Ab initio study of de Haas van Alphen effect in BaRh$_{2}$P$_{2}$ and BaIr$_{2}$P$_{2}$

The de Haas-van Alphen (dHvA) effect is a powerful probe of the Fermi surface (FS) of a metal. Since it measures the area of a cross-section of the Fermi surface, a theoretical description of this surface complements well these experiments. However, a very accurate description of the FS is required from the ab initio calculations in order to calculate the dHvA frequencies. This is achieved using maximally localized Wannier functions (MLWF) (Marzari {\&} Vanderbilt, \textit{Phys. Rev. B}, 56, 12847)to interpolate the Hamiltonian on a dense k-point grid. In this work, we present a dHvA study of BaRh$_{2}$P$_{2}$ and of its isovalent material BaIr$_{2}$P$_{2}$, both structurally analog to the iron pnictide BaFe$_{2}$As$_{2}$. We also present results concerning LaFe$_{2}$P$_{2}$ and CeFe$_{2}$P$_{2}$ which are also related to BaFe$_{2}$As$_{2}$ by a rigid electronic band shift to account for the difference in the number of electrons.