The search for new multiferroic ABF$_4$ fluorides via first-principles structure maps

Transition metal ABF$_4$ fluorides are observed in a wide variety of different structure types. One, the BaMnF$_4$ structure, is an interesting family of polar (possibly ferroelectric) materials that display canted-antiferromagnetism, which has been predicted (Ederer and Spaldin) to reverse when the polarization reverses. This strong coupling between magnetism and polarization has motivated us to explore additional ABF$_4$ structure types. In this talk we will discuss our search for new multiferroic ABF$_4$ fluorides by creating structure maps from first principles. As a first step we categorize the ABF$_4$ compounds found in the ICSD. We focus on structures for which the B-site is octahedrally coordinated; these can be fitted into one of four categories: BaMF$_4$, Dion-Jacobson, and the so-called slip (100) or slip (110) structures. These four categories represent high symmetry structures which allow distortions to lower symmetry structures. Note that most of the known multiferroic ABF$_4$ compounds form in the BaMF$_4$ structure. We elucidate a simple descriptor that helps to build the chemical and physical intuition as to why a compound forms in this structure type needed for the rational design of new multiferroic ABF$_4$ fluorides.