MERRILL
Micromagnetic Earth Related Robust Interpreted Language Laboratory

Glossary

Key terms in micromagnetics, rock magnetism, and the MERRILL workflow — a quick reference for new users

New to the field? Start with the tutorials for hands-on context, or browse Publications for the underlying science.

Terms are grouped by topic. Click any letter in the index to jump to that section.

A

Anisotropy (magnetocrystalline)
The dependence of a crystal's magnetic energy on the orientation of magnetisation relative to its crystal axes. In magnetite, cubic magnetocrystalline anisotropy favours alignment along ⟨111⟩ directions.
Aspect ratio (E-value)
A measure of grain elongation used in MERRILL mesh libraries. E00 = equidimensional (sphere or cube); E50 = strongly elongated. Higher aspect ratios increase shape anisotropy.

C

CNN (Convolutional Neural Network)
In the FORCINN context, a deep learning model trained on simulated FORC diagrams to invert experimental data and return grain assembly statistics (size mean, aspect ratio mean).
Coercive field / Coercivity (Hc)
The applied field required to reduce the net magnetisation of a sample to zero after saturation. A key rock magnetic parameter measured from hysteresis loops.
Coercivity of remanence (Hcr)
The field required to reduce the saturation isothermal remanent magnetisation (SIRM) to zero. Always ≥ Hc; the ratio Hcr/Hc is a standard grain-size indicator.

D

DCD (DC Demagnetisation curve)
A remanence curve measuring how a back-field progressively demagnetises a sample that was previously given a SIRM. Used together with IRM acquisition to construct the Wohlfarth-Cisowski test and derive Hcr.
Demagnetising energy
The magnetostatic self-energy that arises from the divergence of magnetisation inside and at the surface of a grain. MERRILL computes this via finite-element integration of the stray field.
Domain wall
A transition region between two uniformly or non-uniformly magnetised zones in a grain. The wall width is determined by the balance between exchange energy (favouring gradual rotation) and anisotropy energy (favouring fast alignment with easy axes).

E

Energy barrier
The energy difference between a local minimum and the saddle point of the energy landscape separating two remanent states. Determines thermal stability and blocking temperature. Calculated in MERRILL by nudged-elastic-band (NEB) path search.
Exchange energy / Exchange stiffness (A)
Quantum-mechanical energy penalising non-parallel spin alignment between neighbouring atoms. Characterised by the exchange stiffness constant A (J m⁻¹). For magnetite, A ≈ 1.33 × 10⁻¹¹ J m⁻¹.
Exchange length (lex)
The characteristic length at which exchange and magnetostatic energies balance: lex = √(2A / μ₀Ms²). Sets the minimum feature size that must be resolved by the mesh.

F

FEM (Finite Element Method)
A numerical method that discretises a continuous domain (here: a magnetic grain) into small elements (tetrahedra) and solves differential equations on each. MERRILL uses FEM to compute magnetisation distributions and field energies at grain scale.
FORC (First-Order Reversal Curve)
A two-dimensional magnetisation measurement protocol in which the sample is saturated, then brought to a reversal field Hr, then swept back to saturation — repeated for a grid of Hr values. The resulting FORC diagram encodes coercivity and interaction field distributions within a grain population.
FORC diagram
The contour map of the mixed second derivative of magnetisation ∂²M/∂H∂Hr plotted on (Hc, Hb) or (Hr, H) axes. Interpreted as a fingerprint of grain domain state and interaction state.
FORCINN
The FORC CNN Inversion pipeline bundled with this website. Preprocesses raw FORC data, then uses a trained CNN to invert the diagram and extract grain assembly statistics (grain size distribution, aspect ratio).

H

Hysteresis loop
A plot of magnetisation M vs applied field H as the field is cycled between positive and negative saturation. Area enclosed by the loop is proportional to energy dissipated per cycle. Parameters extracted: Ms, Mrs, Hc.
Hb (Interaction field / bias field)
The horizontal axis of a FORC diagram in the standard Hc–Hb coordinate system; reflects the mean interaction field experienced by a grain. Spread in Hb indicates inter-grain magnetostatic interactions.

I

IRM (Isothermal Remanent Magnetisation)
Remanent magnetisation acquired by applying a DC field at constant temperature. Acquisition curves (IRM vs applied field) reveal the coercivity spectrum of a magnetic mineral mixture.

M

Magnetite (Fe3O4)
The most common magnetic mineral in rocks and the primary target material for MERRILL simulations. Cubic symmetry; saturation magnetisation Ms ≈ 480 kA m⁻¹ at room temperature.
MERRILL (Micromagnetic Earth Related Robust Interpreted Language Laboratory)
The finite-element micromagnetic modelling package developed at the University of Edinburgh by the Wyn Williams group. Designed for rock and planetary magnetism applications at grain scale.
Micromagnetics
A continuum theory of magnetism that treats magnetisation as a continuous vector field and minimises a free energy functional (exchange + anisotropy + magnetostatic + Zeeman) to find stable domain configurations. MERRILL solves the micromagnetic problem at grain scale using FEM.
Mrs / Ms ratio (squareness)
Ratio of saturation remanence to saturation magnetisation; ranges from 0 (superparamagnetic) to 0.5 (SD uniaxial) to 1 (magnetically hard). Used in Day diagrams for domain state classification.

N

NEB (Nudged Elastic Band)
A numerical method for finding transition pathways and saddle points on a high-dimensional energy surface. MERRILL uses NEB to calculate switching fields and energy barriers between remanent states.

P

Palaeomagnetic recording
The process by which magnetic grains in cooling rocks lock in a record of the ambient geomagnetic field direction and intensity. MERRILL's energy barrier calculations help assess whether a given grain geometry provides reliable recordings.
PATRAN mesh format
The tetrahedral mesh format natively supported by MERRILL. Meshes are created externally (e.g. with Netgen or GMSH) and exported in PATRAN format before being passed to a MERRILL script.
PSD (Pseudo-Single Domain)
A colloquial term for the intermediate grain-size range between single-domain (SD) and multi-domain (MD) behaviour, characterised by vortex or flower magnetisation states. Most natural magnetic grains fall in this range.

S

SD (Single Domain)
A grain small enough that the magnetisation is uniformly aligned throughout. Below the critical SD size (≈ 70–100 nm for magnetite equidimensional grains), the cost of forming domain walls exceeds the magnetostatic energy reduction.
SIRM (Saturation IRM)
The maximum remanent magnetisation acquired after exposure to a very large field; proportional to the concentration of magnetic minerals after normalisation for mineralogy.
Shape anisotropy
Magnetic anisotropy arising from the non-spherical shape of a grain. In elongated grains, the demagnetising energy is minimised when magnetisation lies along the long axis, creating an effective easy axis.

T

Titanomagnetite (Fe3-xTixO4)
A solid solution between magnetite (x = 0) and ulvöspinel (x = 1). Commonly found in oceanic basalts. Increasing Ti content lowers Ms, lowers the Curie temperature, and changes magnetic anisotropy constants — all configurable in MERRILL.

V

Vortex state
A magnetisation configuration in which the magnetisation curls around a central axis, forming a flux-closed loop. Characteristic of PSD grains; stable over a range of sizes between the SD and MD states. MERRILL can compute and visualise vortex states directly.
VTK (Visualization Toolkit format)
A file format used by MERRILL for exporting magnetisation vector fields. VTK files can be opened directly in ParaView or TecPlot for 3D visualisation of domain structures.