MuMax3-How-To

Installation, scripting, & data generation demo of computational micro and nanomagnetism in MuMax3. Formed & written by Onri Jay Benally.

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Main MuMax3 website: (https://mumax.github.io/index.html)

Uses code heavily-modified for clarity, inspired from: (https://github.com/mumax/3) & (https://mumax.github.io/examples.html)

Some examples computed in this repository were performed on an Nvidia (RTX 4070 Ti Super) GPU, connected externally (via a Thunderbolt 4 to PCIe x16 adapter) to a Microsoft Surface Pro 8, later upgraded to a Surface Pro 10. If you are curious about this kind of GPU-accelerated computing setup, then it is best to make sure your Windows machine is Thunderbolt 4 compatible or greater. Other examples were computed directly in the Google Colab environment using available GPU resources in Colab (T4 [free], L40, A100, etc.)

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To use MuMax3 in Google Colab, simply change the runtime type to one of the GPU accelerators and enter this into the first code cell:

#@title Check GPU + driver
!nvidia-smi --query-gpu="name,driver_version,compute_cap" --format=csv

Then, enter this into the second code cell:

#@title Install MuMax³ (MuMax³ 3.10 CUDA 10.1)
# Download the mumax3 binary
!wget -q https://mumax.ugent.be/mumax3-binaries/mumax3.10_linux_cuda10.1.tar.gz
!tar -xvf mumax3.10_linux_cuda10.1.tar.gz
!rm mumax3.10_linux_cuda10.1.tar.gz
!rm -rf mumax3.10 && mv mumax3.10_linux_cuda10.1 mumax3.10

# Update the PATH environment variable
import os
os.environ["PATH"] += ":/content/mumax3.10"

Now you can write the MuMax3 code and Python visualization scripts in the remaining cells. See the Google Colab notebook examples for more information.

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Some Google Colab Notebooks
Run MuMax3 on the Cloud
Example of Hysteresis Loop Data Imported from a Local MuMax3 Installation
Hysteresis Loop for Dy and Tb Micromagnets, Computed on the GPU Using MuMax3 Installed in Google Colab
Prediction of Temperature Dependence for Dy and Tb, Computed on the GPU Using MuMax3 Installed in Google Colab

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How to Install & Run MuMax3 Locally by Onri
Video Tutorial on How to Install MuMax3 Locally Step-by-Step
The Official MuMax3 Tutorials
Standard Problems from the Center for Theoretical and Computational Materials Science (CTCMS)
Video Example of Onri's MuMax3 Hysteresis Plots in Python
Example MuMax3 Script in TXT Format
Video Animation of Magnetic Orders
Explanation of Hysteresis Curves & Coercivity
Micromagnetism Overview

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If MuMax3 is installed already, start the GUI by typing the following 2 lines into a non-admin command prompt or non-admin PowerShell:

cd <directory_to_your_MuMax3_file>

mumax3 -i <your_MuMax3_TXT_file_name.txt>

Note: MuMax3 scripts can be written as TXT file types. The above script will load and automatically run the script into a browser.

Online OVF file type visualization: (https://mumax.ugent.be/mumax-view). While using the viewer, you can load multiple OVF files to play an animation of the magnetization frame capture.

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Magnetic Unit Comparison Table

