Vector-polarisation mode

Three EMU vector-polarisation projections P_x, P_y, P_z overlaid

Synthetic EMU-style three-axis polarisation projections overlaid in the central plot. The P_z trace carries the dominant slow exponential decay, P_x carries a weak transverse oscillation, and P_y is centred near zero with statistical noise — the standard signature of a sample whose local field is aligned along the z axis of the spectrometer.

Vector-polarisation mode treats the muon-spin polarisation as a three-component vector, exposing the \(P_x\), \(P_y\), and \(P_z\) projections separately rather than collapsing the detector counts onto a single forward/backward asymmetry. This is the right analysis path for anisotropic single crystals — where the precession axis is set by the crystallography rather than by the spectrometer geometry — and for any measurement where the local field at the muon site is canted away from \(\hat{z}\), since the off-axis precession is then carried by the \(P_x\) and \(P_y\) components and is lost in a one-dimensional asymmetry. Powder samples have an orientational average that already collapses onto a single non-trivial component along \(\hat{z}\), so the ordinary F-B asymmetry workflow is sufficient there. EMU’s octant geometry is the canonical example; vector mode is activated automatically when grouping names contain the canonical vector pairs:

  • Pz Forward / Pz Backward from forward/backward detector groups

  • Py Top / Py Bottom (or Py Up / Py Down) from top/bottom detector groups

  • Px Left / Px Right from left/right detector groups

so the same vector workflow can be applied to any instrument whose detector layout supports the same six-group naming convention.

Setup

  1. Open Grouping and choose (or create) a profile for EMU.

  2. Open Detector Layout…

  3. Select instrument EMU.

  4. Apply the Vector Polarization preset.

  5. Return to Grouping and calibrate each axis’s alpha (see below).

Per-axis alpha

When vector mode is active, the Grouping window switches to a vector table with separate alpha values for each axis:

  • alpha_x

  • alpha_y

  • alpha_z

Each axis is its own asymmetry projection (see Detector Grouping and Layout, “Per-projection alpha”), so each calibrates independently through the same alpha calibration dialog used for an ordinary two-group run — open it per axis with that row’s Calibrate… button, or calibrate all three in one action with Estimate All alpha. Because each axis’s alpha and provenance are stored on its own projection, switching between axes never mixes up which value came from which calibration run.

Backwards compatibility:

  • Existing scalar alpha is still supported.

  • Older projects are migrated so vector groupings initialise alpha_x, alpha_y, and alpha_z from scalar alpha.

Display in the main plot

The Polarization selector in the plot header provides:

  • x (P_x)

  • y (P_y)

  • z (P_z)

  • All

Alpha display behaviour:

  • Single-axis views show the alpha for the selected axis.

  • All mode hides alpha in the header.

Persistence

Per-axis alpha values are persisted in:

  • project files (schema v4+)

  • dataset grouping state

This preserves axis-specific alpha values across save/load cycles and across axis switching in vector mode.

Transverse-field dual grouping

The same projection workflow generalises beyond EMU’s three-axis vector mode. A forward/backward asymmetry is the muon polarisation projected onto the axis joining that detector pair, so any preset that exposes more than one such pair is a set of projections. MuSR and HiFi each ship a combined Transverse (Vector) preset that exposes two transverse projections of the same run:

  • MuSR — Top-Bottom and Fwd-Back

  • HiFi — Left-Right and Top-Bottom

Apply it from Detector Layout exactly as for EMU vector mode (select the instrument, apply the Transverse (Vector) preset). The projection chip bar then shows one chip per transverse projection; selecting two stacks them as subplots, and clicking a subplot makes it the fit target with its own per-projection single fit — identical behaviour to the EMU \(P_x\)/ \(P_y\)/\(P_z\) projections, including the tinted Fitting: <label> echo and save/load persistence. Unlike EMU’s octant model, the two transverse pairs use four distinct detector groups so both coexist (the legacy split presets reused the same group IDs and were mutually exclusive).

Detector group composition

EMU vector mode follows octant-style detector composition. The detector layout reference in Detector Grouping and Layout should be used for instrument-consistent verification of assigned groups.

EMU has no facility-documented “vector-polarisation” grouping — the EMU User Guide and the Mantid EMU instrument definition only describe the physical detector numbering (Section 8.1), not a Px/Py/Pz preset. The Vector Polarization preset is therefore an Asymmetry construct: it is verified internally consistent (each octant selection matches the geometric half-plane of the layout’s own detector angles) but is not itself a published EMU convention.

Assumptions and limitations

The vector treatment rests on a small set of geometry assumptions; read the projections with them in mind:

  • Each projection is a forward/backward asymmetry along one detector-pair axis. A forward/backward asymmetry measures the muon polarisation projected onto the axis joining that detector pair, so \(P_x\), \(P_y\), and \(P_z\) are the three orthogonal projections only insofar as the three detector-pair axes are mutually orthogonal and aligned with the spectrometer frame. On a real instrument the octant groups approximate those axes; the reconstruction is exact only for an idealised orthogonal layout.

  • Per-axis α decouples the three projections. Each axis carries its own calibration constant (alpha_x / alpha_y / alpha_z) and is reduced independently, so a miscalibrated α on one axis biases that projection’s amplitude without contaminating the other two — but all three must be calibrated for the vector to be quantitatively balanced.

  • Powder samples do not need it. An orientational average collapses the polarisation onto a single non-trivial component along \(\hat{z}\), so the ordinary F–B asymmetry workflow is sufficient; the vector projections add information only when the local field is canted away from \(\hat{z}\), as in an oriented single crystal.

  • The EMU Px/Py/Pz preset is an Asymmetry construct, not a published EMU convention (see Detector Group Composition): it is verified internally consistent against the layout’s own detector angles, but should be cross-checked against the facility detector numbering before quantitative use.

References

  • S. J. Blundell, R. De Renzi, T. Lancaster, and F. L. Pratt, Muon Spectroscopy: An Introduction (Oxford University Press, Oxford, 2022) — detector geometry and the polarisation-projection observable.