""" Ferromagnetic chain example """


# A ferromagnetic chain is the simplest system that we can simulate with pySpinW, and it makes a good introduction
# to setting up a calculation.

# Import the main pySpinW module, doing this will give access to the majority of pySpinW methods and classes
# that are needed for most tasks.
from pyspinw import *

# Create a 1 angstrom cubed unit cell, with angles of 90 deg
unit_cell = UnitCell(1,1,1)

# Define a "site" (atom/ion/spin) within the unit cell, the position doesn't matter for our system so
# we just choose the centre, $(1/2,1/2,1/2)$. In this case, we have a spin 1 system, with the spin pointing the z direction.
# It is also possible to definite the element type and colour for viewing here.

only_site = Site(1 / 2, 1 / 2, 1 / 2, 0, 0, 1, name="X")

# We now create a `Structure` object.
# `Structure` objects contain information about the crystal structure and spins, and
# contains the sites, the unit cell, the symmetry group and the magnetic unit cell, or "supercell".
# The symmetry group will default to P1, and the supercell to the "trivial supercell" (i.e. where there is no
# magnetic ordering other than that specified in the unit cell).

structure = Structure([only_site], unit_cell=unit_cell)
# Note that in this example, we will see a warning about the choice of unit cell.
# This is because we have chosen a 1x1x1 unit cell, which results in more symmetries than P1 specifies.
# It is not of any consequence.

# We can look at the structure using the viewer, we'll use the `copies` parameter to show five copies in $x$ direction
view(structure, copies=(5,1,1))

# We now come to defining the exchanges, which we will need as a list.
# There are various exchange classes that we can use.
# They all specify the two sites involved by referencing site objects and a "cell offset".
# The offset is used to specify that an exchange is between sites in differing cells,
# and it is zero (same unit cell) by default.
#
# In this case we use the `HeisenbergExchange` object, which defines the exchange matrix
# with a single parameter, "j", which has the same sign as the energy of the exchange, i.e.
# it is negative for ferromagnetic exchanges and positive for antiferromagnetic exchanges.
#
# We only have one exchange, between neighbouring cells in the $x$ direction.

exchanges = [HeisenbergExchange(only_site, only_site, cell_offset=(1,0,0), j=-1)]

# We can also do this using `generate_exchanges`, which makes some things easier for bigger systems and
# is more like the syntax in MATLAB spinW.
# This function is overkill in our case, but we can do the same thing.
# It will generate exchanges of the type specified, with the parameters specified.
# In this case we constrain by distance, but other options are available,
# and we apply a filter to pick out only exchanges that lie in (1,0,0) direction.

exchanges = generate_exchanges(sites=[only_site],
                               unit_cell=unit_cell,
                               max_distance=1.1,
                               exchange_type=HeisenbergExchange,
                               j=-1,
                               direction_filter=filter([1,0,0]))

# Next we construct the `Hamiltonian` object, this contains the magnetic structure (`Structure`)
# and a list of exchanges. It is also possible to specify single ion anisotropies here.

hamiltonian = Hamiltonian(structure, exchanges)

# We can now see the exchanges in the viewer by viewing the hamiltonian object
view(hamiltonian, copies=(5,1,1))


# We'll now plot the magnon spectrum of this chain.
#
# To make a spaghetti plot we need to define a path though reciprocal space,
# which we define here in lattice coordinates.
# We look at the $x$ direction (in the same direction as the exchanges) and go between 0 and 1 reciprocal lattice units.
path = Path([[0,0,0], [1,0,0]])

hamiltonian.spaghetti_plot(path, dE=0.4)