We report the electronic structure and magnetic properties of Co2Ti1-xGexO4(0 ≤ x ≤ 1) spinel by means of the first-principles methods of density functional theory involving generalized gradient approximation (GGA) along with the on-site Coulomb interaction (Ueff) in the exchange-correlation energy functional. Special emphasis has been given to explore the site occupancy of Ge atoms in the spinel lattice by introducing the cationic disorder parameter (y) which is done in such a way that one can tailor the Pyrochlore geometry and determine the electronic/magnetic structure quantitatively. For all the compositions (x), the system exhibits weak tetragonal distortion (c/a ≠ 1) due to the non-degenerate dz2and dx2-y2states (egorbitals) of the B-site Co. We observe large exchange splitting (ΔEX~ 9 eV) between the up and down spin bands of t2gand egstates, respectively, of tetrahedral and octahedral Co+2(4A2(g)(F)) and moderate crystal-field splitting (ΔCF~ 4 eV) and the Jahn-Teller distortion (ΔJT~ 0.9 eV). These features indicate the strong intra-atomic interaction which is also responsible for the alteration of energy band-gap (1.7 eV ≤ Eg≤ 3.3 eV). The exchange interaction (JBB~-4.8 meV, for (x,y) = (0.25, 0)) between the Co2+dominates the overall antiferromagnetic behavior of the system for all 'x' as compared to interactions JAA(~-2.2 meV, for (x,y) = (0.25, 0)) and JAB(~-1.8 meV, for (x,y) = (0.25, 0)). For all the compositions without any disorderness in the system, net ferrimagnetic moment (Δμ) remains constant, however, Δμ increases progressively with x due to the imbalance of Co spins between the A- and B-sites (ΔμMAX~ -4.4μBfor x = 0.75 and y = 1.0).

中文翻译：

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调整烧绿石 Co2Ti1-xGexO4 的电子结构和磁性：GGA+U 从头算研究

我们通过涉及广义梯度近似 (GGA) 的密度泛函理论的第一性原理方法以及现场库仑相互作用 (Ueff) 报告了 Co2Ti1-xGexO4(0 ≤ x ≤ 1) 尖晶石的电子结构和磁性在交换相关能量泛函中。特别强调通过引入阳离子无序参数 (y) 来探索尖晶石晶格中 Ge 原子的位点占有率，该参数以这样一种方式完成，即可以定制烧绿石几何形状并定量确定电子/磁性结构。对于所有成分 (x)，由于 B 位 Co 的非简并 dz2 和 dx2-y2 态 (egorbitals)，系统表现出弱四方畸变 (c/a ≠ 1)。我们观察到四面体和八面体 Co+2(4A2(g)(F)) 的 t2gand egstates 的上下自旋带之间的大交换分裂 (ΔEX~ 9 eV) 和中等晶体场分裂 (ΔCF~ 4 eV) 和 Jahn-Teller 畸变 (ΔJT~ 0.9 eV)。这些特征表明强烈的原子内相互作用也是造成能带隙变化的原因（1.7 eV ≤ Eg≤ 3.3 eV）。与相互作用 JAA（~-2.2 meV , 对于 (x,y) = (0.25, 0)) 和 JAB(~-1.8 meV, 对于 (x,y) = (0.25, 0))。然而，对于系统中没有任何无序的所有成分，净亚铁磁矩（Δμ）保持不变，