  Uranium beryllium-13 is a heavy fermion system whose anomalous behavior may
be explained by its poorly understood internal magnetic structure. Here,
uranium beryllium-13's magnetic distribution is probed via muon spin
spectroscopy ($\mu$SR)-a process where positive muons localize at magnetically
unique sites in the crystal lattice and precess at characteristic Larmor
frequencies, providing measurements of the internal field. Muon spin
experiments using the transverse-field technique conducted at varying
temperatures and external magnetic field strengths are analyzed via statistical
methods on ROOT. Two precession frequencies are observed at low temperatures
with an amplitude ratio in the Fourier transform of 2:1, enabling muon stopping
sites to be traced at the geometric centers of the edges of the crystal
lattice. Characteristic strong and weak magnetic sites are deduced,
additionally verified by mathematical relationships. Results can readily be
applied to other heavy fermion systems, and recent identification of quantum
critical points in a host of heavy fermion compounds show a promising future
for the application of these systems in quantum technology. Note that this
paper is an analysis of data, and all experiments mentioned here are conducted
by a third party.
