Computational study of multiferroic materials

This thesis examines computational approaches to finding novel multiferroic materials in two dimensions. Ferroic materials are characterized by the presence of at least one type of primary ferroic order such as ferromagnetism, ferroelectricity or ferroelasticity. Multiferroics on the other hand contain at least two of these orders simultaneously. This feature has lead to a surge of interest in recent years, from researchers trying to understand the fundamental mechanisms that drive multiferroism. In addition there has been speculation that these materials could potential have various technological applications.
The relevant theoretical framework for understanding the properties of materials is quantum mechanics. This thesis applies density functional theory (DFT), a quantum mechanical computational method that has proven very useful for investigating the electronic structure of solids as well as a variety of condensed phases. Density functional theory is applied in conjunction with the modern theory of polarization to compute the spontaneous polarization in ferroelectric materials from first-principles. This method is applied in order to systematically screen databases for potential ferroelectric candidates. This is achieved by applying high-throughput frameworks that allows researchers to automate a large part of the computational process. The main result presented is a screening for novel two dimensional ferroelectric materials. Spontaneous polarizations are computed for identified ferroelectric candidates. Further analysis includes a thermodynamic classification using phonons as well as computations of upper bounds on coercive electric fields. The identified ferroelectric materials include previously known materials as well as novel ones that will likely be the subject of future investigation.
In addition recent results obtained for the Computational 2D materials database (C2DB) are presented, with an emphasis on the addition of electric polarizations. The thesis also briefly covers a computational study of the formation of charged domain walls due to oxygen vacancies in BaTiO3. Our results indicate that the vacancies are not only stabilizing agents for the negatively charged walls, but are also critical in order to explain how these are formed in the first place.
A chapter of this thesis deals with the anomalous Hall effect in metallic magnets. The chapter covers the necessary theoretical background specifically linear response theory. Benchmark calculations are performed using an implementation of the anomalous Hall conductivity into the DFT code GPAW. The results indicate good agreement with literature in some cases, but is inconclusive in some scenarios. It is concluded that adaptive refinement of k-point grids are necessary in order to conclusively demonstrate the accuracy of the implemented code.