Ferrolith on ferrolith

Demagnetising field

Sun, 15 Mar 2026 00:00:00 +0000

Convergence of the volume-averaged demagnetising field $\langle H_z \rangle$ for uniformly magnetised bodies ($M_s$ = 800,000 A/m, magnetised along $z$). The analytical reference is $\langle H_z \rangle = -\mu_0 M_s^2 N_z$ where $N_z$ is the demagnetising factor.

All methods use the same underlying FEM mesh for the body region. The x-axis shows the number of nodes in the body (material region), giving a fair comparison between plain and shell meshes. Field values are volume-weighted averages using the FEM nodal volumes.

Meshes

Sun, 15 Mar 2026 00:00:00 +0000

All meshes were generated using gmsh and can be downloaded here: meshes.tar.bz2.

Each mesh set contains 15 meshes with logarithmically spaced characteristic lengths from coarse to fine. Plain meshes contain only the magnetic body. Shell meshes add a “space” region (free space around the body) and a “transform” region (coordinate-transformed shell mapping to infinity).

Sphere#

Unit sphere (radius 0.5) centered at the origin.

Geometry: Radius: 0.5
Extent: [-0.49, 0.49] × [-0.50, 0.50] × [-0.50, 0.50]

Getting Started

Sun, 08 Mar 2026 00:00:00 +0000

Building the Python Module#

Ferrolith requires a C++17 compiler, CUDA (tested with 12.5), and NetCDF. All other dependencies (Eigen, H2Lib, AMGCL, pybind11) are fetched automatically by CMake.

cmake -B build -DFERROLITH_PYTHON=ON
cmake --build build -j$(nproc)

To manually set the GPU architecture:

cmake -B build -DFERROLITH_PYTHON=ON \
 -DFERROLITH_FIND_CUDA_ARCH=OFF \
 -DFERROLITH_SET_CUDA_ARCHS="61;75"

The compiled module is placed in build/python/. Add it to your Python path:

export PYTHONPATH=build/python:$PYTHONPATH

Quick Start#

The simplest way to compute a demagnetizing field is with DemagFieldFK:

µMAG Standard Problem #2

Mon, 16 Mar 2026 00:00:00 +0000

μMAG Standard Problem #2 studies the switching behaviour of a Permalloy thin-film rectangular element (length $5d$, width $d$, thickness $0.1d$) as a function of the particle size $d$ measured in exchange lengths $l_{\mathrm{ex}} = \sqrt{2A / \mu_0 M_s^2}$. A saturating field is applied along the diagonal of the film (1,1,0.1) direction, then reversed to obtain the hysteresis loop.

The key results are:

$H_c / M_s$ — coercive field (normalised by $M_s$)
$M_{rx} / M_s$ — remanent magnetisation, $x$-component
$M_{ry} / M_s$ — remanent magnetisation, $y$-component

In the small-particle limit ($d/l_{\mathrm{ex}} \to 0$) the magnetisation is nearly uniform and a 3D Stoner-Wohlfarth analysis gives $H_c / M_s = 0.05707$.

µMAG Standard Problem #3

Mon, 16 Mar 2026 00:00:00 +0000

μMAG Standard Problem #3 determines the single domain limit of a cubic magnetic particle — the critical edge length $L$ (in units of exchange length $l_{\mathrm{ex}} = \sqrt{A / K_m}$, where $K_m = \frac{1}{2} \mu_0 M_s^2$) at which the “flower state” and “vortex state” have equal total energy.

The uniaxial anisotropy constant is $K_u = 0.1,K_m$ with the easy axis along $z$. All energies are normalised by $K_m L^3$.

The expected result is $L \approx 8.47,l_{\mathrm{ex}}$.

Python API Reference

Sat, 14 Mar 2026 00:00:00 +0000

Field Classes#

All field classes follow the same interface:

compute(magnetization) – returns the effective field as an (n, 3) array
energy(magnetization) – returns the energy as a scalar (Joules)

Magnetization m is always an (n, 3) array of unit vectors.

DemagFieldFK#

Demagnetizing field via the Fredkin-Koehler scalar potential method. This is the primary solver and supports multiple BEM backends.

DemagFieldFK(coordinates, elements, Ms, *,
 scale=1.0, tolerance=1e-8,
 solver=SolverType.AMG_CG,
 h2_cache="", h2params=None,
 fmm_params=None, backend=None,
 tree_type=None)

Parameter	Type	Description
`coordinates`	`(n, 3)`	Node positions
`elements`	`(ntet, 4)`	Tetrahedral connectivity, 0-indexed
`Ms`	`(n,)`	Saturation magnetization per node (A/m)
`scale`	`float`	Length unit: `1.0` = m, `1e-9` = nm
`tolerance`	`float`	Iterative solver tolerance
`solver`	`SolverType`	GPU solver preset
`h2_cache`	`str`	H2 matrix cache file path (empty = no caching)
`h2params`	`ParamsFKH2Lib`	H2-matrix compression parameters
`fmm_params`	`ParamsFKFMM`	GPU FMM parameters
`backend`	`BemBackend`	BEM backend (default: `FMM_GPU`)
`tree_type`	`TreeType` or `str`	FMM tree strategy

Additional methods:

µMAG Standard Problem #4

Mon, 16 Mar 2026 00:00:00 +0000

μMAG Standard Problem #4 studies the time-dependent magnetisation reversal of a thin-film Permalloy rectangle (500 nm × 125 nm × 3 nm) with material parameters $M_s$ = 8 × 10⁵ A/m, $A$ = 1.3 × 10⁻¹¹ J/m, $\alpha$ = 0.02.

The system is initialised in an S-state (obtained by relaxing from saturation along the [1, 1, 1] direction) and then subjected to a reversing field:

Field 1: $\mu_0 H$ = −25 mT at 170° from the $+x$ axis
Field 2: $\mu_0 H$ = −36 mT at 190° from the $+x$ axis

The reported quantities are the spatially averaged magnetisation components $\langle M_x \rangle / M_s$, $\langle M_y \rangle / M_s$, $\langle M_z \rangle / M_s$ as a function of time.

Heistracher et al. — Domain wall pinning

Mon, 16 Mar 2026 00:00:00 +0000

The Heistracher et al. standard problem tests domain wall pinning at the interface of a two-phase magnetic rod. It is sensitive to discontinuities in the exchange constant $A$, uniaxial anisotropy $K$, and spontaneous polarisation $J_s$ between phases, making it a targeted test for correct interface handling.

P. Heistracher, C. Abert, F. Bruckner, T. Schrefl, D. Suess, J. Magn. Magn. Mater. 548, 168875 (2022).

Problem setup#

A cuboid rod (80 nm × 1 nm × 1 nm) is divided into two equal halves: