Dzyaloshinkii-Moriya Interaction and Hall Effects in Bulk Chiral Magnets from First Principle Calculations

In this dissertation I will discuss the effect of real, momentum, and mixed space Berry phases in B20 compounds: MnSi, Mn1-xFexGe, and Fe1-yCoyGe. Recently there has been a tremendous experimental effort in stabilizing skyrmion crystal phases in these systems. We calculate, from state of the art first principle calculations, the Dzyaloshiniskii-Moriya interaction (DMI), the anomalous Hall effect (AHE), and the topological Hall effect (THE). These three effects are intimately related through Berry phase physics, where I test how the strength of the exchange interactions and spin-orbit coupling play a role in the underlying physics for these systems. In this dissertation, I compare the strength of different first principle methods in calculating magnetic ground state properties in B20 compounds. In this, I see that Full Potential Linearized Augmented Plane Wave Method treats different magnetic states most accurately. Calculations of spin-spiral states are performed in these B20 compounds showing long wavelength spin-spirals due to the interaction of the exchange stiffness and the DMI field. The DMI in these materials reaches maxima and minima with alloying concentration due the hybridization of d-states, which I complement with an intuitive tight-binding model. The AHE is also calculated in these materials and shows remarkable agreement with experimental measurements. Whereas the THE agrees in sign for these materials and quantitatively in the FeGe, the values in MnGe predict smaller values. This discrepancy, where the DMI is also smaller than expected, is attributed to breakdown of the adiabatic theorem, where in MnGe, the magnetic texture rotates too quickly to capture the real space Berry phase physics. The work of this dissertation is compared with computational results that have followed and ongoing experimental studies