Chemical and magnetic ordering derived from ab initio simulations: the case of β'-LiFeO2.

First-principles periodic calculations (with the B3LYP (Becke, three-parameter, Lee-Yang-Parr) hybrid functional, all-electron localized basis functions, and the CRYSTAL code) were coupled to a cluster expansion scheme in order to investigate the monoclinic β' phase of LiFeO(2), where a partially disordered Fe-Li distribution is observed within a rocksalt-type superstructure. By least-energy optimizing a limited number of ordered configurations, and employing a two-body truncated cluster expansion, the values J(1) = -0.06(2) and J(2) = -0.125(8) eV were obtained for the excess interaction energies J(i) = J(LiFe, i) - (J(LiLi, i) + J(FeFe, i))/2 corresponding to the first and second coordination spheres, respectively; negligible values were computed for third and further coordinations. The ordering phase transformation α−>β'−>γ was then addressed. Antiferromagnetic versus ferromagnetic ordering was taken into account too, and proved to lower the energy by -0.0577 eV/f.u. The corresponding cluster expansion coefficients J(i) = J(AFM, i) - J(FM, i) are J(1) = 0.007(2) and J(2) = -0.044(5) eV.