μSR Study of B20 Magnetic Systems: MnSi, Mn₀.₉Fe₀.₁Si and Cu₂OSeO₃

A skyrmion is a vortex-like spin pattern which has been observed in so-called B20 magnetic systems such as MnSi, (Mn,Fe)Si and a few other metallic magnets as well as in insulating Cu₂OSeO₃. We conduct a comprehensive study of muon spin relaxation (μSR) on bulk single crystals of MnSi and (Mn,Fe)Si, a MBE thin film of MnSi, and a ceramic specimen of Cu₂OSeO₃ in this work. The generic second-order like phase transition indicated by 1/T₁ peaks at T_c in bulk systems is discussed in light of the Brazovskii-type first-order phase transition due to the presence of the DM interaction. We also discuss the different temperature dependences of μ⁺ spin-lattice relaxation rate 1/T₁ in bulk pure systems MnSi and Cu₂OSeO₃ and their commonalities in the paramagnetic state and the ordered state due to the DM interaction. Furthermore, we highlight the enhanced 1/T₁ in the skyrmion crystal (SkX) phase compared to neighboring conical phases due to an abundance of low-energy magnetic fluctuations/excitations. This abundance is corroborated by the reduced static order parameter in the SkX phase of MnSi compared to neighboring conical phases, deduced by combining μSR experiments and magnetic field simulations. The intermediate (IM) region above T_c, where the modification of magnetic transition by the DM interaction starts to appear in MnSi, exhibit multi-time scale spin fluctuations, topologically non-trivial Hall resistivity and non-Fermi-liquid exponent of longitudinal resistivity in single-crystal Mn₀.₉Fe₀.₁Si and the MnSi MBE thin film, similar to the magnetically disordered phase of pure MnSi under hydrostatic pressure. These three defining features indicate a fluctuating skyrmion liquid in this magnetically ordered state, stabilized by pressure, disorder or reduced dimensionality. Moreover, the magnetic transition is strongly first order in the MnSi MBE thin film sample, different from the Brazovskii-type weakly first order transition in bulk samples, suggesting the importance of reduced dimensionality in modifying the nature of magnetic phase transitions in B20 systems