromagnetic metals with low symmetry, such as $C_{4\mathrm{V}}$ and $C_{3\mathrm{V}}$. We find that the anisotropy energy is proportional to a part of the expectation values of the orbital angular momentum and magnetic dipole operator. Although the result is similar to the model proposed by Laan (1998) [2], we have derived a concrete expression for the spin-flip virtual excitation process term, which can be dominant in atoms with small magnetic moments and/or small exchange splitting. Pt monatomic layer with proximity-induced spin polarization grown on Fe is an example of this. Other multilayer systems such as Co/Pd and Co/Ni, and bilayer systems such as Fe(CoB)/MgO can be discussed similarly. Moreover, the relation between perpendicular magnetic anisotropy energy and measurable physical parameters is discussed based on X-ray magnetic circular dichroism spectroscopy.     

Magnetic domain confinement by anisotropy modulation

The spin configuration in a magnet is in general a "natural" consequence of both the intrinsic properties of the material and the sample dimensions. We demonstrate that this limitation can be overcome in a homogeneous ferromagnetic film by engineering an anisotropy contrast. Substrates with laterally modulated single-crystal and polycrystalline surface regions were used to induce selective epitaxial growth of a ferromagnetic Ni film. The resulting spatially varying magnetic anisotropy leads to regular perpendicular and in-plane magnetic domains, separated by a new type of magnetic wall---the "anisotropy constrained" magnetic wall.     

Reflectance anisotropy spectroscopy of metal nanoclusters formed on semiconductor surface

Optical anisotropy of indium nanoclusters formed on the (001) surface of indium arsenide was found by differential reflectance anisotropy spectroscopy. The fact of such an observation for nanocluster arrays unambiguously evidences the presence of their macroscopic anisotropy which could not be disclosed by conventional diagnostics techniques. The scale of the observed plasmonic anisotropy signal exceeds by two orders of magnitude the scale of anisotropy signals from valence-bond structures formed on a semiconductor surface. A resonant feature observed in reflectance anisotropy spectra is interpreted in the model of coupled dipole plasmons belonging to ellipsoidal nanoparticles. Estimation based on the experimental spectra shows that within the sample surface the lengths of ellipsoid semiaxes differ from each other by a few percent.     

铁磁共振法测磁各向异性

采用铁磁共振方法,研究了铁磁/反铁磁双层膜系统中,因交换耦合以及磁晶各向异性而产生的有效各向异性场.结果表明:被测系统有无交换偏置场以及其正负号性质等均能在共振谱中得到辨析.结果还显示:沿着不同结晶方向施加外磁场,共振场的行为与磁晶各向异性以及铁磁/反铁磁交换耦合作用而诱发的单向各向异性等密切相关.将共振频率的变化看成外磁场(包括其方向和大小)的函数,研究得到了单向各向异性,立方各向异性等对共振频率的影响,并同实验结果做了很好的比较. 关键词： 铁磁/反铁磁双层膜 交换耦合 铁磁共振 单向各向异性     

Correlation between elastic anisotropy and magnetic susceptibility anisotropy of sedimentary and metamorphic rock

A correlation has been revealed between the types of acoustic anisotropy and magnetic susceptibility anisotropy for specimens from noncrystalline metamorphic and sedimentary rock has been revealed. This correlation makes it possible to assume that the anisotropy of magnetic and acoustic characteristics has the same origin, namely, the rock texture. The pronounced triaxial acoustic anisotropy for specimens of polycrystalline rock in the absence of external forces makes it possible to judge the fracturing caused by tectonic loads and the degree of this fracturing. The large body of available experimental data allows the expectation that it will be possible to obtain empirical dependences suitable for estimating the intensity of geological processes based on the values of the magnetic susceptibility anisotropy and elasticity tensor anisotropy.     

Constraining the anisotropy of the Universe with the Pantheon supernovae sample

We test the possible dipole anisotropy of the Finslerian cosmological model and the other three dipole-modulated cosmological models, i.e. the dipole-modulated ΛCDM, wCDM and Chevallier–Polarski–Linder (CPL) models, by using the recently released Pantheon sample of SNe Ia. The Markov chain Monte Carlo (MCMC) method is used to explore the whole parameter space. We find that the dipole anisotropy is very weak in all cosmological models used. Although the dipole amplitudes of four cosmological models are consistent with zero within the \begin{document}$1\sigma$\end{document} uncertainty, the dipole directions are close to the axial direction of the plane of the SDSS subsample in Pantheon. This may imply that the weak dipole anisotropy in the Pantheon sample originates from the inhomogeneous distribution of the SDSS subsample. A more homogeneous distribution of SNe Ia is necessary to constrain the cosmic anisotropy.     

