Magnetic monopoles in chiral magnets & frustrated magnetism on the swedenborgite lattice

Abstract

This thesis deals with magnetic order in condensed matter systems and is divided into three parts. The first part gives a closed and self-contained introduction to the Monte Carlo methods used within this thesis with a special emphasis on a recently introduced feedback optimized parallel tempering algorithm. The second part deals with chiral magnets, i.e. magnets without inversion symmetry in their crystal structure. In these systems, weak spin-orbit coupling leads to the formation of smooth helical structures with a long periodicity. In 2009, the existence of a novel magnetic phase consisting of topological stable whirls, so-called skyrmions, was discovered in these materials. Due to their topological stability and the fact that they can be packed very densely, skyrmions are currently considered as promising candidates for future data storage applications. In this part of the thesis, I analyze how the topological protection of these objects is destroyed during the phase transition into another (non-topological) phase. It turns out that the underlying microscopic process is governed by the movement of monopoles of an emergent magnetic field created by the skyrmions. The third part of this thesis deals with frustrated spin systems. In these systems with antiferromagnetic interactions, a special lattice geometry excludes the simultaneous satisfaction of all competing interactions which often results in a macroscopic ground state degeneracy. Fluctuations between these different ground states prevent the system from developing long-range order and it remains disordered at all temperatures, which is why these systems are often referred to as "spin-liquids". Interestingly, there exists an intrinsic effect called "order-by-disorder", in which this degeneracy can be lifted at least partially at finite temperatures due to entropic reasons, provided that the ground states differ in their excitation spectra. I present the first detailed theoretical study of the recently synthesized swedenborgite compounds and show that these systems realize spin-liquid ground states both for the Ising and Heisenberg model. In the latter case, the order-by-disorder effect is found to result in the entropic preference of coplanar ground states at low temperatures.