Separating between ordinary (OHE) and anomalous (AHE) Hall effect in the paramagnetic phase of Mn$_{1-x}$Fe$_{x}$Si reveals OHE sign inversion associated with the hidden quantum critical (QC) point $x^*sim0.11$. The semimetallic behavior at intermedi
ate Fe content leads to verifiable predictions in the field of fermiology, magnetic interactions and QC in Mn$_{1-x}$Fe$_{x}$Si. The change of electron and hole concentrations is considered as a driving force for tuning the QC regime in Mn$_{1-x}$Fe$_{x}$Si via modifying of RKKY exchange interaction within the Heisenberg model of magnetism.
The magnetic inhomogeneity of the A-phase in MnSi chiral magnet is identified for the first time from the precise measurements of transverse magnetoresistance (MR) anisotropy. The area inside the A-phase (A-phase core) corresponds to isotropic MR hav
ing no confinement to the MnSi crystal lattice. Per contra, the MR becomes anisotropic both on the border of the A-phase and in other magnetic phases, the strongest magnetic scattering being observed when external magnetic field applied along [001] or [00-1] directions. We argue here that the established MR features prove the presence of two different types of the skyrmion lattices inside the A-phase, and the dense skyrmion state of the A-phase core is built from individual skyrmions similar to Abrikosov-type magnetic vortexes.
By direct measurements of the complex optical conductivity $sigma( u)$ of FeSi we have discovered a broad absorption peak centered at frequency $ u_{0}(4.2 K) approx 32 cm^{-1}$ that develops at temperatures below 20 K. This feature is caused by spin
-polaronic states formed in the middle of the gap in the electronic density of states. We observe the spin excitations between the electronic levels split by the exchange field of $H_{e}=34pm 6 T$. Spin fluctuations are identified as the main factor determining the formation of the spin polarons and the rich magnetic phase diagram of FeSi.
