E54 · Photoelectron spectroscopy

Spin ARPES: Polarization & Counting

When reversing a spin detector's magnetization changes the count, is that spin or unequal photon flux? It can be either, because unequal flux can fake a spin signal. First divide each count by its own flux monitor reading. Then the asymmetry divided by the detector's Sherman factor, a measure of its spin sensitivity, gives the spin polarization. Keep the energy window narrow: a wide one can mix opposite spins and cancel the polarization.

Measure the same photoelectrons with a VLEED target magnetized one way and then the other. Correct each count with its own flux monitor, divide by the supplied Sherman factor and compare the two momentum branches with their counting errors. Widen the energy gate to see opposite spins mix.

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

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

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

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

More measurements and target

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 $\text{—}$

Simulated examples; each plot identifies its data source.

Normalize each reversal by its monitorReprocesses the stored counts without a new acquisition.Exposure per angle · both reversals

\tau

2\,\mathrm{s}

Spin projection axis rotation

\gamma

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

Positive / negative reversal flux

r

1.8

Advanced settings

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}

Gate center from Fermi level

E_g

-0.1\,\mathrm{eV}

Energy gate width

\Delta E_g

0.06\,\mathrm{eV}

Supplied Sherman calibration

S

0.3

Learning goal and model limits

Reading spin from counts needs a calibrated analyzer

First predict which part of the raw asymmetry survives flux normalization. With a flux ratio above 1.3, recover opposite polarizations on the two branches, each larger than 0.5 in magnitude. Keep the counting errors below 0.1 and match the known emitted spin within 0.15. Use a narrow energy gate on the upper band and the correct Sherman calibration. Then rotate the spin axis or mix both branches.

Model assumptions

The Dirac bands are synthetic: they cross at −0.25 eV, have a velocity of 2 eV angstrom and give the emitted electrons an assumed polarization of up to 0.8. They do not represent a real material or prove topology. Spin here means one projected component of the photoelectron spin, which is not automatically the spin the electron had in the solid. Fermi occupation is applied before the Gaussian energy and angular response, and the response on the finite grid is clamped at the edges of the acquisition window. The grounded sample and the analyzer both have a 4.5 eV work function. A separate 1-second spin-integrated survey comes before a serial scan over angle. At each angle, the total exposure is split equally between the two magnetizations of one Fe target, read by one counting channel. The selected gate integrates both bands and the unpolarized background. The true Sherman coefficient is 0.30 and the reflected efficiency 0.10; transfer, flux, widths and material parameters are teaching assumptions. The positive reversal gets an adjustable flux ratio, which independent Poisson monitors measure. Processing uses only the stored counts and monitor readings. The supplied Sherman factor changes the estimates but not the acquisition. Statistical errors use first-order Poisson propagation with the monitors included; calibration and systematic errors are left out, and estimates are not clipped to physical bounds. If counts are too low or the peak estimates are unphysical, no numerical spin result is reported. The target reflection energy is set schematically at 6.3 eV. The transfer and angular magnification are also schematic; there is no electron-optics ray tracing. Colors use a logarithmic gain. The model does not recover the full spin vector, and it has no matrix-element spin rotation, target aging, real detector calibration, charging, damage or scattering-background correction. Counts are Poisson below a mean of 40 and rounded Gaussian above. The animation does not add counts or exposure.

Start with the essentials

Focus question: Does the count asymmetry come from spin or from unequal flux?
One-sentence intuition: Divide each reversal by its own recorded monitor before turning the asymmetry into a polarization. A broad energy gate can cancel opposite spins even when the peaks are bright.

Core mathematical model

Polarization from monitor-normalized counts

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

The two magnetizations use the same detector, and the monitors measure how much incident flux each one received.

Counting error with equal flux

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

This simplified limit ignores monitor noise; the error propagation in the Lab includes it.

Detector figure of merit

\mathrm{FOM}=\eta S^2

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

Common difficulties

An asymmetry is not yet a polarization

Typical misconceptionThe difference in counts is the polarization.

Better mental modelFirst correct for unequal flux, then divide by a calibrated Sherman factor.

Small error bars do not rule out bias

Typical misconceptionIf the statistical error is small, there is no systematic bias.

Better mental modelErrors in the monitors and in the Sherman calibration can outweigh counting noise, and only the counting part is reported here.

Run the experiment

01
Predict a false spin signal
Choose Unequal flux without correction and look at the raw counts for the two reversals.
What to observe: One branch gives an unphysical polarization, even though the counts look precise.
02
Correct the flux, then calibrate
Turn on Normalize each reversal by its monitor and press Check target. Then change only the Supplied Sherman calibration.
What to observe: Normalization removes the flux bias that was added. The calibration rescales the polarization and its error without changing the recorded counts.
03
Rotate the axis or mix the branches
Change the Spin projection axis rotation, choose Mix both energy branches, then reduce the exposure.
What to observe: Projecting onto a perpendicular axis, or mixing the two branches, cancels the measured component. Fewer counts give a larger statistical error.