We review studies of the electromagnetic response of various classes of correlated electron materials including transition metal oxides, organic and molecular conductors, intermetallic compounds with $d$- and $f$-electrons as well as magnetic semiconductors. Optical inquiry into correlations in all these diverse systems is enabled by experimental access to the fundamental characteristics of an ensemble of electrons including their self-energy and kinetic energy. Steady-state spectroscopy carried out over a broad range of frequencies from microwaves to UV light and fast optics time-resolved techniques provide complimentary prospectives on correlations. Because the theoretical understanding of strong correlations is still evolving, the review is focused on the analysis of the universal trends that are emerging out of a large body of experimental data augmented where possible with insights from numerical studies.

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Electrodynamics of correlated electron materials

The authors have calculated the optical properties (dielectric function, reflectivity and electron energy loss function) of 15 metals, including all the 4d series, some 3d metals and some noble and simple metals. The calculations are based on the LMTO band structure with optical matrix elements. The very good quantitative agreement with optical measurements provides an a posteriori justification of the use of local density functional method in the calculations of the dynamical response in metals and also allows an analysis of the general trends in optical properties from the electronic structure point of view.

http://muri.lci.kent.edu/References/NIM_Papers/Metal_properties/1988_MaksimovMetal_Properties.pdf

First-principles calculations of the optical properties of metals

Publisher Summary Stimulated by technological prospects of high-density magneto-optical (MO) recording and by fundamental research on magnetism, a wealth of experimental data on MO Kerr spectra had been collected until the beginning of the nineties. The theoretical explanation of magneto-optical Kerr effect (MOKE) spectra because of first-principles band-structure calculations was at that time in its infancy, and consequently all the insight that theory could give in the microscopic mechanism leading to large Kerr rotations was mainly speculative, because nothing could be proven by first-principles calculations. This situation has profoundly changed, due to the rapid development of first-principles computational research on MO Kerr spectra during the nineties.

Chapter 3 Magneto-optical kerr spectra

The microscopic quantities that determine the magnitude and frequency position of peaks in the Kerr rotation spectrum are studied on the basis of first-principles band-structure theory. The transition metals Fe, Co and Ni serve as model systems. The magnitude of the magnetooptical Kerr effec (MOKE) is basically brought about by the spin-orbit (SO) coupling strength and it is shown that the Kerr rotation scales linearly with the SO-coupling. Exchange splitting (or magnetization) is found to influence the Kerr effect in a rather complicated way: enlarging the magnetization can both enhance and diminish spectral peaks. A strong effect is found for the dependence of the position of spectral peaks on the lattice spacing: a 3 to 6% increase in lattice parameters can lead to shifts of about 1 eV of the main MOKE peak.

Ab initio investigation of microscopic enhancement factors in tuning the magneto-optical Kerr effect

Being motivated by recent experimental studies, we investigate magnetic structures of the Mo pyrochlores ${A}_{2}{\mathrm{Mo}}_{2}{\mathrm{O}}_{7}$ $(A=\mathrm{Y},$ Nd, and Gd) and their impact on the electronic properties. The latter are closely related with the behavior of twelve $\mathrm{Mo}{(t}_{2g})$ bands, located near the Fermi level and well separated from the rest of the spectrum. We use a mean-field Hartree-Fock approach, which combines fine details of the electronic structure for these bands, extracted from the conventional calculations in the local-density approximation, the spin-orbit interaction, and the on-site Coulomb interactions among the $\mathrm{Mo}(4d)$ electrons, treated in the most general rotationally invariant form. The Coulomb repulsion U plays a very important role in the problem, and the semi-empirical value $U\ensuremath{\sim}1.5--2.5\mathrm{eV}$ accounts simultaneously for the metal-insulator (MI) transition, the ferromagnetic (FM)---spin-glass (SG) transition, and for the observed enhancement of the anomalous Hall effect (AHE). The MI transition is mainly controlled by U. The magnetic structure at the metallic side is nearly collinear FM, due to the double exchange mechanism. The transition into the insulating state is accompanied by the large canting of spin and orbital magnetic moments. The sign of exchange interactions in the insulating state is controlled by the Mo-Mo distances. Smaller distances favor the antiferromagnetic coupling, which predetermines the SG behavior in the frustrated pyrochlore lattice. A large AHE is expected in the nearly collinear FM state, near the point of MI transition, and is related with the unquenched orbital magnetization at the Mo sites. We also predict a large magneto-optical effect in the same FM compounds.

Effects of crystal structure and on-site Coulomb interactions on the electronic and magnetic structure of A 2 Mo 2 O 7 ( A = Y , Gd, and Nd) pyrochlores

Because of the variational character of the most of the modern band structure calculation methods, including LMTO, the calculated electron energies are much more accurate than the wave functions. This affects greatly the optical matrix elements calculations. We investigated the problem of the accurate calculation of the matrix elements in the frameworks of usual band structure methods, basing on the continuity equation for the charge density operator. We have derived an analytical expression for corrections to the common-used formulas for the optical matrix elements. These allow to compute the matrix elements with the same accuracy as the band structure so that the intraband matrix elements are exactly equal to the band electron velocities. A specific prescription is proposed for the optical matrix elements calculation in the frameworks of the LMTO method. The imagine parts of the dielectric functions are calculated for Cu and Pd in the energy range 0.1–20 eV, which agree well with available experimental data.

Sergey Rashkeev

Papers

Calculations of the optical properties of metals by LMTO method