  A thorough description of the physics of a magnetic compound requires the
validation of its microscopic spin Hamiltonian. Here, from the analysis of
muon-spin rotation spectra recorded in the magnetically ordered state at low
temperature in zero and finite magnetic fields, we determine the minimal
Hamiltonian for the chiral binary intermetallic magnet MnSi, consistent with
its high-temperature nonsymmorphic cubic space group P$2_1$3. The model
provides constraints for the orientation of the Moriya vector characterizing
the microscopic Dzyaloshinskii-Moriya interaction, with respect to the Mn
nearest-neighbor bonds. Small twist and canting of the magnetic structure are
revealed. Our result indicates that, within experimental uncertainties, the
magnetoelastic coupling is not strong enough to lower the paramagnetic crystal
symmetry in the magnetically ordered state. Additional implications from our
work are discussed and complementary studies are suggested.
