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.     

Variation in the magnetic structure of a single-domain particle ensemble and its response to an rf pulse

A set of equations in the Gilbert form that describes the motion of the magnetization vector in an ensemble of interacting magnetic nanoparticles is numerically solved for the case of high-amplitude rf pulses. Based on the numerical solution, the magnetic structure of spherical particle ensembles showing cubic anisotropy at certain parameters of the variable field is studied. This phenomenon is shown to have a threshold. The dependence of the field threshold amplitude on the acting pulse repetition rate and amount of magnetic interaction is determined. It is demonstrated that a change in the magnetic structure of the interacting particle ensembles causes a change in the spectrum of the response. This fact can be used for pulsed rf writing and readout of information based on ferromagnetic resonance.     

Non-Langevin high-temperature magnetization of nanoparticles in a weak magnetic field

Experimental evidence and theoretical substantiation are presented for the asymptotic behavior of high-temperature magnetization of an ensemble of nanoparticles in a weak magnetic field, which was predicted earlier and which differs qualitatively from the “Langevin” limit for ideal superparamagnetic particles. It is shown that the physical reason for the new asymptotic behavior is the temperature-independent “positive” tilt of the uniform magnetization vector at local energy minima in the direction of the field; this asymptotic behavior is associated with the nonstandard thermodynamics of single-domain particles, which depends on the ratio of characteristic frequencies of regular precession and random diffusion of this vector. An alternative approach is proposed for describing the magnetic dynamics of an ensemble of nanoparticles in a magnetic field, and the precession orbits of the magnetization vector are considered as stochastic states of each particle, whereas each state is characterized by the trajectory-averaged value of magnetization.     

Effect of the surface anisotropy and the shape on the magnetization behavior in an egg-shaped nanoparticle

Using the classical Heisenberg model and Monte Carlo simulation, we compute the magnetization behavior of a ferromagnetic nanoparticle with an egg-shape in an external magnetic field along the symmetry axis. The particle is in a single-domain state with a surface anisotropy axis perpendicular to the surface of the particle. At low temperature, it is found that exchange bias appears in the hysteresis loop, which does not exist in the spherical and ellipsoidal nanoparticles. The bias field produced by the frozen spins on the surface of the egg-shaped nanoparticle may be the reason to produce the phenomenon of the exchange bias.     

Switching magnetization of a nanoscale ferromagnetic particle using nonlocal spin injection

We have performed nonlocal spin injection into a nanoscale ferromagnetic particle configured in a lateral spin-valve structure to switch its magnetization only by spin current. The nonlocal spin injection aligns the magnetization of the particle parallel to the magnetization of the spin injector. The spin current responsible for switching is estimated from the experiment to be about 200 microA, which is reasonable compared with the values obtained for conventional pillar structures. Interestingly, the switching always occurs from antiparallel to parallel in the particle-injector magnetic configurations, where no opposite switching is observed. Possible reasons for this discrepancy are discussed.     

Magnetization reversal processes in layered high-temperature superconductors with ferromagnetic impurities

The self-consistent interaction of a vortex system of a high-temperature superconductor and ferromagnetic impurities, including single impurities and their clusters, has been considered in the model of a layered high-temperature superconductor. For different temperatures and concentrations of ferromagnetic impurities, the magnetization reversal loops have been calculated by the Monte Carlo method taking into account an ensemble of ferromagnetic particles with different orientations of their easy magnetization axes with respect to the direction of an external magnetic field and for different magnetic anisotropy energies. It has been demonstrated that there is a nonlinear interaction of the high-temperature superconductor with ferromagnetic impurities, in which the initially thermodynamically reversible character of the magnetization reversal of the ferromagnetic ensemble can become irreversible. For a periodic lattice of clusters of ferromagnetic impurities, the magnetization curves of the high-temperature superconductor have been calculated for different sizes and configurations of the clusters. It has been revealed that, when extended defects are oriented parallel to the direction of the entrance of vortices in the sample, the length of the defects does not affect the remanent magnetization. It has been shown that the inclusion of the interaction between the magnetic moments inside the impurity cluster leads to a decrease in the magnetization reversal loop, the coercivity, and, accordingly, the energy loss due to magnetization reversal.     

