Zeeman#

class micromagneticmodel.Zeeman(**kwargs)#

Zeeman energy term.

\[w = -\mu_{0}M_\text{s} \mathbf{m} \cdot \mathbf{H}\]

Zeeman energy term allows defining time-dependent as well as time-independent external magnetic field. If only external magnetic field H is passed, a time-constant field is defined.

The time-dependent field $H(t)$ is obtained by multiplying the time-independent field H with a time-dependent pre-factor $f(t)$:

\[H(t) = f(t) \cdot H\]

Three different methods are available to define the pre-factor for a time-dependent field:

  • pre-defined sine wave and sinc pulse

  • custom time-dependence via Python callable

  • custom tcl code passed directly to OOMMF

There are two built-in functions to specify a time-dependent field. To use these a string must be passed to func. func can be either 'sine' or 'sinc'. If time-dependent external magnetic field is defined using func, f and t0 must be passed. For func='sine', energy density is:

\[w = -\mu_{0}M_\text{s} \mathbf{m} \cdot \mathbf{H} \sin[2\pi f(t-t_{0})]\]

whereas for func='sinc', the energy density is:

\[w = -\mu_{0}M_\text{s} \mathbf{m} \cdot \mathbf{H} \text{sinc}[2\pi f(t-t_{0})]\]

and f is a cut-off frequency.

Arbitrary time-dependence can be specified by passing a callable to func. Additionally dt (in seconds) must be provided. The function is evaluated at all time steps separated by dt (up to the desired run-time). Additionally, the derivative is computed internally (using central differences). Therefore, the function has to be differentiable. In order for this method to be stable a reasonable small time-step must be chosen. As a rough guideline start around dt=1e-13 (s). The callable passed to func must either return a single number that is used to multiply the initial field H or a list of nine values that define a matrix M that is multiplied with the initial field vector. Ordering of the matrix elements is [M11, M12, M13, M21, M22, M23, M31, M32, M33]. The matrix allows for more complicated processes, e.g. a rotating field (for more details see the OOMMF documentation: https://math.nist.gov/oommf/doc/userguide20a3/userguide/Standard_Oxs_Ext_Child_Clas.html#TZ).

To have more control and use the full flexibility of OOMMF it is also possible to directly pass several tcl strings that are added to the mif file without further processing. The dictionary must be passed to tcl_strings and must contain script, energy, type, script_args, and script_name. Please refer to the OOMMF documentation for detailed explanations. In general, specifying time_dependence and tstep is easier for the user and should be preferred, if possible.

Parameters:

  • H ((3,) array_like, dict, discretisedfield.Field) – If a single length-3 array_like (tuple, list, numpy.ndarray) is passed, which consists of numbers.Real, a spatially constant parameter is defined. For a spatially varying parameter, either a dictionary, e.g. H={'region1': (0, 0, 3e6), 'region2': (0, 0, -3e6)} (if the parameter is defined “per region”) or discretisedfield.Field is passed.

  • f (numbers.Real, optional (required for func='sin'/'sinc')) – (Cut-off) frequency in Hz.

  • t0 (numbers.Real, optional (required for func='sin'/'sinc')) – Time for adjusting the phase (time-shift) of a wave.

  • func (str, callable, optional) – Predefined functions can be used by passing 'sin' or 'sinc'. Callables can be used to define arbitrary time-dependence. Called at times that are multiples of dt. Must return either a single number or a list of nine values.

  • dt (numbers.Real, optional (required for callable func)) – Time steps in seconds to evaluate callable func at.

  • tcl_strings (dict, optional) – Dictionary of tcl strings to be included into the mif file for more control over specific time-dependencies. Must contain the following keys: script, energy, type, script_args, and script_name. Refer to the OOMMF documentation for more details: https://math.nist.gov/oommf/doc/userguide20a3/userguide/Standard_Oxs_Ext_Child_Clas.html#SU. script_name refers to what is called script in the function definition on the OOMMF website.

Examples

  1. Defining the Zeeman energy term using a vector.

>>> import micromagneticmodel as mm
...
>>> zeeman = mm.Zeeman(H=(0, 0, 1e6))

  1. Defining the Zeeman energy term using dictionary.

>>> zeeman = mm.Zeeman(H={'region1': (0, 0, 1e6), 'region2': (0, 0, -1e6)})

  1. Defining the Zeeman energy term using discretisedfield.Field.

>>> import discretisedfield as df
...
>>> region = df.Region(p1=(0, 0, 0), p2=(5e-9, 5e-9, 10e-9))
>>> mesh = df.Mesh(region=region, n=(5, 5, 10))
>>> H = df.Field(mesh, nvdim=3, value=(1e6, -1e6, 0))
>>> zeeman = mm.Zeeman(H=H)

  1. Defining the Zeeman energy term using a vector which changes as a sine wave.

>>> zeeman = mm.Zeeman(H=(0, 0, 1e6), func='sin', f=1e9, t0=0)

  1. Defining an exponentially decaying field.

>>> import numpy as np
>>> def decay(t):
...     t_0 = 1e-10
...     return np.exp(-t / t_0)
>>> zeeman = mm.Zeeman(H=(0, 0, 1e6), func=decay, dt=1e-13)

  1. An attempt to define the Zeeman energy term using a wrong value.

>>> zeeman = mm.Zeeman(H=(0, -1e7))  # length-2 vector
Traceback (most recent call last):
...
ValueError: ...

Methods

__add__

Binary + operator.

__dir__

Default dir() implementation.

__eq__

Relational operator ==.

__iter__

Iterator.

__repr__

Representation string.

density

effective_field

energy

Properties

H

Descriptor allowing setting attributes with a value described as descriptor or a dictionary.

dt

Descriptor allowing setting attributes only with scalars (numbers.Real).

f

Descriptor allowing setting attributes only with scalars (numbers.Real).

func

Descriptor allowing setting attributes with a value described as descriptor or a dictionary.

name

Name.

t0

Descriptor allowing setting attributes only with scalars (numbers.Real).

tcl_strings

Descriptor allowing setting attributes with a dictionary, which has keys defined by key_descriptor and values defined by value_descriptor.

wave

Descriptor allowing setting attributes only with a subset of a predefined set.
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