#!/usr/bin/env python
# coding: utf-8

# # Periodic boundary conditions
# 
# In this tutorial, we compute and relax a skyrmion in an interfacial-DMI (Cnv) material in a part of an infinitely large thin film.

# In[1]:


import oommfc as mc
import discretisedfield as df
import micromagneticmodel as mm


# We define mesh in cuboid through corner points `p1` and `p2`, and discretisation cell size `cell`.

# In[2]:


region = df.Region(p1=(-50e-9, -50e-9, 0), p2=(50e-9, 50e-9, 10e-9))
mesh = df.Mesh(region=region, cell=(5e-9, 5e-9, 5e-9), bc="xy")


# Here `bc="xy"` means that we have periodic boundary conditions along the `x` and `y` directions. The mesh we defined is:

# In[3]:


mesh.mpl()


# Now, we can define the system object by first setting up the Hamiltonian:

# In[4]:


system = mm.System(name="skyrmion")

system.energy = (
    mm.Exchange(A=1.6e-11)
    + mm.DMI(D=4e-3, crystalclass="Cnv_z")
    + mm.UniaxialAnisotropy(K=0.2e6, u=(0, 0, 1))
    + mm.Zeeman(H=(0, 0, 1e5))
)

system.energy


# Now, we need to define a function to define the initial magnetisation which is going to relax to skyrmion.

# In[5]:


def m_init(pos):
    """Function to set initial magnetisation direction:
    -z inside cylinder (r=10nm),
    +z outside cylinder.
    y-component to break symmetry.

    """
    x, y, z = pos
    if (x**2 + y**2) ** 0.5 < 10e-9:
        return (0, 0, -1)
    else:
        return (0, 0, 1)


system.m = df.Field(mesh, nvdim=3, value=m_init, norm=1.1e6)


# The initial magnetsation is:

# In[6]:


system.m.sel("z").mpl()


# Finally we can minimise the energy and plot the magnetisation.

# In[7]:


# minimize the energy
md = mc.MinDriver()
md.drive(system)

# Plot relaxed configuration: vectors in z-plane
system.m.sel("z").mpl()


# In[8]:


# Plot z-component only:
system.m.z.sel("z").mpl()


# Finally we can sample and plot the magnetisation along the line:

# In[9]:


system.m.z.line(p1=(-49e-9, 0, 0), p2=(49e-9, 0, 0), n=20).mpl()


# Finally let us compute the skyrmion number
# 
# $$S = \frac{1}{4\pi}\int\mathbf{m}\cdot\left(\frac{\partial \mathbf{m}}{\partial x} \times \frac{\partial \mathbf{m}}{\partial y}\right)dxdy$$

# In[10]:


import math

m = system.m.orientation.sel("z")

1 / (4 * math.pi) * (m.dot(m.diff("x").cross(m.diff("y")))).integrate()


# In[11]:


import discretisedfield.tools as dft

dft.topological_charge(system.m.sel("z"))


# In[12]:


dft.topological_charge(system.m.sel("z"), method="berg-luescher")