Term parameters

Every energy terms requires one or more input parameters for its definition. For example, (second order) uniaxial anisotropy energy requires the anisotropy constant \(K\) and the anisotropy axis \(\mathbf{u}\). There are three ways how these parameters can be defined:

1. Constant parameters

If the energy parameters do not vary in space, they can be defined using constant values.

K = 1e5
u = (0, 0, 1)

2. Parameters defined “per region”

If different regions have different values of parameters, they can be defined “per region”. Let us say there are two regions: “region1” and “region2”. In “region1”, the anisotropy constant is \(5\times10^{5} \text{J}/\text{m}^{3}\) and the anisotropy axis is \((1, 0, 0)\). On the other hand, in “region2”, these parameters are \(3\times10^{5} \text{J}/\text{m}^{3}\) and \((0, 0, 1)\). These two parameters can then be defined using a dictionary:

K = {"region1": 5e5, "region2": 3e5}
u = {"region1": (1, 0, 0), "region2": (0, 0, 1)}

Certain energy terms also require the parameters to be defined between regions. This can be defined by adding an additional item to the dictionary with colon (:) in the key. For example, an exchange energy parameter can be:

A = {"region1": 1e-12, "region2": 2e-12, "region1:region2": 1e-11}

3. Parameters defined using discretisedfield.Field object

If it is not possible to define the energy parameter using a dictionary because of variation in space in a non-trivial manner, a parameter can be defined using a field object. For instance:

import discretisedfield as df

p1 = (0, 0, 0)
p2 = (50e-9, 50e-9, 50e-9)
cell = (2e-9, 2e-9, 2e-9)
mesh = df.Mesh(p1=p1, p2=p2, cell=cell)

K = df.Field(mesh, nvdim=1)
u = df.Field(mesh, nvdim=3)

The values of these two (scalar and vector) fields can be then set using Python functions.