Spin state and phase competition in TbBaCo2O5.5 and the lanthanide series LBaCo2O5+δ (0 ≤=δ≤= 1).

A clear physics picture of TbBaCo$_{2}$O$_{5.5}$ is revealed on the basis of density functional theory calculations. An antiferromagnetic (AFM) superexchange coupling between the almost high-spin Co$^{3+}$ ions competes with a ferromagnetic (FM) interaction mediated by both p-d exchange and double exchange, being responsible for the observed AFM-FM transition. And the metal-insulator transition is accompanied by an xy/xz orbital-ordering transition. Moreover, this picture can be generalized to the whole lanthanide series, and it is predicted that a few room-temperature magnetoresistance materials could be found in LnBa$_{1-x}$A$_{x}$Co$_{2}$O$_{5+\delta}$ (Ln=Ho,Er,Tm,Yb,Lu; A=Sr,Ca,Mg).