Abstract
We discuss the thermodynamic and magnetic properties of a competing high-spin/low-spin two-orbital two-electron model on a square lattice possibly relevant to the nickelates such as ${\mathrm{Ba}}_{2}{\mathrm{NiO}}_{2}{(\mathrm{AgSe})}_{2}$. We focus on parameter regimes where a high-spin ($S=1$) and a low-spin ($S=0$) state are energetically close to each other and discuss various exchange processes in such a system. The model we study is motivated by, but different from, the Kondo-necklace model proposed for the system recently [Jin et al., Phys. Rev. Research 2, 033197 (2020)]. Although there are similarities between the two models in terms of the ground-state phases and their symmetries, the detailed properties of the different phases and the nature of phase transitions are entirely different and should be easy to distinguish from an experimental point of view.
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