E54 · Photoelectron spectroscopy

Spin ARPES: Polarization & Counting

Record opposite magnetizations of a VLEED target. Correct each count with its own flux monitor, divide by the supplied Sherman factor and compare two momentum branches with counting errors. Widen the energy gate to mix opposite spins.

Left branch: measured polarization $\text{—}$

Right branch: measured polarization $\text{—}$

Left / right counting standard errors $\text{—}$

Recorded spin counts · complete scan $\text{—}$

Instrument Gaussian-equivalent FWHM $\text{—}$

Known gate-averaged left / right spin $\text{—}$

Assumed reflected count efficiency $\text{—}$

True detector figure of merit $\text{—}$

Serial scan time · 81 angle bins $\text{—}$

Selected gate edges from Fermi level $\text{—}$

Experiment target $\text{—}$

Counts need a calibrated spin analyzer

Normalize each reversal by its monitorReprocess stored counts; no new acquisition.Photon energy

h\nu

21.2\,\mathrm{eV}

Sample temperature

T

80\,\mathrm{K}

Pass energy

E_p

20\,\mathrm{eV}

Entrance and exit slit width

s

0.4\,\mathrm{mm}

Angular Gaussian FWHM

\Delta\theta

0.5\,\mathrm{{}^\circ}

Exposure per angle · both reversals

\tau

2\,\mathrm{s}

Spin projection axis rotation

\gamma

0\,\mathrm{{}^\circ}

Gate center from Fermi level

E_g

-0.1\,\mathrm{eV}

Energy gate width

\Delta E_g

0.06\,\mathrm{eV}

Positive / negative reversal flux

r

1.8

Supplied Sherman calibration

S

0.3

Predict which raw asymmetry survives flux normalization. With unequal flux above 1.3, recover opposite branches beyond 0.5 magnitude, counting errors below 0.1, and agreement with the known emitted spin within 0.15. Use a narrow upper-band gate and the correct Sherman calibration. Then rotate the axis or mix both branches.

Synthetic Dirac bands have a crossing at −0.25 eV, velocity 2 eV angstrom and assumed emitted-electron polarization up to 0.8. They do not identify a real material or prove topology. Spin refers to one projected photoelectron component, not automatically the original solid spin. Fermi occupation is multiplied before Gaussian energy/angular response; finite-grid response clamps at acquisition boundaries. Grounded specimen and analyzer work functions are both 4.5 eV. A separate 1-second spin-integrated survey precedes a serial angle scan. At each angle, total exposure is split equally between two target magnetizations of one Fe target and one counting channel; the selected gate integrates both bands and unpolarized background. True Sherman coefficient is 0.30 and reflected efficiency 0.10; transfer, flux, widths and material parameters are teaching assumptions. The positive reversal receives a tunable flux ratio; independent Poisson monitors measure that ratio. Processing uses stored counts and monitors only. The supplied Sherman factor changes estimates without changing acquisition. Statistical errors use first-order Poisson propagation, including monitors, and omit calibration/systematic errors; estimates are not clipped to physical bounds. Insufficient counts or unphysical peak estimates suppress the numerical spin result. Target reflection energy is schematically 6.3 eV; transfer and angular magnification are schematic, not electron-optics ray tracing. Colors use log gain. No full spin vector, matrix-element spin rotation, target aging, real detector calibration, charging, damage or scattering background correction. Counts are Poisson below mean 40 and rounded Gaussian above. Animation does not add counts or exposure.

Start with the essentials

Focus question: Is the asymmetry spin—or unequal flux?
One-sentence intuition: Normalize each reversal with its recorded monitor before converting asymmetry to polarization. A broad gate can cancel opposite spins even when the peaks are intense.

Core mathematical model

Monitor-normalized polarization

P=\frac{1}{S}\frac{N_+/M_+-N_-/M_-}{N_+/M_++N_-/M_-}

The two magnetizations share a detector; monitors measure their unequal incident flux.

Equal-flux counting limit

\sigma_P\simeq\frac{\sqrt{1-(SP)^2}}{S\sqrt{N_++N_-}}

This simplified limit neglects monitor noise; the implemented propagation includes it.

Detector figure of merit

\mathrm{FOM}=\eta S^2

An assumed reflectivity of 0.10 and true Sherman coefficient of 0.30 give 0.009.

Common difficulties

Asymmetry needs a reference

Typical misconceptionA count difference directly equals polarization.

Better mental modelNormalize unequal flux and divide by a calibrated Sherman factor.

A precise count is not a calibrated spin

Typical misconceptionA small statistical error excludes systematic bias.

Better mental modelMonitor and Sherman calibration errors can dominate counting noise; only the counting contribution is reported.

Run the experiment

01
Predict a false spin signal
Use Unequal flux without correction and inspect the raw reversals.
What to observe: One branch becomes unphysical even though the counts look precise.
02
Correct and calibrate
Enable monitor normalization, then check the target. Change only the supplied Sherman factor.
What to observe: Normalization removes the imposed flux bias; calibration rescales polarization and its error without changing recorded counts.
03
Project or mix
Rotate the axis, mix both energy branches, then reduce exposure.
What to observe: Perpendicular projection and branch mixing cancel the component; low counts enlarge statistical error.