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Various $\mu^+$SR techniques have been widely used for studying internal magnetic fields in assorted materials [1], such as, antiferromagnets, spin-glasses, paramagnets, and superconductors. However, for ferromagnetic (FM) materials, $\mu^+$SR faces a difficulty in determining the correct dipole field at the muon site $({\bf H}_{\rm dip})$ because the internal magnetic field at the muon site in ferromagnets is expressed by; ${\bf H}_{\mu}={\bf H}_{\rm dip}~+~{\bf H}_{\rm L}~+~{\bf H}_{\rm hf}$, where ${\bf H}_{\rm L}$ is the Lorentz field and ${\bf H}_{\rm hf}$ is the hyperfine field at the muon site. Therefore, the muon sites and the magnetic structure need to be apprehended for evaluating ${\bf H}_{\rm dip}$ but also the saturation magnetization for evaluating ${\bf H}_{\rm L}$ and the local spin density at the muon site for evaluating ${\bf H}_{\rm hf}$.
Considering the three contributions to ${\bf H}_{\rm \mu}$ in the above equation, a combined work with $\mu^+$SR and DFT calculations are needed to provide a reasonable estimate for the ordered magnetic moment of rare earth ($R$) ions in ${\rm Nd}_2{\rm Fe}_{14}{\rm B}$ and related magnets [2]. Following upon this work, we attempt to estimate the ordered magnetic moments of $R$ ions in cobalt-based FM materials, $R_2{\rm Co}_{12}{\rm P}_7$ with such combined work. As a first step, a powder sample of $R_2{\rm Co}_{12}{\rm P}_7$ with $R={\rm Y}$ was measured with $\mu^+$SR and three clear muon spin precession signals below its Curie temperature ($T_{\rm C}=151~$K) were found.
[1] A. Yaouanc and P. D. de R$\acute{\rm e}$otier, ``Muon Spin Rotation, Relaxation, and Resonance, Application to Condensed Matter" (Oxford, New York, 2011).
[2] J. Sugiyama et al., Phys. Rev. Material ${\bf3}$, 064402 (2019).