High-temperature magnetization of nanoparticles in “static” and gamma-resonance measurements in a weak magnetic field

An alternative approach to describing the magnetic dynamics of an ensemble of nanoparticles in a magnetic field is proposed, in which the precession orbits of uniform magnetization are regarded as the stochastic states of each particle. Using this approach, one can describe the nonconventional features of the high-temperature magnetization of nanoparticles that are observed in low-frequency magnetization measurements and Mössbauer spectroscopy.     

Specific features in precession dynamics of magnetization of a uniaxial magnetic film

The precession dynamics of the magnetization of a film with in-plane uniaxial anisotropy in the case of its biasing along the hard magnetization axis has been analyzed by numerically solving the Landau-Lifshitz equations. It has been revealed that the ferromagnetic resonance spectrum near the magnetic anisotropy field exhibits an additional peak, which is associated with the angular bistability due to the presence of two symmetric angular equilibrium positions. The trajectories of precession motion during biasing along the hard magnetization axis differ substantially from the trajectories corresponding to the biasing along the easy axis.     

Ferromagnetic resonance features in anisotropic magnetic films with a metastable state of magnetic moment

In experiments on single-domain magnetic films with uniaxial in-plane anisotropy, a new homogeneous ferromagnetic resonance peak was observed in a planar magnetic field oriented at an angle to the easy magnetization axis and directed opposite to the magnetization projection onto the field direction. The peak was observed in fields smaller than the magnetization reversal field of the film, and the origin of the peak was found to be related to the metastable state of the magnetic moment. A good agreement was obtained between phenomenological calculations and experimental data.     

Chirality of a forming spin spring and remagnetization features of a bilayer ferromagnetic system

Distribution of a magnetic moment in an exchange-coupled bilayer Fe/SmCo epitaxial structure grown on a (110) MgO substrate is visualized by the magnetooptic indicator film technique. The direction and the magnitude of the effective magnetization in this structure are determined both under external magnetic fields of variable magnitude and direction and after the removal of these fields. It is shown that such a heterostructure is remagnetized by a nonuniform rotation of a magnetic moment both along the thickness of a sample and in its plane. A field antiparallel to the axis of unidirectional anisotropy gives rise to spin springs with opposite chiralities in different regions of the magnetically soft ferromagnetic layer. The contributions of these springs to the net magnetization cancel out, thus decreasing the averaged magnetic moment and the remanent magnetization without their rotation. When the external field deviates from the easy axis, the balance is violated and the sample exhibits a quasi-uniform rotation of the magnetic moment. Asymmetry in the rotation of the magnetic moment is observed under the reversal of the field as well as under repeated remagnetization cycles. It is established that a monochiral spin spring is also formed in a rotating in-plane magnetic field when the magnitude of the field exceeds the critical value. Possible mechanisms of remagnetization in this system are discussed with regard to the original disordered orientation of magnetization of the magnetically soft layer with respect to the easy axis, which is defined by the variance of unidirectional anisotropy axes of this layer on the interface.     

The magnetic field and force in a perpendicularly magnetized matrix consisting of parallel ordered ferromagnetic wires

A formula for the magnetic field arising in a periodically ordered array of ferromagnetic wires, whose magnetization is saturated in a perpendicularly applied field, is derived. Thereby it is assumed that the stray fields do not affect the magnetization of the wires. It is shown that for an arbitrary infinite lattice of wires the exact solution of the magnetostatic equations is given by the Weierstrass $\text{p}$-function and how this function can be used to approximate the field in a finite array of wires. In view of applications to HGMS an expression for the magnetic force acting on a small weakly magnetic particle in a ferromagnetic matrix is derived, which is well-suited for numerical calculations.     

Bifurcation magnetic resonance in films magnetized along hard magnetization axis

We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range.     

Electrical manipulation of nanomagnets

We demonstrate that it is possible to manipulate the magnetic coupling between two nanomagnets by means of an ac electric field. In the scheme suggested, the magnetic coupling is mediated by a magnetic particle that is in contact with both nanomagnets via tunnel barriers. The time-dependent electric field is applied so that the height of first one barrier then the other is suppressed in an alternating fashion. We show that the result is a pumping of magnetization from one nanomagnet to the other through the mediating particle. The dynamics of the magnetization of the mediating particle allows the coupling to be switched between being ferromagnetic and being antiferromagnetic.     

