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

# # Negative exchange energy constant
# 
# In this tutorial, we show how to set up a negative value of exchange energy constant between subregions in the mesh. We start by importing the modules we are going to use. We import `random`, because we plan to initialise our magnetisation as a random state.

# In[1]:


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


# In order to make sure we always have the same random state generated, we set up the seed.

# In[2]:


random.seed(2)


# Our sample consists of three identical magnetic layers, which are (for some reason) coupled antiferomagnetically.

# In[3]:


p1 = (0, 0, 0)
p2 = (60e-9, 60e-9, 30e-9)
region = df.Region(p1=p1, p2=p2)
subregions = {
    "r1": df.Region(p1=(0, 0, 0), p2=(60e-9, 60e-9, 10e-9)),
    "r2": df.Region(p1=(0, 0, 10e-9), p2=(60e-9, 60e-9, 20e-9)),
    "r3": df.Region(p1=(0, 0, 20e-9), p2=(60e-9, 60e-9, 30e-9)),
}
mesh = df.Mesh(region=region, n=(20, 20, 9), subregions=subregions)

mesh.mpl.subregions()


# We use a dictionary to set up parameter $A$. For individual subregions, we use `r1`, `r2`, and `r3`, whereas to define $A$ between different subregions, we put a colon in dictionary key - for instance, `r1:r2`.

# In[4]:


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

A = 1e-12
Adict = {"r1": A, "r2": A, "r3": A, "r1:r2": -A, "r2:r3": -A}

system.energy = mm.Exchange(A=Adict) + mm.UniaxialAnisotropy(K=1e4, u=(1, 0, 0))


# As we mentioned previously, we are going to initialise the system using a random state.

# In[5]:


def m_random(point):
    return [2 * random.random() - 1 for i in range(3)]


system.m = df.Field(mesh, nvdim=3, value=m_random, norm=8e6)

system.m.sel("y").mpl(figsize=(12, 3))


# Now, we can minimise the system's energy and plot its magnetisation.

# In[6]:


md = mc.MinDriver()
md.drive(system)

system.m.sel("y").mpl(figsize=(12, 3))


# We can see that all three regions are uniformly magnetised, but mutually coupled antiferromagnetically.