Analysis of charge and orbital order in Fe3O4by FeL2,3

Abstract

To elucidate charge and orbital order below the Verwey transition temperature T V ∼ 125 K, a thin layer of magnetite partially detwined by growth on the stepped MgO(001) substrate has been studied by means of soft x-ray diffraction at the Fe L 2,3 resonance. The azimuth angle, incident photon polarization, and energy dependence of the (00 1 2 ) c and (001) c reflection intensities have been measured, and analyzed using a configuration-interaction FeO 6 cluster model. The azimuth dependence of the (00 1 2 ) c reflection intensities directly represents the space-group symmetry of the orbital order in the initial state rather than indirectly through the intermediate-state level shifts caused by the order-induced lattice distortions. From the analysis of the (00 1 2 ) c reflection intensities, the orbital order in the t 2g orbitals of B sites below T V is proved to have a large monoclinic deformation with the value of Re[F xy ]/Re[F yz ] ∼ 2. This finding contradicts the majority of theories on the Verwey transition so far proposed. We show that the experimentally observed resonance spectra cannot be explained by orbital and charge orders obtained with recent LDA + U and GGA + U band structure calculations but by a complex-number orbital order with excellent agreement.

Weak antilocalization in (111) thin films of a topological crystalline insulator SnTe

“…In the surface transport through the SS of 3D TIs, which is classified into the symplectic group, the value of α should be −0.5 per single transport channel. In the (111) surface of SnTe, the total number of Dirac cones is four, three on the M points which are projections of L points, and one on the Γ point which are projections of Γ or L points [9]. In addition, considering the surface transport through both the top and bottom surfaces of the film, the total number of the channel should be 8, resulting in the value of |α| = 4.…”

“…SnTe was predicted to be one of the TCIs whose SS is protected by mirror symmetry with respect to the {111}, {001}, and {110} planes of the rock-salt crystal structure. The APRES measurement confirmed the topological phase in the (001) and (111) surfaces of SnTe by observing Dirac-cone band dispersion derived from the SS[8] [9] as well as Pb 1−x Sn x Te(x < 0.25) [10] and in the (001) surface of Pb 0.73 Sn 0.27 Se [11]. In addition, the electrical transport properties which are characteristics of two-dimensional (2D) SS have been reported, such as the Shubnikov-de Haas (SdH) oscillation [12], and the Altshuler-Aronov-Spivak (AAS)/ the Aharonov-Bohm (AB) effect [13].…”

Fe3O4 thin films: controlling and manipulating an elusive quantum material

“…This makes the Verwey transition in the tensile strained films even more interesting: would the charge and orbital order be of the same type as in the bulk, for which there is a lot of debate, see Refs. [30], [31], [32], and references therein. In this respect, we would like to note that the resistivity across the Verwey transition changes by about a factor 10 in the films while it is by a factor 100 in the bulk.…”

“…Clearly the presence of the substrate limits a full opening of the conductivity gap by putting constraints on the crystal structure. Nevertheless the transition does take place and so the question arises what are the minimal conditions required in terms of the local electronic structure such as the orbital state for such a transition to occur.It would be extremely interesting to address this question by, for example, carrying out charge and/or orbital sensitive resonant x-ray diffraction experiments, see Ref [32]. and references therein.…”

Measurement of the Resonant Magneto-Optical Kerr Effect Using a Free Electron Laser

“…This technique can determine the magnetic structures of antiferromagnets and helimagnets. Resonant X-ray diffraction is also measured in the hard X-ray range for detection of charges and orbital orders; however, the magnetic scattering cross-section is extremely small in the hard X-ray range when compared with that in the soft X-ray range [30,37]. Additionally, because the 3d states can be accessed directly in the soft X-ray range, resonant magnetic scattering is mainly used in the soft X-ray range.…”