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.     

On features of magnetization self-organization in 1D stochastic ferromagnetic systems

The magnetic structure of a polycrystalline nanowire at the weak or missing magnetostatic interaction exhibits the special self-organization of magnetization. As is known, the magnetization structure forming in a random crystallographic anisotropy field has a characteristic length range, which involves tens and hundreds of crystallites. This leads to the occurrence of stochastic domains. The induced uniform anisotropy of magnetostatic nature or the texture co-directed with the crystallite anisotropy axes masks the picture of stochastic domains. Nevertheless, as we show, the information on stochastic domains remains in the magnetization structure. The experimental techniques for obtaining information on the magnetic properties of stochastic domains are proposed.     

Analytical model for shape anisotropy in thin-film nanostructured arrays: Interaction effects

When reducing the size of array elements and interelement separations to the nanoscale, long-range magnetostatic interactions become important. A methodology that extends the study of conventional single-element magnetostatics is presented, adding the effect of stacking nanoelements into close proximity in arrays and the consequent interaction effects. This would be very time consuming to model by micromagnetic simulations that are also very vulnerable to artifacts due to cell or boundary condition selection. The proposed method considers an analytical expression valid for short interelement separations and not very costly to evaluate by computational means. This approach allows the quantitative study of shape anisotropy in non-square-shaped arrays. It is also shown how it can be used to find anisotropy compensation conditions, where an anisotropy due to a magnetic element shape can be compensated by the shape anisotropy due to the array. The obtained results can be used to establish a criterion for the minimum number of elements to be considered for a micromagnetic simulation of an array to be realistic depending on the element size and separation.     

纯三元及含Zr,Ga元素磁粉的各向异性

未经均匀化热处理的纯三元及含Zr,Ga元素的SC合金铸片经优化的HDDR工艺处理都可以制备各向异性Nd Fe B磁粉.这表明:元素的添加及SC铸片是否进行了均匀化热处理都不是HDDR磁粉各向异性形成的必要条件.磁粉各向异性形成的关键因素在于HDDR工艺的调节,即适当地加快歧化反应过程,减缓脱氢再结合过程以及控制脱氢再结合时的合适氢气压强均有利于磁粉各向异性的形成.本文将为制备低成本高各向异性磁粉提供重要的指导.     

纯三元及含Zr, Ga元素磁粉的各向异性

未经均匀化热处理的纯三元及含Zr, Ga元素的SC合金铸片经优化的HDDR工艺处理都可以制备各向异性NdFeB磁粉。这表明：元素的添加及SC铸片是否进行了均匀化热处理都不是HDDR磁粉各向异性形成的必要条件。磁粉各向异性形成的关键因素在于HDDR工艺的调节,即适当地加快歧化反应过程,减缓脱氢再结合过程以及控制脱氢再结合时的合适氢气压强均有利于磁粉各向异性的形成。本文将为制备低成本高各向异性磁粉提供重要的指导。     

Phase diagram of a two-dimensional square lattice of magnetic particles with perpendicular anisotropy

The ground state of an array of small single-domain magnetic particles having perpendicular anisotropy and forming a square two-dimensional lattice is studied in the presence of a magnetic field. The stability of some basic states with respect to nonuniform perturbations is analyzed in a linear approximation, and analytical model calculations and numerical simulation are used for an analysis. The entire set of states at various anisotropy constants and magnetic fields is considered when a field is normal to the array plane. Two main classes of states are possible for an infinite system, namely, collinear and noncollinear states. For collinear states, the magnetic moments of all particles are normal to the array plane. At a sufficiently high anisotropy, a wide class of collinear states exists. At low fields, a staggered antiferromagnetic order of magnetic moments takes place. An increase in the magnetic field causes an unsaturated state, and this state transforms into a saturated (ferromagnetic) state with a parallel orientation of the magnetic moments of all particles at a sufficiently high field. At a lower anisotropy, the ground state of the system is represented by noncollinear states, which include a complex four-sublattice structure for the components of the magnetic moments in the array plane and a nonzero projection of the magnetic moments of the particles onto the field direction. A phase diagram is plotted for the states of an array of anisotropic magnetic particles in the anisotropy constant-magnetic field coordinates. For a finite array of particles, sample boundaries are shown to play a significant role, which is particularly important for noncollinear states. As a result of the effect of the boundaries at a moderate field or anisotropy, substantially heterogeneous noncollinear states with a heterogeneity size comparable with the sample size can appear in the system.     

