def hysteresis_loop(h_min, h_max, num_h_points, energy_func, derivative, second_derivative, min_x=-pi, max_x=pi, x_steps=50, args=()):
"""Calculate the hysteresis loop for the Stoner Wohlfarth model
Params:
h_min (float): Minimum field
h_max (float): Maximum field
num_h_points (int): Number of field points
energy_func (function):
derivative (function):
second_derivative (function):
min_x (float): Minimum value in which to search for roots
max_x (float): Maximum value in which to search for roots
x_steps (int): Number of trials to do between [min_x, max_x] for finding roots
args (tuple): Extra arguments that will be passed to the energy function and its derivatives
Returns:
np.ndarray: The hysteresis loop as (h, m) pairs
"""
h_values = np.linspace(h_max, h_min, num_h_points)
mh_curve = []
mag = -1
for h in h_values:
_, mag = find_magnetization(energy_func, derivative, second_derivative, mag, min_x, max_x, x_steps, args=((h,) + args))
mh_curve.append((h, mag))
return np.array(mh_curve)
def hysteresis_loop(H, H_dir, Ku_dir, hs, energy_func, derivative, second_derivative, min_x=-pi, max_x=pi, x_steps=50, args=()):
"""Calculate the hysteresis loop for the Stoner Wohlfarth model.
Params:
H (list-like): Field values that we will be simulating
H_dir (list-like (len 3)): The direction of the magnetic field
Ku_dir (list-like (len 3)): The direction of the uniaxial anisotropy
K_shape_dir (list-like (len 3)): The direction of the shape anisotropy
energy_func (function):
derivative (function):
second_derivative (function):
min_x (float): Minimum value in which to search for roots
max_x (float): Maximum value in which to search for roots
x_steps (int): Number of trials to do between [min_x, max_x] for finding roots
args (tuple): Extra arguments that will be passed to the energy function and its derivatives
Returns:
np.ndarray: The hysteresis loop as (h, mx, my, mz) tuples
"""
# Create the transformation matrix that will allow us to convert from problem space into xyz coords
H_dir = np.array(H_dir)
Ku_dir = np.array(Ku_dir)
# If the two vectors are parallel then we cannot define the cross product.
if np.all(H_dir == Ku_dir):
# Just use the 'up' vector (0, 0, 1) or the 'left' vector (1, 0, 0)
if np.all(H_dir == [0, 0, 1]):
v_dir = np.cross(H_dir, [1, 0, 0])
else:
v_dir = np.cross(H_dir, [0, 0, 1])
else:
v_dir = np.cross(H_dir, Ku_dir)
v_dir = v_dir/np.linalg.norm(v_dir)
Kp_dir = np.cross(v_dir, H_dir)
Kp_dir = Kp_dir/np.linalg.norm(Kp_dir)
U = np.array([v_dir, H_dir, Kp_dir]).T
# Alpha is the angle between Ku and H
alpha = np.arccos(np.dot(Ku_dir, H_dir))
# Alpha prime is the angle between Kshape and H
alpha_prime = alpha#np.dot(Kshape_dir, H_dir)
mh_curve = []
mag = -1
for h in sorted(H):
_, mag = find_magnetization(energy_func, derivative, second_derivative, mag, min_x, max_x, x_steps, args=(h, hs, alpha, alpha_prime))
mag_angle = np.arccos(mag)
m = (0, cos(mag_angle), sin(mag_angle))
vals = (h,U.dot(m)[0], U.dot(m)[1], U.dot(m)[2])
mh_curve.append(vals)
return np.array(mh_curve)