Quantity	Symbol	CGS Unit	SI Unit
Field	$H$	$\mathrm{Oe}$	$\mathrm{A\cdot m^{-1}}$
Flux	$\Phi$	$\mathrm{Mx}$	$\mathrm{Wb}$
Flux density	$B$	$\mathrm{G}$	$\mathrm{T}$
Magnetic moment	$m$	$\mathrm{emu}$	$\mathrm{A\cdot m^{2}}$
Magnetization per unit volume	$M$	$\mathrm{emu\cdot cm^{-3}}$	$\mathrm{A\cdot m^{-1}}$
Volume saturation magnetization	$M_{\mathrm{s}}$	$\mathrm{emu\cdot cm^{-3}}$	$\mathrm{A\cdot m^{-1}}$
Magnetization per unit mass	$\sigma$	$\mathrm{emu\cdot g^{-1}}$	$\mathrm{A\cdot m^{2}\cdot kg^{-1}}$
Mass saturation magnetization	$\sigma_{\mathrm{s}}$	$\mathrm{emu\cdot g^{-1}}$	$\mathrm{A\cdot m^{2}\cdot kg^{-1}}$
Magnetic polarization	$J$	$\mathrm{emu\cdot cm^{-3}}$	$\mathrm{T}$
Saturation magnetic polarization	$J_{\mathrm{s}}$	$\mathrm{emu\cdot cm^{-3}}$	$\mathrm{T}$
Volume susceptibility	$\chi_{\mathrm{v}}$	$\mathrm{emu\cdot Oe^{-1}\cdot cm^{-3}}$	dimensionless
Mass susceptibility	$\chi_{\mathrm{m}}$	$\mathrm{cm^{3}\cdot g^{-1}}$	$\mathrm{m^{3}\cdot kg^{-1}}$
Permeability	$\mu$	$\mathrm{G\cdot Oe^{-1}}$	$\mathrm{T\cdot m\cdot A^{-1}}$
Relative permeability	$\mu_{\mathrm{r}}$	dimensionless	dimensionless
Energy density	$W$	$\mathrm{erg\cdot cm^{-3}}$	$\mathrm{J\cdot m^{-3}}$
Demagnetizing factor	$N$	dimensionless	dimensionless
Energy product	$(BH)$	$\mathrm{MG\cdot Oe}$	$\mathrm{kJ\cdot m^{-3}}$

Mx = maxwell, G = gauss, Oe = oersted, Wb = weber, T = tesla, m = meter, A = ampere, J = joule, kg = kilogram, g = gram, cm = centimeter, emu = electromagnetic unit.

