Out-of-plane Hysteresis loop in Mumax plus

[Seok In YOON]

Dear Mumax community members,

Hello, I am Seok In YOON.

I am now trying to use Mumax+ in the Google Colab Pro system to draw the hysteresis loop about the FM layer. 

Unfortunately, I am unable to draw the correct out-of-plane hysteresis loop.

Could you help me find where my code is wrong?

from mumaxplus import Ferromagnet, Grid, World

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

# Simulation parameter

world = World(cellsize=(1e-9, 1e-9, 1e-9))

grid_size = (256, 64, 1)

fm = Ferromagnet(world, Grid(grid_size))

fm.msat = 750e3

fm.aex = 15e-12

fm.dind = 1e-3

fm.ku1 = 5e5

fm.alpha = 0.03

fm.anisU = (0, 0, 1)

# initial magnetization and direction

init_mag = np.zeros(fm.grid.size + (3,))

init_mag[:, :, :, 0] = 0.0

init_mag[:, :, :, 1] = 0.0

init_mag[:, :, :, 2] = 1.0

fm.magnetization.set(init_mag.transpose(3, 2, 1, 0))

fm.minimize()

# Field sweep simulation

B_max = 2  # T

B_step = 0.04  # T

field_sweep = np.concatenate([

    np.arange(0, B_max + B_step, B_step),

    np.arange(B_max, -B_max - B_step, -B_step),

    np.arange(-B_max, B_max + B_step, B_step)

])

loop_log = []

for B in field_sweep:

    fm.bias_magnetic_field.set((0, 0, B))  # 반드시 .set() 사용

    fm.minimize()

    m = np.mean(fm.magnetization.get(), axis=(1, 2, 3))

    loop_log.append([B, m[2]])

# convert the data

df = pd.DataFrame(loop_log, columns=["B_T", "mz"])

# draw the hysteresis loop

plt.figure(figsize=(10, 6))

plt.plot(df['B_T'], df['mz'], 'b.-', linewidth=2, markersize=4)

plt.xlabel('External Magnetic Field B (Tesla)', fontsize=12)

plt.ylabel('Normalized Magnetization mz', fontsize=12)

plt.title('Magnetic Hysteresis (M-H) Loop', fontsize=14)

plt.grid(True, alpha=0.3)

plt.axhline(y=0, color='k', linestyle='--', alpha=0.5)

plt.axvline(x=0, color='k', linestyle='--', alpha=0.5)

plt.show()

[Josh Lauzier]

Hi,

I haven't had the chance to test out Mumax+ extensively yet, but my guess is that it is the same symmetry breaking issue previously reported in mumax3. You can fix it by applying a very small canting to the field, or adding some noise. For more details see these previous discussions.

Best,
Josh L.

[Seok In YOON]

Thank you!

I was able to obtain the correct hysteresis loop!

Sincerely yours,

Seok In YOON

2025년 7월 21일 월요일 오전 7시 21분 28초 UTC+9에 Josh Lauzier님이 작성: