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Register a new userDensity-operator theory of orbital magnetic susceptibility in periodic insulators
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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.
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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.
We present a constrained density functional perturbation theory scheme for the calculation of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period and the photocarrier concentration is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties and the electron-phonon interaction. We discuss in detail the case of zone center optical phonons not conserving the number of electrons and inducing a Fermi shift in the photo-electron and hole distributions. We validate our implementation by comparing with finite differences in Te and VSe2. By calculating the evolution of the phonon spectrum of Te, Si and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approximately 0.1 photocarriers per cell, the phonon spectrum is substantially modified with respect to the ground state one with new Kohn anomalies appearing and a substantial softening of zone center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transition induced by ultrafast light absorption.
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.
Starting from exact expression for the dynamical spin susceptibility in the time-dependent density functional theory a controversial issue about exchange interaction parameters and spin-wave excitation spectra of itinerant electron ferromagnets is reconsidered. It is shown that the original expressions for exchange integrals based on the magnetic force theorem (J. Phys. F14 L125 (1984)) are optimal for the calculations of the magnon spectrum whereas static response function is better described by the ``renormalized magnetic force theorem by P. Bruno (Phys. Rev. Lett. 90, 087205 (2003)). This conclusion is confirmed by the {it ab initio} calculations for Fe and Ni.
In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
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