Polarization anisotropy of exciton in self-assembled elliptical InP/InGaP quantum dots

Optical anisotropy of self-assembled elliptical InP quantum dots has been investigated in terms of the polarization dependence of excitons. Although large size inhomogeneity is present, two kinds of characteristic quantum dots, which are classified into large and small quantum dots, were found in terms of the polarization anisotropy. We have confirmed that the large quantum dots are more pronounced in the polarization anisotropy, where the degree of linear polarization for the large quantum dots is significantly larger (∼60%) than that for the small ones (∼36%). The effective shape of quantum dots is also estimated by using the size dependence of oscillator strength, which is in agreement with the AFM image. We also suggest that the anisotropy of exciton oscillator strength can be modified via the dipole–dipole interaction between nearest exciton dipoles.     

具有条纹磁畴结构的NiFe薄膜的制备与磁各向异性研究

具有条纹磁畴结构的磁性薄膜表现出面内转动磁各向异性,对于解决高频电子器件的方向性问题起着至关重要的作用.本文采用射频磁控溅射的方法,研究了NiFe薄膜的厚度、溅射功率密度、溅射气压等制备工艺参数对条纹磁畴结构、面内静态磁各向异性、面内转动磁各向异性、垂直磁各向异性的影响规律.研究发现,在功率密度15.6 W/cm~2与溅射气压2 mTorr(1 Torr=1.33322×102Pa)下生长的NiFe薄膜,表现出条纹磁畴的临界厚度在250 nm到300 nm之间.厚度为300 nm的薄膜比250 nm薄膜的垂直磁各向异性场增大近一倍,从而磁矩偏离膜面形成条纹磁畴结构,并表现出面内转动磁各向异性.高溅射功率密度可以降低薄膜出现条纹磁畴的临界厚度.在相同功率密度15.6 W/cm~2下生长300 nm的NiFe薄膜,随着溅射气压由2 mTorr增大到9 mTorr,NiFe薄膜的垂直磁各向异性场逐渐由1247.8 Oe(1 Oe=79.5775 A/m)增大到3248.0 Oe,面内转动磁各向异性场由72.5 Oe增大到141.9 Oe,条纹磁畴周期从0.53μm单调减小到0.24μm.NiFe薄膜的断面结构表明柱状晶的形成是表现出条纹磁畴结构的本质原因,高功率密度下低溅射气压有利于柱状晶结构的形成,表现出规整的条纹磁畴结构,高溅射气压会导致柱状晶纤细化,面内转动磁各向异性与面外垂直磁各向异性增强,条纹磁畴结构变得混乱.     

Magnetic field anisotropy based MR tractography

Non-invasive measurements of structural orientation provide unique information regarding the connectivity and functionality of fiber materials. In the present study, we use a capillary model to demonstrate that the direction of fiber structure can be obtained from susceptibility-induced magnetic field anisotropy. The interference pattern between internal and external magnetic field gradients carries the signature of the underlying anisotropic structure and can be measured by MRI-based water diffusion measurements. Through both numerical simulation and experiments, we found that this technique can determine the capillary orientation within 3°. Therefore, susceptibility-induced magnetic field anisotropy may be useful for an alternative tractography method when diffusion anisotropy is small at higher magnetic field strength without the need to rotate the subject inside the scanner.     

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     

Dipole solitons in nonlocal nonlinear media with anisotropy

We investigate the existence and stability of dipole-mode solitons in two-dimensional models of nonlocal media with anisotropic Kerr nonlinearity analytically and numerically. We obtain the approximate solution of such elliptic dipole solitons by using the variational approximation. The dynamics of such dipole-mode solitons is governed by the eccentricity of both the input beam and the nonlocal response function. We also compute the stability of the solitons by direct numerical simulations. The effects of the anisotropy of the nonlocal response function on the propagation of the dipole beam are also discussed in detail.