Influence of a metallic substrate’s magnetic state on the huge magnetoresistance of a ferromagnet-polymer structure

The association between the threshold value of conductance switching in an external magnetic field and the initial magnetic state of a ferromagnetic plate substrate is shown for a ferromagnet/polymer/nonmagnetic metal system. The threshold magnetic field change is explained by appearance of residual magnetization after being held in an external magnetic field and, correspondingly, by the change in the initial state upon further remagnetization.     

Singularity in high-frequency susceptibility of thin magnetic films with uniaxial anisotropy

A sharp peak of magnetic susceptibility has been observed in the ferromagnetic resonance spectra of uniaxial magnetic films placed in a planar field directed orthogonal to the easy magnetization axis, along which a pumping high-frequency magnetic field has been oriented. The peak width is considerably narrower than the line width of the uniform ferromagnetic resonance, and its position in a field equal to the film anisotropy field does not depend on the pumping frequency. The nature of the peak is associated with a drastic increase in the static transverse susceptibility of the film in the vicinity of the anisotropy field. It is shown phenomenologically that the peak can be observed only for quality samples with small angular and amplitude dispersion of the uniaxial anisotropy.     

Asymmetrically shaped hysteresis loop in exchange-biased FeNi/FeMn film

The magnetization reversal of the bilayer polycrystalline FeNi(50 Å)/FeMn(50 Å) film sputtered in a magnetic field has been studied by magnetic and magneto-optical techniques. The external magnetic fields were applied along the easy or hard magnetization axis of the ferromagnetic permalloy layer. The asymmetry of hysteresis loop has been found. Appreciable asymmetry and the exchange bias were observed only in the field applied along the easy axis. The specific features of magnetization reversal were explained within the phenomenological model that involves high-order exchange anisotropy and misalignment of the easy axes of the antiferromagnetic and ferromagnetic layers. It has been shown that the film can exist in one of three equilibrium magnetic states in the field applied along the easy axis. The transitions between these states occur as first-order phase transitions. The observed hysteresis loop asymmetry is related to the existence of the metastable state.     

Microscopic field in nanocrystalline ferromagnetic metal films and the opportunity for studying it by the μSR method

The relation of the microscopic (local) field in nanocrystalline ferromagnetic metal films to macroscopic characteristics (the external magnetic field, average magnetization, saturation magnetization) is determined for the case where a nanocrystalline ferromagnetic film consists of crystallographically ordered grains separated by disordered regions and where the dimensions of grains along a normal to the film plane are much smaller than those in the film plane. In the case of a strong external field (? ? M), the magnetization direction is determined in grains in the form of oblate ellipsoids for metals with uniaxial or cubic magnetocrystalline anisotropy. Expressions are derived for the spin polarization of an ensemble of rapidly diffusing and nondiffusing muons in nanocrystalline ferromagnetic films. It is shown that experiments with “slow” positive muons make it possible to measure all parameters of such structures and to obtain important information for studying phase transition physics.     

Structure of the inhomogeneous magnetic state of an FeBO<Subscript>3</Subscript>: Mg easy-plane weak ferromagnet

The magnetic linear birefringence of an FeBO₃: Mg ferromagnetic crystal is investigated as a function of the magnetic field strength, the magnetic field orientation, and the coordinates. The structure of the inhomogeneous magnetic phase of this weak ferromagnet is determined by analyzing the experimental results obtained. It is shown that, in an inhomogeneous magnetic state, the ferromagnetic moment does not deviate from the basal plane of the crystal and the angle of its deviation from the direction of the applied magnetic field is described by a one-dimensional harmonic function of the spatial coordinate along the axis of magnetization.     

Interaction of a magnetic vortex with the probe field of a magnetic force microscope

The interaction of a magnetic vortex in a circular ferromagnetic nanoparticle with the probe field of a magnetic force microscope (MFM) is theoretically investigated. In the calculations, the probe field is approximated by the point dipole field. The rigid magnetic vortex model is used to describe the vortex state of magnetization. It is found that the effect of the probe field on the rigid magnetic vortex shell is similar to the effect of a uniform magnetic field parallel to the particle plane. The effect of the Z component of the probe field on the core of the vortex results in mutual probe-vortex attraction or repulsion. It is shown that the magnetization direction of the core of the vortex in the MFM probe field can be changed without a change in the shell vorticity direction.