|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)
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.
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.
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.
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.
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.
This example demonstrates how LLG leverages its 2D Greens
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.
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
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.