Walker, Adam Harold; (2022) Introducing collective order into Density Functional Theory and modelling the magnetic reorientation transition in Ca3Ru2O7. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis contains two distinct pieces of work. In the first, a framework is presented in which arbitrary electronic order that is driven by collective charge and spin fluctuations is introduced into Density Functional Theory. This is achieved using the Quantum Order-By-Disorder approach, in which a desired collective order is introduced into a system using a variational order parameter, and the free energy of fluctuations about the ordered mean-field state are evaluated self-consistently within perturbation theory. This method is applied to the Kohn-Sham auxiliary system, resulting in a minimal optimisation problem in which the order parameter and the Kohn-Sham quasiparticle states must be solved for in a self-consistent manner. This framework is illustrated with two examples: fluctuation-driven superconductivity and spin nematic order, which are representative of orders in the particle-particle and particle-hole channels. Implementation schemes are considered in both cases. The second piece of work models the spin reorientation transition in the correlated metal Ca3Ru2O7. This is a coupled structural-electronic transition in which the direction of antiferromagnetic ordering reorientates as a function of temperature and applied stress. We identify that the lattice couples to the electronic system via the tilting and rotational of the RuO6 octahedra, which modify the orbital overlaps. This motivates a minimal model for Ca3Ru2O7 in which a phenomenological lattice strain couples to the hopping parameter of an electronic model. This model successfully captures the phenomenology of the spin reorientation transition with varying temperature, including most of its structural and electronic features. It reveals a transition mechanism in which the lattice spontaneously deforms in order to self-consistently lower the electronic energy by modulating the electronic bandwidth, which is validated by temperature-dependent structure measurements. The model also captures the transition with applied stress in a way that is consistent with experimental observations.

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