Magnetic layers

A layer can be given a magnetisation, so that the two neutron spin states see different scattering length densities. This page covers the Model page controls; loading and fitting measured spin channels is described in polarised data.

Note

Magnetic layers can only be calculated by refl1d. refnx has no magnetism, so the app asks to switch the project’s calculation engine the first time a layer is made magnetic.

The Magnetism group

The Magnetism group is in the basic controls of the Model page, below the layer editor. It is titled after the assembly currently selected in the Layer editor, for example Magnetism: Multi-layer, and shows one row per layer of that assembly.

Column	Meaning
No.	Position of the layer in the assembly.
Layer	Layer name, as in the Layer editor.
ρM/10⁻⁶Å⁻²	Magnetic scattering length density of the layer.
θM/°	In-plane angle of the magnetic moment.
Magn.	Makes the layer magnetic. Unticking it removes the magnetisation.

ρM and θM are only editable once Magn. is ticked.

Note

With the default in-plane guide field (270°), θM = 270° aligns the moment with the field, which produces no spin-flip scattering. This is the value to start from for a simple saturated film.

ρM from a magnetic material

ρM can also come from the layer’s material instead of being typed. Add magnetic material in the Materials group creates a material with a formula, a mass density and a Moment in Bohr magnetons per formula unit (bulk iron to start with: Fe, 7.874 g/cm³, 2.2 µB). The material editor shows the resulting ρM and the number density N: ρM = N × moment × 2.6991·10⁻⁵ Å.

Give a layer that material, make it magnetic, select its row and tick ρM from material below the table. The layer’s ρM then follows the material’s moment and density and is no longer editable in the table; θM stays the layer’s own, so two layers of one material can point different ways. Unticking keeps the current value.

The moment is the effective in-plane net moment per formula unit, which is the moment per atom only for a formula unit of one atom, such as Fe (Fe2 is one element but two atoms). In the Analysis table it is greyed out until some layer takes ρM from the material, and when the last such layer stops doing so the moment is taken out of the fit. If the material’s SLD is set directly (unticked SLD computed from formula and density), its density still sets ρM while a layer takes ρM from it; the data then constrain only density × moment, so ticking one of the two for fitting unticks the other. Without such a layer the density sets nothing and is greyed out too.

A layer whose ρM is given a constraint in the Analysis page no longer takes it from the material: ρM from material is unticked, and the constraint is kept when the layer’s material changes.

The guide field

Below the table, Guide field angle and Applied field (T) set the field of the current model (refl1d’s Aguide and H). They are shown while the current model has a magnetic layer and the engine is refl1d:

Guide field angle	Field direction
270° or −90° (default)	in the sample plane
90°	in the sample plane, reversed
0° or 180°	along the surface normal
anything else	tilted out of the sample plane

The applied field adds a Zeeman term along the field, so its effect depends on the field and its direction relative to the moments. Both appear in the Analysis parameter table, named after the model, and can be fitted; they are shown only while the model is magnetic and the engine is refl1d, and are taken out of the fit otherwise. The ORSO model language has no field, so model export warns when it is not the default.

Magnetic samples from ORSO files

Load sample reads an ORSO model’s magnetic_moment: a material with a formula, a density and a moment becomes a magnetic material, and its layer is magnetic with ρM from material ticked and θM = 270°, since the file has no direction. Whatever the import could not carry over (a moment without a density, an unknown unit, an ignored relative_density, magnetic layers in a repeated stack) is listed in a warning after the sample loads. A magnetic sample cannot be loaded while the engine cannot model magnetism: the load is refused with a message naming the engine to switch to, and the project is left as it was.

The moment angle slider

Selecting a magnetic row shows a slider below the table, spanning the whole 0-360° range of θM, with the guide field reference H → and the resulting arrow beside it - the same arrow the Structure tab draws. Its tooltip gives the angle both ways: φ from H, and the θM the table edits.

Dragging the slider sets θM, snapped to 5°; the text field remains the precise input. The slider is read-only - and says so in its tooltip - while a fit is running, or when θM follows a constraint, because then the parameter is not the user’s to set.

The slider edits θM itself, exactly as the table column does. The arrow beside it shows φ, the direction the moment physically points, so with a negative ρM the arrow points opposite the angle on the slider - the moment is reversed while the parameter stays where it was put.

Switching the calculation engine

Ticking Magn. while the project uses an engine that cannot model magnetism opens the Switch calculation engine? dialog. Accepting it makes the layer magnetic and switches the project to refl1d in one step - the page does not change under you.

