Magnetism is an active area of research as it is believed to play an important role in the understanding of important materials like the cuprate superconductors and the more recently discovered iron pnictide/chalcogenide superconductors.
Magnetism is also of fundamental interest as very little, and no systematics, is known about a class of magnets known as frustrated magnets. Frustration means here that it is impossible to satisfy energetically all the magnetic interactions in the material simultaneously. An example of this is magnetic moments with interactions that favor antiparallel alignment of neighboring moments that are located on the corners of a triangle.
This masters project is a followup study on a recently developed theory framework for studying frustrated Heisenberg magnets (M. Schecter, O.F. Syljuasen, and J. Paaske, "Nematic Bond Theory of Heisenberg Helimagnets", Phys. Rev. Lett. 119, 157202, (2017).) This framework uses diagrammatic techniques from statistical field theory to arrive at a set of self-consistent approximate equations which are then solved numerically to give information about phases, phase transitions, their universality class and critical temperatures. An advantage with the method is that it also captures phase transitions that break lattice symmetries like nematic phases.
The framework has up to now been applied to the simplest cases, but extensions to non-Bravais lattices is needed, as well as a more systematic study of what type of magnetic orders to expect in various cases. It is also possible to improve the accuracy of the approximations by including more diagrams. The type of work in this project will be partly analytic; involving the use of Feynman diagrams and classifying possible order parameters using group theory, and numerical; solving the equations on a computer.