Effects of electron correlation and spin-orbit coupling on the electronic and magnetic properties of TbCu₃Mn₄O₁₂

Electronic and magnetic properties of the three magnetic-sublattice double perovskite TbCu₃Mn₄O₁₂ (TCMO) are investigated by performing first-principles density-functional theory calculations. Our electronic structure calculations show that TCMO is half-metallic and its half-metallicity can only be correctly described when the electron correlation on Tb³⁺ 4f⁸ electrons are considered. The energies of different magnetic configurations among the three magnetic sublattices are also calculated, revealing that the magnetic configuration with Mn and Cu spins in the antiparallel arrangement and with the Tb magnetic moments ferromagnetically/antiferromagnetically (FM/AFM) coupled to Cu/Mn spins (that is Tb^↓Cu₃^↓Mn₄^↑O₁₂) is the lowest energetic magnetic state, which is consistent with recent experimental results. The magnetic anisotropy is further calculated for the [1 1 1], [1 1 0], and [0 0 1] spin quantization directions. It is found that the [1 1 1]-direction is more stable than the [1 1 0]- and [0 0 1]-directions by 123 and 135 meV per formula unit, respectively, indicating a significant magnetic anisotropy. Our detailed projected partial density of states analysis finally shows that Cu and Mn are antiferromagnetically coupled by superexchange interaction and Tb is expected to interact FM with A-site Cu and AFM with B-site Mn sublattices by way of 4f-2p-3d.