The example problems in this section do not in any way represent an exhaustive display of LLG's capabilities. LLG has been designed for flexibility, accessibility and robustness, so that it can deal with most (approaching all) micromagnetics problems.

3D Current

This example displays LLG's function for computing current flow in 3D. For problems in MRAM, current enters and leaves the cell in a way that breaks the symmetry at the entry and exit points. These asymmetries introduce bias into the configuration; in LLG, this bias can be computed without approximation.  

Computing the Transfer Curve with Shields in an AMR Head

This example demonstrates how you can use LLG to compute the transfer function for a shielded GMR read-head. The finite permeability shields shunt stray field from the device when the transition is not directly beneath the head. LLG incorporates standard disk transition models for media that can be dynamically scanned beneath a read-head, which alter the magnetization of that head and change its resistance. Therefore, the transfer curve can be computed directly.

Dynamic Bit Response

This very simple example demonstrates how you can use LLG to simulate dynamic phenomena; this case shows the response of a bit of Permalloy to a pulsed field. LLG's capability to define arbitrary current and field pulses in space and time make it effective for modeling real transient behavior.

Interaction of an MFM Tip with a Permalloy Platelet

This example demonstrates one of LLG's image contrast modes, but one where the imaging tool, an MFM tip, is strongly coupled to the sample. Normal mode imaging using MFM would require the appropriate derivatives of the magnetization to be taken and summed. When the tip interacts strongly with the specimen, the tip itself must become part of the simulation and must be allowed to relax along with the sample. This example demonstrates how a strongly magnetized tip can in fact alter the magnetization in the sample.

Layers with Demagnetization Coupling in a Fe/Permalloy MRAM

This example demonstrates a simple two-layer problem, where a heavy layer (iron) is coupled via the demagnetization field to a light layer (Permalloy). The two layers have differing intrinsic coercivities, such that, in this extremely simplified example, stable memory states are achieved. You can compute the switching curve and MR response directly with LLG. 


This example demonstrates how LLG has been optimized to generate position dependent parameters that make modeling media and granular material extremely easy. In this example, the anisotropy has been assigned a random axis orientation, such that the equilibrium domain structure has the spread in directions that are typical of media of this type.

Rotational Hysteresis Loops

This example demonstrates how you can use LLG to generate rotational hysteresis loops. The LLG rotational hysteresis loop utility allows you to set the sense (CW or CCW) and the number of passes around the loop (n) arbitrarily.

Semi-infiinite 2D Wall Surfaces: 2D Walls in Fe

This example demonstrates how LLG leverages its 2D Greens Function in the modeling of a bulk terminated block wall in Fe. In this case, the bulk wall terminates in a Neel wall cap at the surface. LLG is ideal for probing topological structures, such as walls, vortices and lines.

Dynamic Relaxation of a Single Spin

This is the simplest example. It demonstrates the relaxation of a single spin in a magnetic field, for which a closed form solution exists. (See A. Arrott's upcoming article in the Heinrich and Bland series this winter.)

Spin Torques Transferred in Ultra-small Surfaces

This example demonstrates a new feature in LLG: spin-torques. Slonczewski's JMMM paper predicted that high current densities, directed perpendicular to a FM/P/FM sandwich, can transfer angular momentum between the layers. LLG self consistently includes the effects of spin torques and the current-generated field torques. This extremely simple example shows that it is not always as easy as it might seem, since the reciprocal torque on the polarizing layer generated spin waves even when the layer was strictly pinned.

Edge Corrections

This example demonstrates LLG's facility to correct edge effects for shaped structures. All numerical methods approximate solutions by suitably discretizing the structure. Cartesian discretization is easy to implement and understand (in contrast to complex finite-element 3D grid algorithms). Artifacts can be the result when the edges do not align with the Cartesian axes.  To remove artifacts due to discretization, with LLG you can correct both the demagnetization and the exchange fields in the proximity to an edge.