# ================================== LICENSE ===================================
# Magnopy - Python package for magnons.
# Copyright (C) 2023-2026 Magnopy Team
#
# e-mail: anry@uv.es, web: magnopy.org
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
#
# ================================ END LICENSE =================================
import numpy as np
from magnopy._parameters._p22 import from_dmi, from_iso
from magnopy._spinham._convention import Convention
from magnopy._spinham._hamiltonian import SpinHamiltonian
# Save local scope at this moment
old_dir = set(dir())
old_dir.add("old_dir")
[docs]
def ivuzjo(N=10, J=10):
r"""
Prepares a Hamiltonian from the paper by Ivanov, Uzdin and Jónsson.
See [1]_ for details. The Hamiltonian is defined as
.. math::
\mathcal{H}
=
-\dfrac{1}{2}
\sum_{\mu, \nu}
J
\boldsymbol{S}_{\mu}
\cdot
\boldsymbol{S}_{\mu+\nu}
-
\dfrac{1}{2}
\sum_{\mu, \nu}
\dfrac{J}{2}
\boldsymbol{r}_{\nu}
\left(
\boldsymbol{S}_{\mu}
\times
\boldsymbol{S}_{\mu+\nu}
\right)
+
\sum_{\mu}
J
\boldsymbol{\hat{z}}
\boldsymbol{S}_{\mu}
Parameters
----------
N : int, default 10
Size of the supercell (N x N).
J : float, default 10
Value of the isotropic exchange in energy units (meV), sign is *not* ignored.
Returns
-------
spinham : :py:class:`.SpinHamiltonian`
Spin Hamiltonian (with magnetic field)
References
----------
.. [1] Ivanov, A.V., Uzdin, V.M. and Jónsson, H., 2021.
Fast and robust algorithm for energy minimization of spin systems applied
in an analysis of high temperature spin configurations in terms of skyrmion
density.
Computer Physics Communications, 260, p.107749.
Examples
--------
To create an example Hamiltonian use
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.ivuzjo()
"""
D = J / 2
BOHR_MAGNETON = 0.057883818060 # meV / Tesla
cell = np.eye(3, dtype=float) * N
atoms = dict(names=[], positions=[], g_factors=[], spins=[])
names_to_index = {}
atom_index = 0
for i in range(0, N):
for j in range(0, N):
atoms["names"].append(f"Fe_{i + 1}_{j + 1}")
atoms["positions"].append([i + 0.5, j + 0.5, 0])
atoms["spins"].append(1)
atoms["g_factors"].append(2)
names_to_index[f"Fe_{i + 1}_{j + 1}"] = atom_index
atom_index += 1
convention = Convention(
multiple_counting=True, spin_normalized=False, c21=-1, c22=-0.5
)
spinham = SpinHamiltonian(cell=cell, atoms=atoms, convention=convention)
# For each atom add bonds
for i in range(0, N):
for j in range(0, N):
alpha = names_to_index[f"Fe_{i + 1}_{j + 1}"]
# 1 0 0
if i == N - 1:
nu = (1, 0, 0)
beta = names_to_index[f"Fe_1_{j + 1}"]
else:
nu = (0, 0, 0)
beta = names_to_index[f"Fe_{i + 2}_{j + 1}"]
parameter = from_iso(iso=J) + from_dmi(dmi=[D, 0, 0])
spinham.add_22(alpha=alpha, beta=beta, nu=nu, parameter=parameter)
# 0 1 0
if j == N - 1:
nu = (0, 1, 0)
beta = names_to_index[f"Fe_{i + 1}_1"]
else:
nu = (0, 0, 0)
beta = names_to_index[f"Fe_{i + 1}_{j + 2}"]
parameter = from_iso(iso=J) + from_dmi(dmi=[0, D, 0])
spinham.add_22(alpha=alpha, beta=beta, nu=nu, parameter=parameter)
spinham.add_magnetic_field(B=[0, 0, J / 5 / BOHR_MAGNETON / 2])
return spinham
[docs]
def full_ham():
r"""
Prepares a Hamiltonian with all parameters being populated.
