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Magnetic layer imperfect

This example extends polarized reflectometry to a more realistic instrument with nonideal polarizer and analyzer efficiencies, finite $q$ resolution, and a constant background. The model, inspired by Devishvili et al., consists of a saturated iron film on an MgO substrate with a thin palladium cap and rough interfaces.

All four polarization channels are simulated. Because the polarizer and analyzer have different transmission and suppression efficiencies, the two spin-flip curves are no longer identical. This example therefore combines the sample magnetization, polarization analysis, resolution, roughness, and background corrections in one calculation.

Result

Magnetic layer imperfect result

Sample

Magnetic layer imperfect sample

Python script

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#!/usr/bin/env python3
# /// script
# requires-python = ">=3.10"
# dependencies = ["bornagain>=25,<26"]
# ///
"""
Realistic (imperfect) example for polarized reflectometry.
Sample contains a magnetic layer,
similar to Devishvili et al., Rev. Sci. Instrum. 84, 025112 (2013).
"""
import numpy as np
import bornagain as ba
ba.require_versions("bornagain>=25,<26")
from bornagain import nm, deg, R3
from math import sin, cos

def get_sample():
    # Materials
    Bmag = 1.6e6
    Bangle = 0 * deg
    B = R3(Bmag*sin(Bangle), Bmag*cos(Bangle), 0)
    vacuum = ba.Vacuum()
    pd_color = (0.93, 0.72, 0.25)
    pd_mat = ba.SLDMaterial("Pd", pd_color, 4.0099e-6, 1.3019e-09)
    fe_color = (0.48, 0.32, 0.80)
    fe_mat = ba.SLDMaterial("Fe", fe_color, 8.0241e-06, 6.0448e-10, B)
    substrate_color = (0.28, 0.57, 0.82)
    substrate_mat = ba.SLDMaterial("MgO", substrate_color, 5.9803e-06, 9.3996e-12)

    autocorr = ba.SelfAffineFractalModel(2*nm, 0.7, 25*nm)
    transient = ba.TanhTransient()
    roughness = ba.Roughness(autocorr, transient)

    # Layers
    layer_vacuum = ba.Layer(vacuum)
    layer_Pd = ba.Layer(pd_mat, 12*nm, roughness)
    layer_Fe = ba.Layer(fe_mat, 100*nm, roughness)
    layer_substrate = ba.Layer(substrate_mat, roughness)

    # Multilayer
    sample = ba.Sample()
    sample.addLayer(layer_vacuum)
    sample.addLayer(layer_Pd)
    sample.addLayer(layer_Fe)
    sample.addLayer(layer_substrate)

    return sample


def simulate(p_dir, a_dir, p_eff, a_trans, a_supp, title):
    sample = get_sample()

    qzs = np.linspace(0.1, 1.5, 1500)
    distr = ba.DistributionGaussian(0., 1., 25, 4.)

    scan = ba.QzScan(qzs)
    scan.setAbsoluteQResolution(distr, 0.008)

    scan.setPolarization(p_dir*p_eff)
    scan.setAnalyzer(a_dir, a_trans, a_supp)

    simulation = ba.SpecularSimulation(scan, sample)
    simulation.setBackground(ba.ConstantBackground(1e-7))

    result = simulation.simulate()
    result.setTitle(title)

    return result


if __name__ == '__main__':
    ba.showSample3D(get_sample(), sample_size=80*nm, seed=0)
    # polarizer and analyzer efficiencies
    p_eff = 0.986
    a_trans = 0.970
    a_supp = 0.015

    results_pp = simulate(R3(0, +1, 0), R3(0, +1, 0), p_eff, a_trans, a_supp, "$++$")
    results_pm = simulate(R3(0, +1, 0), R3(0, -1, 0), p_eff, a_trans, a_supp, "$+-$")
    results_mp = simulate(R3(0, -1, 0), R3(0, +1, 0), p_eff, a_trans, a_supp, "$-+$")
    results_mm = simulate(R3(0, -1, 0), R3(0, -1, 0), p_eff, a_trans, a_supp, "$--$")

    results = [results_pp, results_pm, results_mp, results_mm]
    ba.plot_multicurve(results)
    ba.plt.show()
auto/Examples/specular/magnetic/MagneticLayerImperfect.py