Binuclear unit(Ti2Cl9)3−: A new development for the exchange between orbitally unquenched ions

The problem of exchange interaction between two ${\mathrm{Ti}}^{3+}$ ($d^1$) ions in a binuclear unit ${\left({\mathrm{Ti}}_2{\mathrm{Cl}}_9\right)}^{3-}$ is investigated from a microscopic description of the exchange mechanisms. With the use of pseudofermion operators, the effective Hamiltonian between the orbitally degenerate ground terms ${}_{}{}^2{}_{}{}^{}T_{2g}^{}{}_{}{}^{}$ is determined with the various excited configurations being taken into account. Further, local trigonal distortion, spin-orbit coupling, and covalency effects are introduced for describing the real magnetic behavior of the entity. Thus it is shown that the use of the Heisenberg Hamiltonian for distorted systems is often a poor approximation. Lastly, a least-squares fitting of the experimental data of ${\mathrm{Cs}}_3$ ${\mathrm{Ti}}_2$ ${\mathrm{Cl}}_9$ is proposed from the developed model.