"""
Functions that define a term in the magnetic Hamiltonian. They will be added into <class interaction> for automatic differentiation.
"""
# This file is part of OpenFerro.
import jax.numpy as jnp
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def get_isotropic_exchange_energy_engine(rollers):
"""Returns the exchange energy engine for a R^3 field defined on a lattice with periodic boundary conditions.
Parameters
----------
rollers : list
List of jnp.roll functions specifying the neighbors
Returns
-------
callable
Energy engine function
"""
def energy_engine(field, parameters):
coupling = - parameters[0] * 2 # the double counting should be made under adopted convention
energy = 0
for roller in rollers:
field_rolled = roller(field)
energy += jnp.sum(field * field_rolled)
return coupling * energy
return energy_engine
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def cubic_anisotropy_energy(field, parameters):
"""Returns the anisotropy energy of the field.
Parameters
----------
field : ndarray
The magnetic field
parameters : ndarray
Array containing K1 and K2 anisotropy constants
Returns
-------
float
The anisotropy energy: -K1*(mx^2*my^2 + my^2*mz^2 + mx^2*mz^2) - K2*mx^2*my^2*mz^2
"""
K1 = parameters[0]
K2 = parameters[1]
energy = -K1 * (field[:,:,:,0]**2 * field[:,:,:,1]**2 + field[:,:,:,1]**2 * field[:,:,:,2]**2 + field[:,:,:,0]**2 * field[:,:,:,2]**2).sum()
energy += -K2 * (field[:,:,:,0]**2 * field[:,:,:,1]**2 * field[:,:,:,2]**2).sum()
return energy
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def Dzyaloshinskii_Moriya_energy(field, parameters):
"""Returns the Dzyaloshinskii-Moriya energy of the field.
Parameters
----------
field : ndarray
The magnetic field
parameters : ndarray
Array of parameters
Returns
-------
float
The Dzyaloshinskii-Moriya energy
"""
pass
[docs]
def external_field_energy(field, parameters):
"""Returns the external field energy of the field.
Parameters
----------
field : ndarray
The magnetic field
parameters : ndarray
Array containing the external field B_ext
Returns
-------
float
The external field energy: -field·B_ext
"""
B_ext = parameters[0]
energy = - jnp.sum(field * B_ext)
return energy