Numerical Micromagnetics Research Articles

Defect manipulation for the coercivity enhancement of Nd-Fe-B permanent magnets

The demand for rare-earth based permanent magnets is expected to rise for various climate friendly technologies. This motivates for the search of better designed permanent magnets with optimal use of rare-earth elements without compromising the key magnetic properties. We simulate Nd2Fe14B based permanent magnets to study the effects of microstructure on coercivity (HC). We demonstrate a fast method to compute the microstructural parameters in numerical micromagnetics. We report a novel magnetic reversal process, which is primarily driven by defect thickness. By selective replacement of the defect with a hard magnetic phase HC is expected to rise by 1.5 times to that of single grain model with soft defect. This study is extended to a multigrain polycrystal model. Our systematic approach helps in identifying specific microstructural features pertinent for enhancement of coercivity. This work provides implications for future work to design improved defect engineered permanent magnets for green technologies.

Cavity magnonics for large and small amplitude precession

Excitations that may appear in cavity magnonics experiments are examined with numerical micromagnetics using a recently developed semi-classical cavity magnonics theory. The theory is generally applicable to linear and nonlinear dynamic systems. In this paper, example applications of the theory for magnetic systems are presented where the dynamics is described using numerical micromagnetics for field driven ferromagnets. Examples of large amplitude driving are studied as a function of drive field amplitude and frequency. We comment also on large amplitude dynamics under elliptically polarized driving fields. The main conclusion is that when implemented together with micromagnetics, the theory can be used to describe cavity photon–magnon coupling for a wide variety of linear and nonlinear magnetic dynamics, thereby providing a useful technique for cavity magnonics.

Searching the weakest link: Demagnetizing fields and magnetization reversal in permanent magnets

Magnetization reversal in permanent magnets occurs by the nucleation and expansion of reversed domains. Micromagnetic theory offers the possibility to localize the spots within the complex structure of the magnet where magnetization reversal starts. We compute maps of the local nucleation field in a Nd2Fe14B permanent magnet using a model order reduction approach. Considering thermal fluctuations in numerical micromagnetics we can also quantify the reduction of the coercive field due to thermal activation. However, the major reduction of the coercive field is caused by the soft magnetic grain boundary phases and misorientation if there is no surface damage.

Asymmetric driven dynamics of Dzyaloshinskii domain walls in ultrathin ferromagnetic strips with perpendicular magnetic anisotropy

The dynamics of domain walls in ultrathin ferromagnetic strips with perpendicular magnetic anisotropy is studied from both numerical and analytical micromagnetics. The influence of a moderate interfacial Dzyaloshinskii–Moriya interaction associated to a bi-layer strip arrangement has been considered, giving rise to the formation of Dzyaloshinskii domain walls. Such walls possess under equilibrium conditions an inner magnetization structure defined by a certain orientation angle that make them to be considered as intermediate configurations between Bloch and Néel walls. Two different dynamics are considered, a field-driven and a current-driven dynamics, in particular, the one promoted by the spin torque due to the spin-Hall effect. Results show an inherent asymmetry associated with the rotation of the domain wall magnetization orientation before reaching the stationary regime, characterized by a constant terminal speed. For a certain initial DW magnetization orientation at rest, the rotation determines whether the reorientation of the DW magnetization prior to reach stationary motion is smooth or abrupt. This asymmetry affects the DW motion, which can even reverse for a short period of time. Additionally, it is found that the terminal speed in the case of the current-driven dynamics may depend on either the initial DW magnetization orientation at rest or the sign of the longitudinally injected current.

Stability of topological charge of magnetic skyrmion configurations

We analyze the topological charge of a skyrmion qs, and the corresponding Hall conductivity σxy, which can serve as an electrical read-out for skyrmion-based memory. We derived the general form of the Dzyaloshinskii–Moriya (DM) interaction for any arbitrary orientation of the DM vector D. Based on the DM interaction energy, we obtained the dependence the skyrmion helicity angle γ on the orientation of D. We showed via general mathematical arguments, the topological nature of the skyrmionic charge qs, and its independence of γ and specific details of the interior of the skyrmion (e.g., its core size). Finally, we showed via numerical micromagnetics the stability of qs under varying applied B-fields till the annihilation field, despite the drastic reduction in the skyrmion core size.

SPICE Circuit Modeling of PMA Spin Wave Bus Excited Using Magnetoelectric Effect

We propose a formalism of a compact model for circuit simulations of spin wave interconnects. The developed SPICE Spin Wave model is based on the theory of numerical micromagnetics, and serves as a building block for a hierarchical circuit simulation tool for spintronic circuits and systems. We demonstrate excellent agreement between the SPICE model simulations and full micromagnetic solver results. We also present a scheme of exciting spin waves in spin wave bus having perpendicular magnetic anisotropy. Spin waves are excited with an oscillating change of magnetocrystalline anisotropy in a magnetoelectric cell. We use our proposed SPICE model to analyze this structure: determine the length of spin wave attenuation, delay in the bus, and the dependence of amplitude on the change of anisotropy.

