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The spatially-inhomogeneous magnetization dynamics in a cylindrical magnetic nanodot driven by ac spin-torque is analyzed. To this end, the Landau-Lifshitz-Gilbert-Slonczewski equation is reformulated as a system of coupled nonlinear ordinary differential equations which describe the time-evolution of normal modes amplitudes. This approach provides a class of models with reduced number of degrees of freedom and incremental accuracy between macrospin and full micromagnetics. By using this approach, the onset of foldover effect for fundamental and higher-order modes is demonstrated. The results are confirmed by full micromagnetic simulations. [ABSTRACT FROM AUTHOR]

Demagnetization curves of sub-micron Nd2Fe14B particles with rectangular prism shapes were simulated by micromagnetic simulations. Coercivity decreases with increasing particle thickness for same particle volumes. This unexpected behavior can be explained by different resulting angles of the total effective field when superimposing the applied field vector with the stray field vector at the point of the first reversal event. The angular dependence of the nucleation field follows a Stoner-Wohlfarth like behavior. [ABSTRACT FROM AUTHOR]

Fast stray field calculation is commonly considered of great importance for micromagnetic simulations, since it is the most time consuming part of the simulation. The Fast Multipole Method (FMM) has displayed linear O(N) parallelization behavior on many cores. This article investigates the error of a recent FMM approach approximating sources using linear—instead of constant—finite elements in the singular integral for calculating the stray field and the corresponding potential. After measuring performance in an earlier manuscript, this manuscript investigates the convergence of the relative L2 error for several FMM simulation parameters. Various scenarios either calculating the stray field directly or via potential are discussed. [ABSTRACT FROM AUTHOR]

One essential feature in magnetic random access memory cells is the spin torque efficiency, which describes the ratio of the critical switching current to the energy barrier. In this paper, it is reported that the spin torque efficiency can be improved by a factor of 3.2 by the use of a dual free layer device, which consists of one layer with perpendicular crystalline anisotropy and another layer with in-plane crystalline anisotropy. Detailed simulations solving the spin transport equations simultaneously with the micromagnetics equation were performed in order to understand the origin of the switching current reduction by a factor of 4 for the dual layer structure compared to a single layer structure. The main reason could be attributed to an increased spin accumulation within the free layer due to the dynamical tilting of the magnetization within the in-plane region of the dual free layer. [ABSTRACT FROM AUTHOR]

Conjugate gradient methods for energy minimization in micromagnetics are compared. The comparison of analytic results with numerical simulation shows that standard conjugate gradient method may fail to produce correct results. A method that restricts the step length in the line search is introduced, in order to avoid this problem. When the step length in the line search is controlled, conjugate gradient techniques are a fast and reliable way to compute the hysteresis properties of permanent magnets. The method is applied to investigate demagnetizing effects in NdFe12 based permanent magnets. The reduction of the coercive field by demagnetizing effects is μ0ΔH = 1.4 T at 450 K. [ABSTRACT FROM AUTHOR]

Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau-Lifshitz-Gilbert equation (LLG) constrains the maximum element size to the exchange length within the media, it is numerically not attractive to simulate macroscopic parts with this approach. On the other hand, the magnetostatic Maxwell equations do not constrain the element size, but cannot describe the short-range exchange interaction accurately. A combination of both methods allows one to describe magnetic domains within the micromagnetic regime by use of LLG and also considers the macroscopic parts by a nonlinear material law using the Maxwell equations. In our work, we prove that under certain assumptions on the nonlinear material law, this multiscale version of LLG admits weak solutions. Our proof is constructive in the sense that we provide a linear-implicit numerical integrator for the multiscale model such that the numerically computable finite element solutions admit weak H¹- convergence (at least for a subsequence) towards a weak solution. [ABSTRACT FROM AUTHOR]

Magnetization reversal processes in Co/Pt multilayers prepared on nanoperforated templates are probed by magnetization relaxation measurements. The signature of pinning controlled domain wall movement as expected for percolated media is identified. This contrasts with the nucleation-type reversal mechanism of a Co/Pt reference film prepared on a smooth substrate. A zero field energy barrier of 93kBT is determined by fluctuation field measurements and is elucidated by micromagnetic calculations using the nudged elastic band method. This value is sufficiently large to qualify the material as a promising percolated medium. [ABSTRACT FROM AUTHOR]

Lateral exchange spring media are a combination of percolation media and exchange spring media. A soft magnetic track is introduced that acts as a nucleation center during writing in a percolated media. Driven by the head field, the nucleated domains propagate in the hard magnetic data layer. A soft magnetic track with a width of 4 nm is sufficient to be able to write extremely hard materials such as FePt. The thermal stability of the bits in the data layer depends on the diameter and distance of the inclusion and the exchange constant. If the exchange of FePt can be reduced by a factor of two, thermally stable bits can be obtained with defects of about 3 am in diameter. [ABSTRACT FROM AUTHOR]

Vortex nucleation and vortex motion are the main mechanisms of magnetization reversal in micrometer-sized magnetic elements. The critical field required to nucleate a vortex depends on the temperature. We propose a method that combines standard Landau-Lifshitz-Gilbert (LLG) micromagnetics and an elastic band method to simulate nonzero temperature hysteresis curves of magnetic thin film elements. Whereas the LLG simulations gives the equilibriums states before and after a vortex enters the element, the elastic band method gives the height of the energy barrier between these two states. Thus temperature-dependent nucleation fields can be computed without the need to perform stochastic LLG simulations. [ABSTRACT FROM AUTHOR]

We perform multiscale finite element simulation of the write process in perpendicular media. The Landau-Lifshitz-Gilbert equation is solved simultaneously for the head, the data layer, and the soft under layer during the motion of the head. All magnetostatic interactions between head, data layer and soft underlayer are concurrently taken into account. This fully integrated recording model enables a detailed analysis of the head field as seen by the media grains. [ABSTRACT FROM AUTHOR]

