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.