Title: Muon Spin Relaxation Study of MnGe and Development of Pair Distribution Function Methods
Description: The first half of the thesis presents our experimental study of a helical magnet MnGe. We apply μSR technique to study the dynamic as well as the static magnetism in MnGe. Our key findings are as follows. From the muon dynamic relaxation 1/T1 results, no apparent critical behavior or anomaly was observed at the boundary between param- agnetic and the induced-ferromagnetic regions. Our study revealed linear relation between the transverse field relaxation rate and the static magnetization. Furthermore, their ratio, which can be regarded a form of hyperfine coupling constant, is very similar in the induced ferromagnetic region and the paramagnetic region. This suggest that the Z component of the Mn moment is static in both regions. On the other hand, the single relaxation rate in the transverse spectra suggest that the internal field is highly homogeneous in the induced ferromagnetic region. We therefore speculate that the induced ferromagnetic region and the paramagnetic region are not separate phases, but rather a single phase with different tendencies as temperature decrease.

With decreasing temperature, the paramagnetic region is marked with the winning of the tendency towards ferromagnetic ordering over random ordering, and the induced ferromagnetic region is marked with the winning of the tendency towards the helical order over ferromagnetic order.At lower temperature, we observed dynamic critical behavior in the boundary between the induced ferromagnetic region and the Skyrmion region. Specifically, in low fields, the 1/T1 relaxation rate behaves qualitatively different from the prediction of SCR theory for itinerant ferromagnet for large temperature regime above Tc. In high fields, on the other hand, the system recovers the SCR itinerant ferromagnetic behavior. Through analyzing field effect on spin fluctuation and phase transition in the low and high field regimes, we speculate that this could be due to the suppression of helical fluctuation into ferromagnetic-like fluc- tuation by large magnetic fields. Our μSR results, which show 2nd order signature for the transition between the induced ferromagnetic region into the Skyrmion region, is consistent with considerations based on the topology of the magnetic structure in each phase.

At low temperatures within the Skyrmion region of MnGe, our analysis of the transverse field data shows that all the three components of the Mn moment is frozen. The quadratic tempera- ture dependence of 1/T1 at low temperatures suggest the two-magnon spin wave to be the dominant spin excitation in the Skyrmion region. This is similar to those seen in local- ized moment magnets and is qualitatively different from the linear temperature dependence predicted from SCR theory for itinerant ferromagnets. The second half of the thesis present our derivation of the structure function and the pair distribution function (PDF) for textured materials. We also derive the analytical form of the PDF for a few special cases of texture. In this study, we start from the general form of a 3D structure function and derive the general and orientationally averaged form of the structure function and PDF for textured samples. In particular for a thin film sample with fibre texture, our formalism gives the result known as the 2 dimensional PDF.

We developed open-software that calculates the 2 dimensional PDF for a textured thin film, and showed that the experimental PDF was well fitted using the model. On the other hand, the PDF method could be extended to an energy-dependent form, which could reveal explicitly the effect of lattice dynamics on the local arrangement of the atoms. This is usually called the dynamic PDF method. In this thesis we derive the analytical form of the dynamic PDF for a simple molecule that contains two identical atoms. And we interpret the mathematical results with physical consideration of the lattice dynamics. In addition, we also propose a new definition for the dynamic PDF which can be shown to reduce to the atomic PDF by integrating over energy. This new definition of the dynamic PDF incorporates the contribution from multi-phonon scattering effects, and can be computed conveniently from inelastic neutron scattering.