The importance of many-body effects on electronic and magnetic properties and stability of different structural phases was studied in novel iron oxide - Fe$_2$O. It was found that while Hubbard repulsion hardly affects the electronic spectrum of this material ($m^*/m sim 1.2$), but it strongly changes its phase diagram shifting critical pressures of structural transitions to much lower values. Moreover, one of the previously obtained in the density functional theory (DFT) structures (P$bar 3$m1) becomes energetically unstable if many-body effects are taken into consideration. It is shown that this is an account of magnetic moment fluctuations in the DFT+DMFT approach, which strongly contributes to modification of the phase diagram of Fe$_2$O.
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