Dynamics of Dzyaloshinskii domain walls in ultrathin magnetic films

We explore a new type of domain wall structure in ultrathin films with perpendicular anisotropy, that is influenced by the Dzyaloshinskii-Moriya interaction due to the adjacent layers. This study is performed by numerical and analytical micromagnetics. We show that these walls can behave like Néel walls with very high stability, moving in stationary conditions at large velocities under large fields. We discuss the relevance of such walls, that we propose to call Dzyaloshinskii domain walls, for current-driven domain wall motion under the spin Hall effect.

Magnetic neutron scattering on nanocomposites: Decrypting cross-section images using micromagnetic simulations

We have used numerical micromagnetics for the calculation of the magnetic (small-angle) neutron scattering cross section of nanocomposites. The novel aspect of our approach consists in the possibility to study the applied-field dependence of the individual contributions to the total magnetic scattering. Such a micromagnetic tool ideally complements neutron experiments in which one generally measures only a weighted sum of the Fourier components of the magnetization. The procedure furnishes unique and fundamental information regarding the magnetic microstructure and corresponding magnetic scattering from nanomagnets. In particular, our simulation results explain the recent observation of dipolar correlations in two-phase nanocomposites and provide an answer to the question of the explicit dependence of the magnetization Fourier coefficients on the scattering vector.

Micromagnetic method of s-parameter characterization of magnonic devices

Designers of nano-scale magnonic devices would benefit from methods of their evaluation that do not require one to access the microscopic level of description or to construct device prototypes. Here, we propose a numerical micromagnetics version of such a method, in which magnonic devices are considered as two-port linear networks and can therefore be described in terms of their s-parameters (i.e., reflection and transmission characteristics). In the micromagnetic model, the sample is composed from a magnonic device-under-test situated between input and output magnonic waveguides. First, dispersion relations and amplitudes of spin waves in the input and output waveguides are calculated from the simulations. The results are then compared to derive the s-parameters of the device-under-test. We use a simple rectangular magnetic nonuniformity, for which analytical results are readily obtained, to evaluate the efficiency and limitations of the technique in the sub-terahertz band.

Magnetic domain walls displacement: Automotion versus spin-transfer torque

The magnetization dynamics equation predicts that a domain wall that changes structure should undergo a displacement by itself - automotion - due to the relaxation of the linear momentum that is associated with the wall structure. We experimentally demonstrate this effect in soft nanostrips,transforming under spin transfer torque a metastable asymmetric transverse wall into a vortex wall. Displacements more than three times as large as under spin transfer torque only are measured for 1~ns pulses. The results are explained by analytical and numerical micromagnetics. Their relevance to domain wall motion under spin transfer torque is emphasized.

Optimization of magnetic anisotropy and applied fields for hyperthermia applications

Magnetic anisotropy and applied fields for hyperthermia applications have been optimized for iron cobalt nanocrystalline particles using numerical micromagnetics. The optimized anisotropy energy is 7.6 kBT at 500 KHz and the hysteresis loss at this optimized energy is approximately 120×106 ergs/(s∗g) for a very small oscillating field of magnitude 10 Oe. We have also investigated the effects of varying the applied field and find that the addition of a 20 Oe static field applied perpendicular to the oscillating field approximately doubles the energy loss without subjecting the patient to additional radiation. This is an important benefit for magnetic hyperthermia.

Domain wall assisted magnetic recording (invited)

The domain wall assisted switching in the hard/soft composite nanostructures is studied using numerical and analytic micromagnetics. The switching occurs via domain wall nucleation, compression in the applied field, depinning, and propagation through the hard/soft interface. Optimizing hard and soft layer parameters yields a significant increase of the maximum switchable anisotropy for a fixed applied field, and hence an enhancement of the energy barrier that can be translated into grain diameter reduction and magnetic recording density gains. The switching fields for the media with quadratic variation of the anisotropy were calculated and optimized to achieve the largest energy barrier gain. Domain wall assisted switching was studied in the field of a single pole write head.

Numerical micromagnetics of interacting superparamagnetic nanoparticles assembled in clusters with different dimensionalities

We analyze here the equilibrium magnetization state of densely packed interacting superparamagnetic nanoparticles assembled in clusters of various sizes and dimensionalities by comparison with the non-interacting case. We demonstrate that the average magnetization of individual particles is strongly increased in linear chains aligned parallel with the external magnetic field. Two-dimensional (2D) distributions of superparamagnetic nanoparticles present weaker increases of their average magnetization with respect to the non-interacting approximation whereas volume distributions (3D) are almost equivalent with the non-interacting case. A large number of nanoparticles densely packed in 2D superparamagnetic clusters present almost the same magnetic moment as infinite superparamagnetic chains. The effect of mutual interactions on the total magnetic moment of 3D surfaces (spheroids with various aspect ratios) uniformly covered with densely packed monolayers of superparamagnetic nanoparticles is also investigated.

