Electronic structure, cohesive properties and magnetism of SrRuO$_3$; a theoretical investigation

We have performed an extensive test of the ability of density functional theory within several approximations for the exchange-correlation functional, local density approximation+Hubbard $U$ and local density approximation + dynamic mean field theory to describe magnetic and electronic properties of SrRuO$_3$. We focus on the ferromagnetic phase, illustrating differences between the orthorhombic low temperature structure vs the cubic high temperature structure. We assess how magnetism, spectral function, and cohesive properties are affected by methodology, on-site Hubbard $U$ and double counting corrections. Further, we compare the impact of the impurity solver on the quasiparticle weight $Z$, which is in turn compared to experimental results. The spectral functions resulting from the different treatments are also compared to experimental data. The impact of spin-orbit coupling is also studied, allowing us to determine the orbital moments. In the orthorhombic phase the orbital moments are found to be tilted with respect to the spin moments, emphasising the importance of taking into account the distortion of the oxygen octahedra.