We extend the recently-developed theory of bulk orbital magnetization to finite electric fields, and use it to calculate the orbital magnetoelectric response of periodic insulators. Working in the independent-particle framework, we find that the finite-field orbital magnetization can be written as a sum of three gauge-invariant contributions, one of which has no counterpart at zero field. The extra contribution is collinear with and explicitly dependent on the electric field. The expression for the orbital magnetization is suitable for first-principles implementations, allowing to calculate the magnetoelectric response coefficients by numerical differentiation. Alternatively, perturbation-theory techniques may be used, and for that purpose we derive an expression directly for the linear magnetoelectric tensor by taking the first field-derivative analytically. Two types of terms are obtained. One, the 'Chern-Simons' term, depends only on the unperturbed occupied orbitals and is purely isotropic. The other, 'Kubo' terms, involve the first-order change in the orbitals and give isotropic as well as anisotropic contributions to the response. In ordinary magnetoelectric insulators all terms are generally present, while in strong Z 2 topological insulators only the Chern-Simons term is allowed, and is quantized. In order to validate the theory we have calculated under periodic boundary conditions the linear magnetoelectric susceptibility for a 3-D tight-binding model of an ordinary magnetoelectric insulator, using both the finite-field and perturbation-theory expressions. The results are in excellent agreement with calculations on bounded samples. PACS numbers: 75.85.+t,03.65.Vf,71.15.Rf Submitted to: New J. Phys. ‡ An analogous situation occurs in the theory of polarization: inversion symmetry, which takes P into −P, allows for a nontrivial solution which does not include P = 0 in the "lattice" of values [20]. An important difference is that while θ is a directly measurable response, only changes in P are detectable, so that the experimental implications of the nontrivial solution are less clear in this case.

We carry out a first-principles theoretical study of the magnetically induced polarization in orthorhombic TbMnO3, a prototypical material in which a cycloidal-spin structure generates an electric polarization via the spin-orbit interaction. We compute both the electronic and the lattice-mediated contributions to the polarization and find that the latter is strongly dominant. We analyze the spin-orbit induced forces and lattice displacements from both atomic and mode-decomposition viewpoints, and show that a simple model based on nearest Mn-Mn neighbor Dzyaloshinskii-Moriya interactions is not able to account fully for the results. The direction and magnitude of our computed polarization are in good agreement with experiment.

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Metallic electronic transport in nickelate heterostructures can be induced and confined to two dimensions (2D) by controlling the structural parameters of the nickel-oxygen planes.

We present a Wannier-based method to calculate the Chern-Simons orbital magnetoelectric coupling in the framework of first-principles density-functional theory. In view of recent developments in connection with strong 2 topological insulators, we anticipate that the Chern-Simons contribution to the magnetoelectric coupling could, in special cases, be as large or larger than the total magnetoelectric coupling in known magnetoelectrics like Cr2O3. The results of our calculations for the ordinary magnetoelectrics Cr2O3, BiFeO3 and GdAlO3 confirm that the Chern-Simons contribution is quite small in these cases. On the other hand, we show that if the spatial inversion and time-reversal symmetries of the 2 topological insulator Bi2Se3 are broken by hand, large induced changes appear in the Chern-Simons magnetoelectric coupling.

Working in the crystal-momentum representation, we calculate the optical conductivity of noncentrosymmetric insulating crystals at first order in the wave vector of light. The time-even part of this tensor describes natural optical activity and the time-odd part describes nonreciprocal effects such as gyrotropic birefringence. The time-odd part can be uniquely decomposed into magnetoelectriclike and purely quadrupolar contributions. The magnetoelectriclike component reduces in the static limit to the traceless part of the frozen-ion static magnetoelectric polarizability while at finite frequencies it acquires some quadrupolar character in order to remain translationally invariant. The expression for the orbital contribution to the conductivity at transparent frequencies is validated by comparing numerical tight-binding calculations for finite and periodic samples.Comment: 9 pages, 4 figure

Density functional theory was used to assess the viability of approaches to controlling the structure of a recently discovered two-dimensional form of SiO2. In accord with prior work, a hexagonal bilayer of mirror image planes of corner-sharing SiO4 tetrahedra in six-membered rings yielded only a slightly higher energy than α-quartz. Structures including four- through eight-membered rings were evaluated and in certain cases found to be as little as 17 meV/Si higher in energy than the hexagonal bilayer. When either biaxial or uniaxial tensile strain was applied, combinations of eight-, six-, and four-membered rings became favored due to the lower density of structures with larger rings. These findings, together with experiments that reveal expansion of silica bilayers to match the lattice of metal substrates, suggest that epitaxial strain may be used to control the bilayer structure. Replacement of Si with Ge and Al as prototypical tetravalent and trivalent dopants was also investigated. Substituting Ge for Si was energetically unfavorable and offered no obvious advantage for structural control over pure SiO2 bilayers. In contrast, Al substitution was energetically favorable and only minimally distorted the bilayer. It was found that while the hexagonal bilayer remained favored, the extra-framework electron donors K and H that accompany each Al preferred to occupy larger rings when possible, thus forcing Al to reside in large rings as well. This suggests that the bilayer structure may be controlled through substitution of Si for trivalent dopants and selection of extra-framework electron donors that favor larger rings.

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