A numerical implementation of the transition state theory is presented which can be used to calculate the attempt frequency f0 of arbitrary shaped magnetic nanostructures. The micromagnetic equations are discretized using the finite element method. The climbing image nudged elastic band method is used to calculate the saddle point configuration, which is required for the calculation of f0. Excellent agreement of the implemented numerical model and analytical solutions is obtained for single domain particles. The developed method is applied to compare f0 for single phase and graded media grains of advanced recording media. f0 is predicted to be comparable if the maximum anisotropy is the same in these two media types. [ABSTRACT FROM AUTHOR]

Minimum energy paths and energy barriers are calculated for complex micromagnetic systems. The method is based on the nudged elastic band method and uses finite-element techniques to represent granular structures. The method was found to be robust and fast for both simple test problems as well as for large systems such as patterned granular media. The method is used to estimate the energy barriers in CoCr-based perpendicular recording media. [Copyright &y& Elsevier]

Graphical abstract Highlights • Introducing a new type of spin-torque-oscillator (STO), all-in-plane STO for MAMR. • All-in-plane STO consisting of Spin-Injection-Layer and Field-Generating-Layer. • Large oscillation cone angle of FGL after magnetization switching of SIL. • Design of SIL for oscillation of FGL at a frequency above 20 GHz. Abstract A new type of spin-torque-oscillator (STO), all-in-plane STO, is introduced for microwave assisted magnetic recording (MAMR) that consist of a spin-injection-layer (SIL) and a field-generating-layer (FGL) with an effective in-plane easy axis due to the shape anisotropy separated with a metallic spacer. In this device, electrons are injected from SIL to FGL while the magnetization of the SIL and FGL is saturated to the out-of-plane by the external magnetic field of ∼1.0 T. Micromagnetic simulations showed that the magnetization direction of SIL can be switched to the opposite direction to that of the applied external magnetic field by the use of spin-transfer-torque. This results in a larger spin accumulation in FGL and its oscillation with a large cone angle at a low bias current density. We designed SIL to reduce the critical current density, J c , required for the magnetization switching of SIL. Materials with a smaller saturation magnetization in SIL reduce J c. Smaller spin polarization of SIL leads to a larger spin accumulation in SIL with an opposite direction to the magnetization, resulting in a reduction of J c. This enables magnetization switching of SIL in small J c followed by oscillation of FGL with frequency above 20 GHz with a large out-of-plane oscillation cone angle of 45–50°. The validity of this finding was studied experimentally by developing STO with two SIL materials, Co 2 Fe(Al 0.5 Si 0.5) Heusler alloy and Fe 67 Co 33 , the former has the B2 crystal structure with a large spin polarization and the latter has the A2 crystal structure with a smaller spin polarization. The magnetization configuration of SIL and FGL in STO with a diameter of ∼60 nm is investigated experimentally based on the field dependent resistance change and the oscillation behavior is discussed based on the micromagnetic simulations. [ABSTRACT FROM AUTHOR]

The long-range magnetic field is the most time-consuming part in micromagnetic simulations. Computational improvements can relieve problems related to this bottleneck. This work presents an efficient implementation of the Fast Multipole Method [FMM] for the magnetic scalar potential as used in micromagnetics. The novelty lies in extending FMM to linearly magnetized tetrahedral sources making it interesting also for other areas of computational physics. We treat the near field directly and in use (exact) numerical integration on the multipole expansion in the far field. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. By using FMM the calculations scale linearly in time and memory. [ABSTRACT FROM AUTHOR]

The Landau–Lifshitz equation governing magnetization dynamics is written in terms of the amplitudes of normal modes associated with the micromagnetic system's appropriate ground state. This results in a system of nonlinear ordinary differential equations (ODEs), the right-hand side of which can be expressed as the sum of a linear term and nonlinear terms with increasing order of nonlinearity (quadratic, cubic, etc.). The application of the method to nanostructured magnetic systems demonstrates that the accurate description of magnetization dynamics requires a limited number of normal modes, which results in a considerable improvement in computational speed. The proposed method can be used to obtain a reduced-order dynamical description of magnetic nanostructures which allows to adjust the accuracy between low-dimensional models, such as macrospin, and micromagnetic models with full spatial discretization. This new paradigm for micromagnetic simulations is tested for three problems relevant to the areas of spintronics and magnonics: directional spin–wave coupling in magnonic waveguides, high power ferromagnetic resonance in a magnetic nanodot, and injection-locking in spin-torque nano-oscillators. The case studies considered demonstrate the validity of the proposed approach to systematically obtain an intermediate order dynamical model based on normal modes for the analysis of magnetic nanosystems. The time-consuming calculation of the normal modes has to be done only one time for the system. These modes can be used to optimize and predict the system response for all possible time-varying external excitations (magnetic fields, spin currents). This is of utmost importance for applications where fast and accurate system simulations are required, such as in electronic circuits including magnetic devices. • Description of nonlinear LLG magnetization dynamics in terms of normal modes • Reduced-order, accurate and fast models alternative to Computational Micromagnetics • Application to magnonic waveguides, ferromagnetic resonance, spin-torque oscillators [ABSTRACT FROM AUTHOR]

We have investigated the magnetic properties of submicron soft magnetic cylindrical nanodots using an analytical model as well as three dimensional numerical finite element simulations. A detailed comparison of the magnetic vortex state shows the differences between these two models. It appears that the magnetic surface charges play a crucial role in the equilibrium magnetization distribution especially for shifted vortices. Finally, the magnetic phase diagram for soft magnetic particles with varying aspect ratio is presented. [Copyright &y& Elsevier]