  In positive muon spin rotation and relaxation spectroscopy it is becoming
nowadays customary to take advantage of Density Functional Theory (DFT) based
computational methods to aid the experimental data analysis. DFT aided muon
site determination is especially useful for measurements performed in magnetic
materials, where large contact hyperfine interactions may arise. Here we
present a systematic analysis of the accuracy of the ab initio estimation of
muon's hyperfine contact field on elemental transition metals, performing state
of the art spin-polarized plane wave DFT and using the projector augmented
pseudopotential approach, which allows to include the core state effects due to
the spin ordering. We further validate this method in not-so-simple,
non-centrosymmetric metallic compounds, presently of topical interest for their
spiral magnetic structure giving rise to skyrmion phases, such as MnSi and
MnGe. The calculated hyperfine fields agree with experimental values in all
cases, provided the spontaneous spin magnetization of the metal is well
reproduced within the approach. To overcome the known limits of the
conventional mean field approximation of DFT on itinerant magnets, we adopt the
so-called reduced Stoner theory [L. Ortenzi et al.,Phys. Rev. B 86, 064437
(2012)]. We establish the accuracy of the estimated muon contact field in
metallic compounds with DFT and our results show improved agreement with
experiments compared to those of earlier publications.
