Rok Dittrich

Scalable parallel micromagnetic solvers for magnetic nanostructures

A parallel finite element micromagnetics package has been implemented, that is highly scalable, easily portable and combines different solvers for the micromagnetic equations. The implementation is based on the standard Galerkin discretization on tetrahedral meshes with linear basis functions. A static energy minimization, a dynamic time integration, and the nudged elastic band method have been implemented. The details of the implementation and some aspects of the optimization are discussed and timing and speedup results are given. Nucleation and magnetization reversal processes in permalloy nanodots are investigated with this micromagnetics package.

A path method for finding energy barriers and minimum energy paths in complex micromagnetic systems

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.

Time resolved micromagnetics using a preconditioned time integration method

A detailed description for the solution of the Landau–Lifshitz–Gilbert equation with the finite element method is given. The use of implicit time integration schemes with proper preconditioning is reported. Simulations of a single-phase magnetic nanoelement without surface roughness and a magnetic nanoelement with a granular structure are performed to investigate the influence of the microstructure on the numerical behavior. Nanoelements with a granular structure cause an inhomogeneous computational grid. In granular systems preconditioning for time integration speeds up the simulations by three orders of magnitude as compared to conventional time integration schemes like the Adams method. r 2002 Elsevier Science B.V. All rights reserved.

Domain wall motion in nanowires using moving grids (invited)

The magnetization reversal process of Co nanowires was investigated using a moving mesh technique. The nucleation and expansion of reversed domains is calculated by solving the Gilbert equation of motion for different damping constants. The adaptive finite element method reduces the total CPU time by more than a factor of 4 as compared to a uniform mesh. Two different domain wall types are observed. For a wire diameter of d=10 nm transverse walls occur and gyromagnetic precession limits the domain wall velocity. The domain wall velocity increases from 50 to 520 m/s as the Gilbert damping constant increases from α=0.05 to α=1 at an applied field of 500 kA/m. For a diameter greater than 20 nm vortex walls are formed. The vortex mobility increases with decreasing damping constant. Thus velocities up to 2000 m/s are reached for a wire diameter of 40 nm, α=0.05, and an applied field of 250 kA/m.

Fast boundary methods for magnetostatic interactions in micromagnetics

In this paper, we compare a treecode-method as used for particle simulations, hierarchical matrices or so called supermatrices, and the fully populated boundary element matrix.

Angular dependence of the switching field in patterned magnetic elements

Recent experimental studies on the switching behaviour of Co∕Pd multilayer islands with sizes in a range from 20–100 nm shows the classical angular dependence for uniform rotation. We compare measured angular dependence of the switching field with micromagnetic finite element simulations. Simulation results show reversal modes close to uniform rotation for islands smaller than 30 nm. Larger islands (>70nm) reverse by nucleation of a reversed domain followed by domain wall propagation. However, the angular dependence does not change its character with the island size. The nucleation of the reversed domain determines the switching field.

Reversible magnetization processes and energy density product in Sm–CoFe and Sm–Co/Co bilayers

The hysteresis properties of epitaxial SmCo/Co and SmCo/Fe bilayers are calculated by the solution of the Landau–Lifshitz Gilbert equation. The thin film grain structure is taken into account using appropriate finite element techniques. The J(H) curve shows the typical exchange spring behavior for the bilayer if the soft magnetic layer thickness exceeds 10 nm. However, the reversible rotations of the magnetization for low external field deteriorate the maximum energy density product. Straight B(H) curves are obtained only for a Fe layer thickness of 5 nm. Magnetization reversal starts with the reversible rotation of the soft layer magnetization. Initially, the magnetization rotates in opposite directions in different regions of the film. The reversible rotations penetrate substantially into the hard layer.

Magnetization reversal in granular nanowires

The switching process of granular Co nanowires is investigated using the finite element method. The wires have a diameter of 55 nm and a length of 1000 nm. Transmission electron microscopy (TEM) investigations show two different types of hcp-structured grains. For one, the c axis is randomly oriented in a plane perpendicular to the long axis of the wire, and the other has the c axis parallel to the long axis. The numerical results show that finite element micromagnetics can explain the influence of the microstructure in magnetic nanosystems.

Energy barrier and effective thermal reversal volume in columnar grains

Abstract A method to determine the minimum energy path between two stable states in a magnetic system is used to investigate magnetic reversal of an irregularly shaped columnar grain. The method describes the magnetization reversal process initiated by thermal excitations in zero applied field or fields below the intrinsic switching field. In addition to the energy barrier, an effective volume V eff is calculated as a function of material exchange interaction, uniaxial crystalline anisotropy, and particle length. The minimum energy barrier paths follow that of intrinsic switching where with decreasing exchange the reversal modes go from uniform rotation to end nucleation and subsequent expansion to reversal by vortex excitation. The effective reversal volume decreases with decreasing exchange and increasing crystalline anisotropy. Decreasing the particle length also decreases the effective volume once the length becomes less than the excitation length. A very simple analytic wall model nicely indicates these trends. Analysis of measured thermal reversal fields for CrO 2 and Fe explain the inferred effective volumes in these particles.

Energy barriers in magnetic random access memory elements

In this paper, energy barriers in magnetic random access memory elements were calculated. Three minimum energy paths for the thermal reversal of a thin NiFeCo MRAM element were found between the two stable states.