Correcting the Energy-Dependent Asymmetry in Low-Energy $\mu$SR

TL;DR

This paper presents updated calibration methods and simulation-based corrections for low-energy muon spin rotation measurements, improving depth-resolved magnetic studies by addressing energy-dependent asymmetry variations.

Contribution

It introduces a comprehensive framework combining experimental calibration and simulations to correct asymmetry measurements in LE-$bc$SR under current beam conditions.

Findings

Established energy-dependent maximum asymmetry using silver reference.

Quantified spurious contributions from reflected muons with nickel reference.

Developed a sample-size-dependent correction factor benchmarked with SrTiO$_3$ samples.

Abstract

Low-energy $\mu$SR (LE-$\mu$SR) enables depth-resolved studies of magnetic and electronic properties from the surface into the near-surface region, but the measured transverse-field asymmetry is not an intrinsic constant and depends on implantation energy and beamline conditions. Following an upgrade of the single-muon tagging system at the LEM beamline at PSI in 2023, updated asymmetry calibrations became necessary. Here, we present updated reference measurements that establish the energy-dependent maximum asymmetry using a silver reference and quantify spurious contributions from reflected muons using a nickel reference. In addition, we address systematic reductions of the measured asymmetry arising from incomplete beam--sample overlap by introducing a sample-size-dependent correction factor. This factor is obtained from musrSim/Geant4 simulations incorporating an updated electrostatic field map of the sample environment and is benchmarked using implantation-energy scans on SrTiO$_3$ samples of different lateral dimensions. Together, these updated calibrations and the simulation-based overlap correction provide a practical and up-to-date framework for LE-$\mu$SR data correction under current beam conditions and enable quantitative depth-resolved analysis of volume fractions.