Magnetic anisotropies of late transition metal atomic clusters

We analyze the impact of the magnetic anisotropy on the geometric structure and magnetic ordering of small atomic clusters of palladium, iridium, platinum, and gold. We have employed a noncollinear implementation of density functional theory where the spin-orbit interaction has been included self-consistently. The size of the clusters ranges from two to five, six, or seven atoms, depending on the element. Our results highlight the relevance of the spin-orbit interaction in the magnetic properties of small atomic clusters made of fourth- and fifth-row elements.     

Simple theory of superparamagnetism and spin-tunneling in Mössbauer spectroscopy

The magnetic relaxation of isolated small (< 100 Å) monodomain magnetic particles is due to superparamagnetic relaxation (predominant at high temperatures) and eventually quantum tunneling of the magnetic moment (at low temperatures). The superparamagnetic relaxation process can be formally described by an (multiple phonon absorption and emission) Orbach process with an anisotropy Hamiltonian due to crystalline or form anisotropy \widehat_Ion = S² _z and a usual dynamical spin-Hamiltonian for the spin--phonon interaction. From this Mössbauer spectra can be calculated using ab-initio or stochastic methods. Phonon-assisted tunneling and its influence on Mössbauer spectra are discussed.     

Correlation properties of the stochastic magnetic structure of ultradispersed ferromagnetic materials

The properties of the stochastic magnetic structure of ultradispersed ferromagnetic materials are studied. The correlation coefficients of the magnetization of a magnetic material are calculated for various types of chaos in the anisotropy field. The effects of different types of disorder on the parameters of a stochastic magnetic structure are compared. Numerical simulations by various methods confirm the theoretical results. Fiz. Tverd. Tela (St. Petersburg) 41, 1432–1436 (August 1999)     

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     

The study of the shape anisotropy in patterned permalloy films

In this paper a systematic ferromagnetic resonance study shows that an in-plane magnetic anisotropy in the patterned micron octagon permalloy (Ni透磁合金;定型薄膜;形状各向异性;铁磁共振patterned film, shape anisotropy, ferromagnetic resonanceProject supported by the National Natural Science Foundation of China (Grant No~50171020) and the Foundation for youth of Liaocheng University (Grant No~X051050).1/5/2007 12:00:00 AMIn this paper a systematic ferromagnetic resonance study shows that an in-plane magnetic anisotropy in the patterned micron octagon permalloy （Ni80Fe20） elements is mainly determined by the element geometry. The easy-axis is along the edge of the elements, and the hard-axis is along the diagonal. The shape anisotropy of the octagon elements is determined by square and equilateral octagon, and the theoretical calculation was studied on the shape anisotropy. The shape anisotropy of rectangular was calculated by using the same theory.     

Stochastic resonance in single-domain nanoparticles with cubic anisotropy

The signal-to-noise ratio for magnetic stochastic resonance in a superparamagnetic particle with cubic anisotropy is shown to be strongly dependent on the Larmor precession damping α. This phenomenon is due to the coupling of the relaxation and precession modes and can be used for measuring α. The dependence of the signal-to-noise ratio on α is characteristic of particles with nonaxial anisotropy; so the effect is absent in uniaxial particles.     

Effective anisotropy and coercivity in nanocrystalline single-phase NdFeB permanent magnetic material

The effect of exchange-coupling interaction on the effective anisotropy and its varying tendency in nanocrystalline single-phase NdFeB permanent magnetic material have been investigated. The results show that the exchange-coupling interaction between grains makes the effective anisotropy of material, Keff, decrease with the reduction of grain size. The variation of Keff is basically the same as that of coercivity. The decrease in effective anisotropy is the main reason of the reduction of coercivity for nanocrystalline single-phase NdFeB permanent magnetic material. In order to get high anisotropy and coercivity in nanocrystalline single-phase NdFeB permanent material, the grain size should be larger than 35 nm.     

Stochastic resonance in low-disperse magnets: Mechanism of subbarrier magnetization reversal

The phenomenon of stochastic resonance is studied theoretically in a system of single-domain particles with an “easy-axis”-type magnetic anisotropy at temperatures close to absolute zero, for which the tunneling of the magnetic moment vector between stable states dominates. Calculations are made on the basis of the master equation in the model of discrete orientations in the quasi-adiabatic approximation. The dynamic magnetic susceptibility components of the system under the action of a weak rf field are calculated. The critical temperature at which a transition from the above-the-barrier mechanism of magnetization reversal to the subbarrier mechanism occurs is estimated.     