Magnetic Conversion Table

Quantity	Symbol	Conversion
Field	$H$	$\dfrac{\mathrm{Oe}}{\mathrm{A}\cdot\mathrm{m}^{-1}}=\dfrac{10^{3}}{4\pi}=79.6$
Flux	$\Phi$	$\dfrac{\mathrm{Mx}}{\mathrm{Wb}}=\dfrac{\mathrm{Mx}}{\mathrm{V}\cdot\mathrm{s}}=10^{-8}$
Flux density	$B$	$\dfrac{\mathrm{G}}{\mathrm{T}}=\dfrac{\mathrm{G}}{\mathrm{Wb}\cdot\mathrm{m}^{-2}}=10^{-4}$
Magnetic moment	$m$	$\dfrac{\mathrm{emu}}{\mathrm{A}\cdot\mathrm{m}^{2}}=\dfrac{\mathrm{erg}\cdot\mathrm{Oe}^{-1}}{\mathrm{A}\cdot\mathrm{m}^{2}}=\dfrac{10,\mathrm{A}\cdot\mathrm{cm}^{2}}{\mathrm{A}\cdot\mathrm{m}^{2}}=\dfrac{\mathrm{emu}}{\mathrm{J}\cdot\mathrm{T}^{-1}}=10^{-3}$
Magnetization per unit volume	$M$	$\dfrac{\mathrm{emu}\cdot\mathrm{cm}^{-3}}{\mathrm{A}\cdot\mathrm{m}^{-1}}=\dfrac{\left(\mathrm{erg}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{cm}^{-3}}{\mathrm{A}\cdot\mathrm{m}^{-1}}=10^{3}$
Volume saturation magnetization	$M_{\mathrm{s}}$	$\dfrac{\mathrm{emu}\cdot\mathrm{cm}^{-3}}{\mathrm{A}\cdot\mathrm{m}^{-1}}=\dfrac{\left(\mathrm{erg}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{cm}^{-3}}{\mathrm{A}\cdot\mathrm{m}^{-1}}=10^{3}$
Magnetization per unit mass	$\sigma$	$\dfrac{\mathrm{emu}\cdot\mathrm{g}^{-1}}{\left(\mathrm{A}\cdot\mathrm{m}^{2}\right)\cdot\mathrm{kg}^{-1}}=\dfrac{\left(\mathrm{erg}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{g}^{-1}}{\left(\mathrm{A}\cdot\mathrm{m}^{2}\right)\cdot\mathrm{kg}^{-1}}=1$
Mass saturation magnetization	$\sigma_{\mathrm{s}}$	$\dfrac{\mathrm{emu}\cdot\mathrm{g}^{-1}}{\left(\mathrm{A}\cdot\mathrm{m}^{2}\right)\cdot\mathrm{kg}^{-1}}=\dfrac{\left(\mathrm{erg}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{g}^{-1}}{\left(\mathrm{A}\cdot\mathrm{m}^{2}\right)\cdot\mathrm{kg}^{-1}}=1$
Magnetic polarization	$J$	$\dfrac{\mathrm{emu}\cdot\mathrm{cm}^{-3}}{\mathrm{T}}=\dfrac{\left(\mathrm{erg}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{cm}^{-3}}{\mathrm{T}}=10^{3}\mu_{0}=4\pi\cdot10^{-4}$
Saturation magnetic polarization	$J_{\mathrm{s}}$	$\dfrac{\mathrm{emu}\cdot{cm}^{-3}}{\mathrm{T}}=\dfrac{\left(\mathrm{erg}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{cm}^{-3}}{\mathrm{T}}=10^{3}\mu_{0}=4\pi\cdot10^{-4}$
Volume susceptibility	$\chi_{\mathrm{v}}$	$\dfrac{\left(\mathrm{emu}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{cm}^{-3}}{\left(\mathrm{A}\cdot\mathrm{m}^{2}\right)\cdot\left(\mathrm{A}\cdot\mathrm{m}^{-1}\right)^{-1}\cdot\mathrm{m}^{-3}}=4\pi$
Mass susceptibility	$\chi_{\mathrm{m}}$	$\dfrac{\left(\mathrm{emu}\cdot\mathrm{Oe}^{-1}\right)\cdot\mathrm{g}^{-1}}{\left(\mathrm{A}\cdot{m}^{2}\right)\cdot\left(\mathrm{A}\cdot\mathrm{m}^{-1}\right)^{-1}\cdot\mathrm{kg}^{-1}}=4\pi\cdot10^{-3}$
Permeability	$\mu=\dfrac{B}{H}$	$\dfrac{\mathrm{G}\cdot\mathrm{Oe}^{-1}}{\mathrm{T}\cdot\left(\mathrm{A}\cdot\mathrm{m}^{-1}\right)^{-1}}=\mu_{0}=4\pi\cdot10^{-7}$
Relative permeability (SI)	$\mu_{\mathrm{r}}$	$\dfrac{\mu_{\mathrm{SI}}}{\mu_{0}}=\mu_{\mathrm{r}}=\mu_{\mathrm{cgs}}$
Energy density	$W$	$\dfrac{\mathrm{erg}\cdot\mathrm{cm}^{-3}}{\mathrm{J}\cdot\mathrm{m}^{-3}}=0.1$
Demagnetizing factor	$N$	$\dfrac{N_{\mathrm{cgs}}}{N_{\mathrm{SI}}}=4\pi$
Energy product	$(BH)$	$\dfrac{\mathrm{G}\cdot\mathrm{Oe}}{\mathrm{T}\cdot\left(\mathrm{A}\cdot\mathrm{m}^{-1}\right)}=\dfrac{\mathrm{G}\cdot\mathrm{Oe}}{\mathrm{J}\cdot\mathrm{m}^{-3}}=4\pi\cdot10^{1}=126$ $\dfrac{\mathrm{MG}\cdot\mathrm{Oe}}{\mathrm{kJ}\cdot\mathrm{m}^{-3}}=4\pi\cdot10^{-2}=0.126$

Mx = maxwell, G = gauss, Oe = oersted, Wb = weber, V = volt, s = second, T = tesla, m = meter, A = ampere, J = joule, kg = kilogram, g = gram, cm = centimeter, with $\mu_0=4\pi\times10^{-7}$.

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Hysteresis loop, from the local MuMax3 computation data:

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Hysteresis loops for dysprosium at various low temperatures, from the MuMax3 Colab computation:

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Ferromagnetic response for dysprosium and terbium at various low temperatures, from the MuMax3 Colab computation:

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Magnetic material visualization example ran in MuMax3:

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Magnetic geometry (300 nm x 100 nm x 3 nm) visualization in 3D using MuMax View in the browser:

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More examples:

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Related Animated Videos for Your Reference:
Tunnel Effect
Quantum Difference Between Metals & Insulators
Magnetic Orders
Frustrated Magnets
Bose-Einstein Condensation
Nuclear Magnetic Resonance (NMR)
Transmission Electron Microscopy
Scanning Tunneling Microscopy
Scanning Electron Microscopy
Atomic Force Microscopy