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A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the one-particle band structure of the system and a part that contains the effects of exchange and correlations carried by the Green function. The derived formula provides a convenient means of including the effects of exchange and correlations beyond the commonly used local density approximation of density functional theory.
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We derive a quantum-mechanical formula of the orbital magnetic quadrupole moment (MQM) in periodic systems by using the gauge-covariant gradient expansion. This formula is valid for insulators and metals at zero and finite temperature. We also prove a direct relation between the MQM and magnetoelectric (ME) susceptibility for insulators at zero temperature. It indicates that the MQM is a microscopic origin of the ME effect. Using the formula, we quantitatively estimate these quantities for room-temperature antiferromagnetic semiconductors BaMn$_2$As$_2$ and CeMn$_2$Ge$_{2 - x}$Si$_x$. We find that the orbital contribution to the ME susceptibility is comparable with or even dominant over the spin contribution.
Kinetic energy (KE) approximations are key elements in orbital-free density functional theory. To date, the use of non-local functionals, possibly employing system dependent parameters, has been considered mandatory in order to obtain satisfactory accuracy for different solid-state systems, whereas semilocal approximations are generally regarded as unfit to this aim. Here, we show that instead properly constructed semilocal approximations, the Pauli-Gaussian (PG) KE functionals, especially at the Laplacian-level of theory, can indeed achieve similar accuracy as non-local functionals and can be accurate for both metals and semiconductors, without the need of system-dependent parameters.
The theoretical treatment of homogeneous static magnetic fields in periodic systems is challenging, as the corresponding vector potential breaks the translational invariance of the Hamiltonian. Based on density operators and perturbation theory, we propose, for insulators, a periodic framework for the treatment of magnetic fields up to arbitrary order of perturbation, similar to widely used schemes for electric fields. The second-order term delivers a new, remarkably simple, formulation of the macroscopic orbital magnetic susceptibility for periodic insulators. We validate the latter expression using a tight-binding model, analytically from the present theory and numerically from the large-size limit of a finite cluster, with excellent numerical agreement.
We herein present a first-principles formulation of the Green-Kubo method that allows the accurate assessment of the non-radiative thermal conductivity of solid semiconductors and insulators in equilibrium ab initio molecular dynamics calculations. Using the virial for the nuclei, we propose a unique ab initio definition of the heat flux. Accurate size- and time convergence are achieved within moderate computational effort by a robust, asymptotically exact extrapolation scheme. We demonstrate the capabilities of the technique by investigating the thermal conductivity of extreme high and low heat conducting materials, namely diamond Si and tetragonal ZrO$_2$.
We report electronic structure calculations of an iron impurity in gold host. The spin, orbital and dipole magnetic moments were investigated using the LDA+$U$ correlated band theory. We show that the {em around-mean-field}-LDA+$U$ reproduces the XMCD experimental data well and does not lead to formation of a large orbital moment on the Fe atom. Furthermore, exact diagonalization of the multi-orbital Anderson impurity model with the full Coulomb interaction matrix and the spin-orbit coupling is performed in order to estimate the spin Hall angle. The obtained value $gamma_S approx 0.025$ suggests that there is no giant extrinsic spin Hall effect due to scattering on iron impurities in gold.
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