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Fermi surface topology and de Hass-van Alphen orbits in PuIn$_{\rm 3}$ and PuSn$_{\rm 3}$ compounds

Since the recent discovery of plutonium-based superconductors such as PuCoIn$_{\rm 5}$, systematic studies of the electronic properties for plutonium compounds are providing insight into the itinerancy-localization crossover of Pu 5$f$ electrons. We are particularly interested in understanding the Fermi surface properties of PuIn$_{3}$ compound, which serves as the building block for the PuCoIn$_{\rm 5}$ superconductor. Motivated by the first observation of quantum oscillation and renewed interest in the de-Hass van-Alphen (dHvA) measurements on PuIn$_{\rm 3}$, we study the Fermi surface (FS) topology and the band dispersion in both paramagnetic and antiferromagnetic state of PuIn$_{\rm 3}$, based on density functional theory with generalized gradient approximation. We compare the results with its isostructural paramagnetic compound PuSn$_{\rm 3}$. We show the detailed Fermi surfaces of compounds PuIn$_{\rm 3}$ and PuSn$_{\rm 3}$ and conclude that the FS topology of an antiferromagnetic PuIn$_3$ agrees better with dHvA measurements. In addition, we show the magnetization of the antiferromagnetic order can alter the angle dependence and values of the effective mass for the dHvA orbits. We point out the accurate determination of the magnetic order orientation with respect to the crystal orientation is crucial to advance the understanding of the electronic structures of the PuIn$_{\rm 3}$ compound.