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Register a new userMuffin Tin Orbitals of Arbitrary Order
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We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and overlap matrices, are specified by the values on the energy mesh of the screened resolvent and its first energy derivative. These orbitals are a generalization of the 3rd-generation linear MTOs and should be useful for electronic-structure calculations in general.
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By the example of sp^3-bonded semiconductors, we illustrate what 3rd-generation muffin-tin orbitals (MTOs) are. We demonstrate that they can be downfolded to smaller and smaller basis sets: sp^3d^10,sp^3, and bond orbitals. For isolated bands, it is possible to generate Wannier functions a priori. Also for bands, which overlap other bands, Wannier-like MTOs can be generated a priori. Hence, MTOs have a unique capability for providing chemical understanding.
We present a self-consistent electronic structure calculation method based on the {it Exact Muffin-Tin Orbitals} (EMTO) Theory developed by O. K. Andersen, O. Jepsen and G. Krier (in {it Lectures on Methods of Electronic Structure Calculations}, Ed. by V. Kumar, O.K. Andersen, A. Mookerjee, Word Scientific, 1994 pp. 63-124) and O. K. Andersen, C. Arcangeli, R. W. Tank, T. Saha-Dasgupta, G. Krier, O. Jepsen, and I. Dasgupta, (in {it Mat. Res. Soc. Symp. Proc.} {bf 491}, 1998 pp. 3-34). The EMTO Theory can be considered as an {it improved screened} KKR (Korringa-Kohn-Rostoker) method which is able to treat large overlapping potential spheres. Within the present implementation of the EMTO Theory the one electron equations are solved exactly using the Greens function formalism, and the Poissons equation is solved within the {it Spherical Cell Approximation} (SCA). To demonstrate the accuracy of the SCA-EMTO method test calculations have been carried out.
Based on the exact muffin-tin orbitals (EMTOs), we developed a first-principles method to calculate the current operators and investigated the anomalous Hall effect in bcc Fe as an example, with which we successfully separated the skew scattering contribution from the side jump and intrinsic contributions by fitting the scaling law with the introduction of sparse impurities. By investigating the temperature dependence of the anomalous Hall effect in bulk Fe, we predicted a fluctuated anomalous Hall angle as a function of temperature when considering only phonons, which, in the future, can be measured in experiments by suppressing magnon excitation, e.g., by applying a high external magnetic field.
We present the formalism and demonstrate the use of the overlapping muffin-tin approximation (OMTA). This fits a full potential to a superposition of spherically symmetric short-ranged potential wells plus a constant. For one-electron potentials of this form, the standard multiple-scattering methods can solve Schr{o}dingers equation correctly to 1st order in the potential overlap. Choosing an augmented-plane-wave method as the source of the full potential, we illustrate the procedure for diamond-structured Si. First, we compare the potential in the Si-centered OMTA with the full potential, and then compare the corresponding OMTA $N$-th order muffin-tin orbital and full-potential LAPW band structures. We find that the two latter agree qualitatively for a wide range of overlaps and that the valence bands have an rms deviation of 20 meV/electron for 30% radial overlap. Smaller overlaps give worse potentials and larger overlaps give larger 2nd-order errors of the multiple-scattering method. To further remove the mean error of the bands for small overlaps is simple.
The most popular electronic structure method, the linear muffin-tin orbital method (LMTO), in its full-potential (FP) and relativistic forms has been extended to calculate the spectroscopic properties of materials form first principles, i.e, optical spectra, x-ray magnetic circular dichroism (XMCD) and magneto-optical kerr effect (MOKE). The paper describes an overview of the FP-LMTO basis set and the calculation of the momentum matrix elements. Some applications concerning the computation of optical properties of semiconductors and XMCD spectra of transition metal alloys are reviewed.
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