Synthesis and magnetic properties of size-selected CoPt nanoparticles

CoPt nanoparticles are widely studied, in particular for their potentially very high magnetic anisotropy. However, their magnetic properties can differ from the bulk ones and they are expected to vary with the particle size. In this paper, we report the synthesis and characterization of well-defined CoPt nanoparticle samples produced in ultrahigh vacuum conditions following a physical route: the mass-selected low energy cluster beam deposition technique. This approach relies on an electrostatic deviation of ionized clusters which allows us to easily adjust the particle size, independently from the deposited equivalent thickness (i.e. the surface or volume particle density in a sample). Diluted samples made of CoPt particles, with different diameters, embedded in amorphous carbon are studied by transmission electron microscopy and superconducting interference device magnetometry, which gives access to the magnetic anisotropy energy distribution. We then compare the magnetic properties of two different particle sizes. The results are found to be consistent with an anisotropy constant (including its distribution) which does not evolve with the particle size in the range considered.     

Magnetic hyperfine splitting in mössbauer spectra of microcrystals

Below the superparamagnetic blocking temperature of a microcrystal the magnetization direction is in general not fixed, but fluctuates in directions close to an easy direction of magnetization. Such fluctuations (collective magnetic excitations) result in a reduction in the magnetic splitting of the Mössbauer spectrum. A low-temperature approximation for this reduction is derived for microcrystals with arbitrary magnetic energy. Moreover, explicit expressions are presented for particles with special types of magnetic anisotropy and for particles exposed to external magnetic fields. The reduction in the magnetic hyperfine field has its maximum value just below the blocking temperature but does not exceed 5–15% in isolated particles with uniaxial anisotropy in zero applied magnetic field. However, ferro- and ferrimagnetic particles, exposed to external magnetic fields, and particles for which exchange anisotropy is predominant, may exhibit any magnetic hyperfine splitting between zero and the saturation value. It is shown that in special cases an assembly of microcrystals in close contact with each other may behave like a spin-glass. We discuss how studies of the magnetic hyperfine splitting ofMössbauer spectra of microcrystals give information of the particle size and the prevailing magnetic anisotropies.     

Effect of an arbitrarily directed permanent magnetic field on the dynamic susceptibility of a superparamagnetic particle under the conditions of stochastic resonance

Theoretically, based on the approximation of discrete orientations, the effect of thermal stochastic resonance is considered for a superparamagnetic particle with magnetic anisotropy of the “easy axis” type in view of an additional external permanent magnetic field applied at an arbitrary angle relative to the easy magnetization axis. The dynamic susceptibility has been calculated for a single-domain iron particle under the conditions of its modulation by a weak external radio-frequency field at various absolute values and directions of the additional permanent magnetic field vector. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 67–71, March, 2006.     

Exchange anisotropy in Co/NiO bilayers: time-dependent effects

The time dependence of the exchange anisotropy was studied in Co/NiO bilayers. In order to only observe the relaxation phenomena inside the antiferromagnetic (AF) layer and to eliminate the dynamic behaviour inside the ferromagnetic (F) layer, we have developed an experimental method where a small a.c. magnetic field is applied perpendicular to the main anisotropy axis. All data are obtained by magneto-optical (m.o.) experiments. We observe a logarithmic time dependence of Hud, the exchange unidirectional anisotropy. We prove that the key parameter for the rate of relaxation is the anisotropy of the AF layer which depends strongly of the preparation method. We use the random field model as proposed by Malozemoff and suppose a breakdown of the AF interface into regular domains of size close to the crystallite size (10 nm width). If we further develop a Fulcomer and Charap relaxation model, we can propose from the distribution of relaxation times an analysis in terms of a spread of AF anisotropy energies. High magnetic pulsed field experiments (55 T) complete the experimental study and the results are analysed assuming that the Zeeman energy balances the anisotropy energy of the AF domains and switches them into the opposite direction.     

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.     

Dependence of the Dynamic Susceptibility of Superparamagnetic Particles on the Strength of a Constant Magnetic Field Perpendicular to the Direction of Particle Easy Magnetization

The dynamic magnetic susceptibility of single-domain iron particles with magnetic anisotropy in the form of the direction of easy magnetization is calculated under conditions of stochastic resonance with allowance for a constant magnetic field perpendicular to the direction of particle easy magnetization. Calculations are carried out in the approximation of discrete orientations based on the guiding equation for the Kramers above-the-barrier transition rates of the particle magnetic moment vector. It is demonstrated that changing the constant field strength, the internal noise level in the system can be controlled, for example, to obtain a maximum response to an external radio-frequency perturbation. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 64–68, May, 2005.