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Cation spin and superexchange interaction in oxide materials below and above spin crossover under high pressure

We derived simple rules for the sign of superexchange interaction based on the multielectron calculations of the superexchange interaction in the transition metal oxides that are valid both below and above spin crossover under high pressure. The superexchange interaction between two cations in d$^n$ configurations is given by a sum of individual contributions related to the electron-hole virtual excitations to the different states of the d$^{n + 1}$ and d$^{n - 1}$ configurations. Using these rules, we have analyzed the sign of the superexchange interaction of a number of oxides with magnetic cations in electron configurations from d$^2$ till d$^8$: the iron, cobalt, chromium, nickel, copper and manganese oxides with increasing pressure. The most interesting result concerns the magnetic state of cobalt and nickel oxides CoO, Ni$_2$O$_3$ and also La$_2$CoO$_4$, LaNiO$_3$ isostructural to well-known high-T$_C$ and colossal magnetoresistance materials. These oxides have a spin $\frac{1}{2}$ at the high pressure. Change of the interaction from antiferromagnetic below spin crossover to ferromagnetic above spin crossover is predicted for oxide materials with cations in d$^5$(FeBO$_3$) and d$^7$(CoO) configurations, while for materials with the other d$^n$ configurations spin crossover under high pressure does not change the sign of the superexchange interaction.