Domain wall assisted magnetic recording

Using numerical and analytical micromagnetics the authors calculated the switching fields and energy barriers of the composite (exchange spring) magnetic recording media, which consist of layers with high and low magnetocrystalline anisotropies. The authors demonstrate that the ultimate potential of the composite media is realized if the interfacial domain wall fits inside the layers. The switching occurs via domain wall nucleation, compression in the applied field, depinning, and propagation through the hard/soft interface. The authors demonstrate that the domain wall assisted magnetic recording offers up to a threefold areal density gain over conventional single layer recording.

Edge saturation fields and dynamic edge modes in ideal and nonideal magnetic film edges

This paper describes modeling of the micromagnetic behavior near edges of ferromagnetic thin films when uniform fields are applied in plane and perpendicular to the edge. For ideal film edges with vertical edge surfaces, the field required to saturate the magnetization perpendicular to the edge, ${H}_{\mathrm{sat}}$, and the frequency of precession in the localized edge mode are calculated using numerical micromagnetics for a wide range of film thicknesses. Analysis of the critical state at the saturation field and the full micromagnetic results are used to develop a simple macrospin model for the edge magnetization. This model predicts both ${H}_{\mathrm{sat}}$ and edge mode precession frequency values that agree well with the micromagnetic results. Three classes of nonideal edges are also modeled: tilted edge surfaces, diluted magnetization near the edge, and surface anisotropy on the edge surface. Despite their different physical mechanisms, all three of these defects produce similar reductions in ${H}_{\mathrm{sat}}$ and similar dynamic properties of the edge magnetization.

Full micromagnetics of recording on patterned media

Numerical micromagnetics of the bit writing process revealed the theoretical limits for remanence, coercive field, switching behaviour at a short time scale of less than 1 ns for patterned recording media. We discuss our recent results concerning the influence of the granular microstructure on the fast switching processes of typical CoCrPtX, FePt and CoPd thin films used for high density magnetic recording with longitudinal and perpendicular anisotropy. In detail, we will show that the degree of the exchange coupling between neighbouring grains, the grain size and its distribution and the offset between recording head and bit structure finally control the magnetization reversal properties of the individual bits.

Role of the Surface Anisotropy in Magnetization Reversal of a Spherical Nanoparticle

Numerical micromagnetics is used to investigate the influence of the surface anisotropy on the magnetic behaviour of single domain spherical nanoparticles. Two kinds of surface anisotropy are considered: easy axis type (radial) and easy plane type (tangential). It is shown that the coercivity increases whereas the remanence decreases with the increase of the surface anisotropy and this tendency is more pronounced for radial surface anisotropy (Ks < 0) than for tangential one (Ks > 0). It is additionally shown that the enhancement of the coercivity depends on the particle size and is the strongest for the smallest particles.

Phase Transformations of the Magnetic Structure in Film Nanobridges

The magnetic structure of a plane nanobridge consisting of two ferromagnetic film electrodes connected by a nanosized crossbar of the same material is studied. Due to their magnetoresistive properties, such bridges are of considerable interest for microelectronics. Using a numerical micromagnetics method, it is shown that a domain wall is displaced from the center of the bridge crossbar as the anisotropy constant of the system decreases and reaches a critical value. A phase diagram is constructed, which makes it possible to determine the possible magnetic states of real nanobridges. The mechanism of the phase transformation is described in terms of an analytical model. This model explains the shape of the phase diagram of the nanobridge. Formally, the transformations of the magnetic structure of the nanocontact can be described in terms of the Landau theory of phase transitions in a certain range of parameters of the system.

Diagram of the states in arrays of iron nanocylinders

The magnetic states of two-dimensional cylinder arrays of iron are studied as function of thickness, diameter, and separation by means of numerical micromagnetics. The corresponding diagram of the states for cylinders with thickness and diameter in the nanoscale regime is presented. The diagram is composed of regions with a single minimum of the free energy, relevant for applications, and regions with multiple minima. The effect of the magnetostatic coupling is highlighted by comparing the state diagram for cylinders with 10nm perimetrical separation with the one for isolated cylinders.

Exchange energy formulations for 3D micromagnetics

Exchange energy is especially sensitive to the numerical representation selected. We compare three discretized exchange energy formulations for 3D numerical micromagnetics on rectangular grids. Explicit formulae are provided for both Neumann and Dirichlet boundary conditions. Results illustrate the convergence order of these methods as a function of discretization cell size and the effect of cell size on vortex pinning.