Title: Multiple localized-itinerant dualities in magnetism of 5f electron systems. The case of UPt$_2$Si$_2$

Abstract: The paper deals with the U based compound UPt$_2$Si$_2$ (UPS). The material was first treated as a localized 5f-electron system. Later, an opposite opinion of a predominantly itinerant nature of the system was put forward. The most recent publications treat UPS as a dual material. We suggest a material specific theoretical model based on the density functional theory plus Hubbard $U$ (DFT+$U$) calculations that describes the set of fundamental ground-state properties and high magnetic field experiment. The ground state properties include antiferromagnetic magnetic structure, magnetic easy axis, and the value of the U atomic moment. The in-field experiment shows the presence of a strong metamagnetic transition for the field parallel to the easy axis in contrast to the hard field direction where such a feature is absent. On the other hand, comparable induced magnetization values are obtained for both easy and hard field directions. Within the framework of the suggested model we show that the compound possesses well-formed atomic moments built by electrons treated as delocalized. To understand the experimental high-field properties we estimate exchange energy, magnetic anisotropy energy, and Zeeman energy. All three energies are shown to have comparable values what is crucial for the interpretation of the experiment. At all steps of the study we devote special attention to revealing and emphasizing the dual itinerant-localized properties of the material. The obtained forms of the duality are different: well defined atomic moments formed by the itinerant electrons, interplay of the single-site and two-site anisotropies, strong localization of two of the 5f electrons in contrast to the itinerant nature of the 5f electrons contributing to the states around the Fermi level.