Returns
-------
spinham : :py:class:`.SpinHamiltonian`
Spin Hamiltonian.
Examples
--------
To create an example Hamiltonian use
.. doctest::
>>> import magnopy
>>> spinham = magnopy.examples.full_ham()
"""
cell = np.eye(3, dtype=float)
atoms = dict(
names=["Cr1", "Cr2", "Cr3", "Cr4"],
g_factors=[2, 2, 2, 2],
spins=[3 / 2, 3 / 2, 3 / 2, 3 / 2],
positions=[
[0.0, 0.0, 0.0],
[0.0, 0.0, 0.5],
[0.0, 0.5, 0.0],
[0.0, 0.0, 0.5],
],
)
convention = Convention(
spin_normalized=False,
multiple_counting=True,
c1=1,
c21=1,
c22=1,
c31=1,
c32=1,
c33=1,
c41=1,
c421=1,
c422=1,
c43=1,
c44=1,
)
spinham = SpinHamiltonian(cell=cell, atoms=atoms, convention=convention)
############################################################################
# One site #
############################################################################
for alpha in range(4):
spinham.add_1(alpha=alpha, parameter=[0, 0, 1])
spinham.add_21(alpha=alpha, parameter=[0.5, 1, 1.5])
spinham.add_31(alpha=alpha, parameter=[-0.4, 0.1, 1])
spinham.add_41(alpha=alpha, parameter=[0.1, 0.2, 1])
############################################################################
# Two sites #
############################################################################
for alpha, beta, nu in [
[0, 0, (1, 0, 0)],
[1, 1, (1, 0, 0)],
[2, 2, (1, 0, 0)],
[3, 3, (1, 0, 0)],
]:
spinham.add_22(alpha=alpha, beta=beta, nu=nu, parameter=-np.eye(3))
spinham.add_32(alpha=alpha, beta=beta, nu=nu, parameter=-np.ones((3, 3, 3)))
spinham.add_421(alpha=alpha, beta=beta, nu=nu, parameter=-np.ones((3, 3, 3, 3)))
spinham.add_422(alpha=alpha, beta=beta, nu=nu, parameter=-np.ones((3, 3, 3, 3)))
for alpha, beta in [[0, 1], [1, 2], [2, 3], [3, 1]]:
spinham.add_22(alpha=alpha, beta=beta, nu=nu, parameter=0.5 * np.eye(3))
spinham.add_32(
alpha=alpha, beta=beta, nu=nu, parameter=0.5 * np.ones((3, 3, 3))
)
spinham.add_421(
alpha=alpha, beta=beta, nu=nu, parameter=0.5 * np.ones((3, 3, 3, 3))
)
spinham.add_422(
alpha=alpha, beta=beta, nu=nu, parameter=0.5 * np.ones((3, 3, 3, 3))
)
############################################################################
# Three sites #
############################################################################
for alpha, beta, gamma, nu, _lambda in [[0, 1, 2, (0, 0, 0), (0, 0, 0)]]:
spinham.add_33(
alpha=alpha,
beta=beta,
gamma=gamma,
nu=nu,
_lambda=_lambda,
parameter=0.3 * np.ones((3, 3, 3)),
)
spinham.add_43(
alpha=alpha,
beta=beta,
gamma=gamma,
nu=nu,
_lambda=_lambda,
parameter=0.3 * np.ones((3, 3, 3, 3)),
)
############################################################################
# Four sites #
############################################################################
for alpha, beta, gamma, epsilon, nu, _lambda, rho in [
[0, 1, 2, 3, (0, 0, 0), (0, 0, 0), (0, 0, 0)]
]:
spinham.add_44(
alpha=alpha,
beta=beta,
gamma=gamma,
epsilon=epsilon,
nu=nu,
_lambda=_lambda,
rho=rho,
parameter=-0.1 * np.ones((3, 3, 3, 3)),
)
return spinham
# Populate __all__ with objects defined in this file
__all__ = list(set(dir()) - old_dir)
# Remove all semi-private objects
__all__ = [i for i in __all__ if not i.startswith("_")]
del old_dir
