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首页> 外文期刊>Physical review >Hybrid density functional theory applied to magnetite: Crystal structure, charge order, and phonons
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Hybrid density functional theory applied to magnetite: Crystal structure, charge order, and phonons

机译：混合密度泛函理论应用于磁铁矿：晶体结构，电荷序和声子

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The electronic structure and equilibrium structure of magnetite (Fe_3O_4) in the high temperature cubic Fd3m and low temperature monoclinic P2/c unit cells have been computed using the Perdew-Wang generalized gradient approximation (GGA) to density functional theory (DFT) and the B3LYP hybrid density functional. The ground state for the GGA-DFT is an itinerant electron metallic state in the cubic unit cell and the ground state for the B3LYP functional is a charge ordered semiconducting state in the monoclinic unit cell. The equilibrium structure predicted by the B3LYP functional for Fe_3O_4 in the P2/c unit cell has been calculated with lattice parameters fixed at values obtained in recent x-ray diffraction work and with the lattice fully relaxed. Bond lengths obtained with lattice parameters fixed at experimental values are in excellent agreement with x-ray measurements [J. P. Wright et al, Phys. Rev. B 66, 214422 (2002)]. The degree of charge order, measured as disproportionation of charge on octahedral B sites, is considerably less than unity and in reasonable agreement with values from resonant x-ray diffraction measurements. However, conduction electrons are found to be fully localized on B1 and B4 sites in orbitally ordered t_(2g) states. This shows that they are formally Fe~(2+) ions while Fe B2 and B3 sites are formally Fe~(3+) sites. Therefore Verwey's original conjecture regarding charge localization in Fe_3O_4 applies, even though the specific pattern of charge order is different. GGA-DFT and B3LYP density functionals were used to calculate phonons at the Γ point of the Brillouin zone. Phonon frequencies predicted for these crystal structures are compared to frequencies from infrared conductivity and Raman scattering experiments. Charge ordering causes symmetry breaking of force constants on symmetry lowering from the cubic Fd3m unit cell to the P2/c unit cell. This produces frequency splitting of modes which are degenerate in the cubic unit cell and concentration of ion displacements in phonon eigenvectors on particular Fe octahedral B site chains, especially in the highest frequency bands.
机译：利用Perdew-Wang广义梯度近似（GGA），密度泛函理论（DFT）和B3LYP计算了高温立方Fd3m和低温单斜P2 / c晶胞中磁铁矿（Fe_3O_4）的电子结构和平衡结构。杂种密度功能。在立方晶胞中，GGA-DFT的基态是流动电子金属态，而在单斜晶胞中，B3LYP官能团的基态是电荷有序半导体态。在P2 / c晶胞中B3LYP对Fe_3O_4的功能预测的平衡结构的晶格参数固定为最近X射线衍射工作中获得的值，并且晶格完全松弛。用固定在实验值上的晶格参数获得的键长与X射线测量结果非常吻合[J． P.Wright等人，《物理学报》。修订版B 66，214422（2002）]。以八面体B位置上电荷的歧化度衡量的电荷阶数大大小于1，并且与共振X射线衍射测量的值合理地吻合。但是，发现导电电子完全位于轨道有序t_（2g）状态的B1和B4位置上。这表明它们在形式上是Fe〜（2+）离子，而Fe B2和B3位置在形式上是Fe〜（3+）位置。因此，即使电荷顺序的特定模式不同，Verwey关于Fe_3O_4中的电荷定位的原始推测也适用。 GGA-DFT和B3LYP密度泛函用于计算布里渊区Γ点的声子。将针对这些晶体结构预测的声子频率与来自红外电导率和拉曼散射实验的频率进行比较。电荷排序导致力常数的对称破坏，对称性从立方Fd3m晶胞降低到P2 / c晶胞。这会产生模式分裂的频率分裂，这些模式在立方晶胞中退化，并且在特定的Fe八面体B位点链上，尤其是在最高频带中，声子本征向量中的离子位移集中。

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