Switching recalculates the reflectivity and makes any existing fit result stale; the sample and the loaded data are untouched. The engine can be switched back once no layer is magnetic any more.

The engine itself lives in the Calculation engine group of the advanced controls on the Model page (and in Analysis › Advanced, see simple fitting). Selecting an engine that cannot model magnetism while the sample still has magnetic layers is refused, with a message on both pages.

Fitting ρM and θM

ρM and θM appear in the Analysis parameter table like any other layer parameter, named after their assembly and model - for example Model Fe rho_m. They come with default limits, a fit checkbox and can be used in constraints. The parameter name filter accepts magnetic as a keyword to show only the magnetic parameters: ρM, θM, the material moments and the field.

Magnetic depth profiles

Once at least one layer is magnetic, the Magnetic profile group appears in the basic controls, below Magnetism. The same switches are repeated in Analysis › Advanced › Plot control, and the two share one selection.

• Show ρ ± ρM∥ - adds the nuclear SLD plus and minus the magnetic SLD along the field for each magnetic model to the SLD chart, dashed in the model’s colour. These are the potentials of the two spin states only when every moment is parallel to the field and there is no applied field; a moment across the field mixes the spin states instead. For non-magnetic layers, and for moments across the field, the two curves collapse onto the nuclear SLD.

• Show ρM - the magnetic SLD profile on its own.

• Show θM - the in-plane moment angle, on its own right-hand axis. θM is only defined where there is a moment, so the curve is drawn in pieces rather than joined across the gaps.

• Show R↑↑ and R↓↓ - splits each magnetic model’s reflectivity into its two non-spin-flip cross-sections on the Model page reflectivity chart, dashed in the model’s colour with their own legend rows. Off by default.

The y-range of the SLD chart covers every visible curve and grows when a curve is switched on, so ρ + ρM is never clipped. If no model is magnetic, the chart, its legend and the sidebar are unchanged.

Note

The refl1d calculator cannot repeat slabs that carry magnetism, so a magnetic model with a repeating multilayer has no magnetic depth profile at all - and therefore none of these curves. The Magnetic profile group reports the reason.

Note

For a magnetic sample the plain model curve is not an unpolarised average - the calculator returns the ↑↑ cross-section - so R↑↑ is drawn on top of it. The sidebar says so as well.

The Analysis reflectivity chart is unaffected by this switch: it already draws one calculated curve per measured spin channel when the experiment is polarised.

Which way the moments point

θM is a number, and a stack of numbers does not show at a glance whether a model is collinear, canted or twisted. The app therefore draws the moment as an arrow, in a single convention shared by every view:

• the arrows are a top view along the surface normal - a compass laid over the sample;

• screen right is the default guide field H (in the sample plane at 270°), and the angle drawn is φ, measured from it counterclockwise: φ = θM − 270°. The arrows stay in this frame when the field is changed; the H reference follows the field instead, pointing left for a reversed in-plane field and replaced by its angle when the field is tilted out of the sample plane;

• a negative ρM is the same moment reversed, so the arrow points the opposite way and the tooltip carries the signed parameter;

• a magnetic layer whose ρM is below 1 % of the largest one in the model gets a hollow dot - “magnetic, but no moment”: the direction of a zero-length vector means nothing. A layer with no magnetism at all gets nothing.

θM	Arrow	Physics
270° (default)	→ along H	collinear, no spin flip
90°	← against H	collinear reversed, no spin flip
0° / 180°	↑ / ↓	fully transverse, maximal spin flip
40°	↖ (φ = 130°)	canted

Every arrow view shows the H reference on screen. Tooltips lead with φ, then the θM and signed ρM the sidebar edits, then the part of the moment along the field and the size of the part across it - what the non-spin-flip and the spin-flip channels mostly see.

Arrows are constant length everywhere: they encode direction only. The magnitude is the ρM curve’s job, and the exact value is in the tooltip.

On the Structure tab

Each magnetic layer’s box gets an arrow between its name and its thickness annotation. This needs no switch: attaching magnetism is the request to see it. Boxes too short for a readable glyph drop the arrow and keep it in the tooltip, and the box layout of a non-magnetic sample is unchanged.

The Structure tab draws the current model; switch models in the header to inspect another one. A repeating multilayer that the tab collapses to its repeat unit shows one arrow per drawn box - the direction of the repeat unit, which every repeat shares.

Gradient layers get no arrow. A gradient has no single moment of its own, and one “representative” arrow would be actively misleading when its slices oppose; the ρM(z) and θM(z) curves remain the truth for graded structures.