Evolution of magneto-crystalline anisotropies in Mn$_{1-x}$Fe$_x$Si and Mn$_{1-x}$Co$_x$Si as inferred from small-angle neutron scattering and bulk properties

We report a comprehensive small-angle neutron scattering~(SANS) study of Mn$_{1-x}$Fe$_{x}$Si at zero magnetic field. To delineate changes of magneto-crystalline anisotropies (MCAs) from effects due to defects and disorder, we recorded complementary susceptibility and specific heat data, and investigated selected compositions of Mn$_{1-x}$Co$_{x}$Si. For all systems studied the transition temperature and magnetic phase diagrams evolve monotonically with composition consistent with literature. The SANS patterns of the magnetic order recorded under zero-field cooling display strong changes of the directions of the intensity maxima and smeared out intensity distributions as a function of composition. We show that cubic MCAs account for the complex evolution of the SANS patterns, where for increasing $x$ the character of the MCAs shifts from terms that are fourth-order to terms that are sixth order in spin--orbit coupling. The magnetic field dependence of the susceptibility and SANS establishes that the helix reorientation as a function of magnetic field for Fe- or Co-doped MnSi is dominated by pinning due to defects and disorder. The presence of thermodynamic anomalies of the specific heat at the phase boundaries of the skyrmion lattice phase in the doped samples and properties observed in Mn$_{1-x}$Co$_{x}$Si establishes that the pinning due to defects and disorder remains, however, weak and comparable to the field scale of the helix reorientation. The observation that MCAs, that are sixth order in spin-orbit coupling, play an important role for the spontaneous order in Mn$_{1-x}$Fe$_{x}$Si and Mn$_{1-x}$Co$_{x}$Si, offering a fresh perspective for a wide range of topics in cubic chiral magnets such as the generic magnetic phase diagram, the morphology of topological spin textures, the paramagnetic-to-helical transition, and quantum phase transitions.