Ab initio calculations of the magnon dispersion in ferromagnetic materials typically rely on the adiabatic local density approximation (ALDA) in which the effective exchange-correlation field is everywhere parallel to the magnetization. These calcula
tions, however, tend to overestimate the magnon stiffness, defined as the curvature of the magnon frequency vs. wave vector relation evaluated at zero wave vector. Here we suggest a simple procedure to improve the magnon dispersion by taking into account gradient corrections to the ALDA at the exchange-only level. We find that this gradient correction always reduces the magnon stiffness. The surprisingly large size of these corrections ($sim 30%$) greatly improves the agreement between the calculated and the observed magnon stiffness for cobalt and nickel, which are known to be overestimated within the ALDA.
A semi-relativistic density-functional theory that includes spin-orbit couplings and Zeeman fields on equal footing with the electromagnetic potentials, is an appealing framework to develop a unified first-principles computational approach for non-co
llinear magnetism, spintronics, orbitronics, and topological states. The basic variables of this theory include the paramagnetic current and the spin-current density, besides the particle and the spin density, and the corresponding exchange-correlation (xc) energy functional is invariant under local U(1)$times$SU(2) gauge transformations. The xc-energy functional must be approximated to enable practical applications, but, contrary to the case of the standard density functional theory, finding simple approximations suited to deal with realistic atomistic inhomogeneities has been a long-standing challenge. Here, we propose a way out of this impasse by showing that approximate gauge-invariant functionals can be easily generated from existing approximate functionals of ordinary density-functional theory by applying a simple {it minimal substitution} on the kinetic energy density, which controls the short-range behavior of the exchange hole. Our proposal opens the way to the construction of approximate, yet non-empirical functionals, which do not assume weak inhomogeneity and should therefore have a wide range of applicability in atomic, molecular and condensed matter physics.
We discuss the potential advantages of calculating the effective mass of quasiparticles in the interacting electron liquid from the low-temperature free energy vis-a-vis the conventional approach, in which the effective mass is obtained from approxim
ate calculations of the self-energy, or from a quantum Monte Carlo evaluation of the energy of a variational quasiparticle wave function. While raw quantum Monte Carlo data are presently too sparse to allow for an accurate determination of the effective mass, the values estimated by this method are numerically close to the ones obtained in previous calculations using diagrammatic many-body theory. In contrast to this, a recently published parametrization of quantum Monte Carlo data for the free energy of the homogeneous electron liquid yields effective masses that considerably deviate from previous calculations and even change sign for low densities, reflecting an unphysical negative entropy. We suggest that this anomaly is related to the treatment of the exchange energy at finite temperature.
We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by introducing the
formal structure of emph{thermal density functional theory}, a density functional theory with two basic variables -- the density and the energy density -- and two conjugate fields -- the ordinary scalar potential and Luttingers thermomechanical potential. The static version of this theory is contrasted with the familiar finite-temperature density functional theory, in which only the density is a variable. We then proceed to constructing the full time-dependent non equilibrium theory, including the practically important Kohn-Sham equations that go with it. The theory is shown to recover standard results of the Landauer theory for thermal transport in the steady state, while showing greater flexibility by allowing a description of fast thermal response, temperature oscillations and related phenomena. Several results are presented here for the first time, i.e., the proof of invertibility of the thermal response function in the linear regime, the full expression of the thermal currents in the presence of Luttingers thermomechanical potential, an explicit prescription for the evaluation of the Kohn-Sham potentials in the adiabatic local density approximation, a detailed discussion of the leading dissipative corrections to the adiabatic local density approximation and the thermal corrections to the resistivity that follow from it.
Quantized spin waves, or magnons, in a magnetic insulator are assumed to interact weakly with the surroundings, and to flow with little dissipation or drag, producing exceptionally long diffusion lengths and relaxation times. In analogy to Coulomb dr
ag in bilayer two dimensional electron gases, in which the contribution of the Coulomb interaction to the electric resistivity is studied by measuring the interlayer resistivity (transresistivity), we predict a nonlocal drag of magnons in a ferromagnetic bilayer structure based on semiclassical Boltzmann equations. Nonlocal magnon drag depends on magnetic dipolar interactions between the layers and manifests in the magnon current transresistivity and the magnon thermal transresistivity, whereby a magnon current in one layer induces a chemical potential gradient and/or a temperature gradient in the other layer. The largest drag effect occurs when the magnon current flows parallel to the magnetization, however for oblique magnon currents a large transverse current of magnons emerges. We examine the effect for practical parameters, and find that the predicted induced temperature gradient is readily observable.
We study spin relaxation in dilute magnetic semiconductors near a ferromagnetic transition, where spin fluctuations become strong. An enhancement in the scattering rate of itinerant carriers from the spin fluctuations of localized impurities leads to
a change in the dominant spin relaxation mechanism from Dyakonov-Perel to spin flips in scattering. On the ferromagnetic side of the transition, we show that due to the presence of two magnetic components -- the itinerant carriers and the magnetic impurities -- with different gyromagnetic ratios, the relaxation rate of the total magnetization can be quite different from the relaxation rate of the spin. Following a disturbance of the equilibrium magnetization, the spin is initially redistributed between the two components to restore the equilibrium magnetization. It is only on a longer time scale, controlled by the spin-orbit interaction, that the total spin itself relaxes to its equilibrium state.
The localized Hartree-Fock potential has proven to be a computationally efficient alternative to the optimized effective potential, preserving the numerical accuracy of the latter and respecting the exact properties of being self-interaction free and
having the correct $-1/r$ asymptotics. In this paper we extend the localized Hartree-Fock potential to fractional particle numbers and observe that it yields derivative discontinuities in the energy as required by the exact theory. The discontinuities are numerically close to those of the computationally more demanding Hartree-Fock method. Our potential enjoys a direct-energy property, whereby the energy of the system is given by the sum of the single-particle eigenvalues multiplied by the corresponding occupation numbers. The discontinuities $c_uparrow$ and $c_downarrow$ of the spin-components of the potential at integer particle numbers $N_uparrow$ and $N_downarrow$ satisfy the condition $c_uparrow N_uparrow+c_downarrow N_downarrow=0$. Thus, joining the family of effective potentials which support a derivative discontinuity, but being considerably easier to implement, the localized Hartree-Fock potential becomes a powerful tool in the broad area of applications in which the fundamental gap is an issue.
The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surfac
e properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by ${bf S} =-gamma hbar {bf hat z}times {bf j}$, where ${bf j}$ is the particle current density in the bulk, ${bf hat z}$ the unit vector normal to the surface, and $gamma=frac{hbar}{4mc^2}$ contains only fundamental constants. For a general metallic solid $gamma$ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an {it ab initio} calculation of the spin polarization of the current-carrying film, enables a determination of $gamma$, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface.
Spin-orbit interactions in two-dimensional electron liquids are responsible for many interesting transport phenomena in which particle currents are converted to spin polarizations and spin currents and viceversa. Prime examples are the spin Hall effe
ct, the Edelstein effect, and their inverses. By similar mechanisms it is also possible to partially convert an optically induced electron-hole density wave to a spin density wave and viceversa. In this paper we present a unified theoretical treatment of these effects based on quantum kinetic equations that include not only the intrinsic spin-orbit coupling from the band structure of the host material, but also the spin-orbit coupling due to an external electric field and a random impurity potential. The drift-diffusion equations we derive in the diffusive regime are applicable to a broad variety of experimental situations, both homogeneous and non-homogeneous, and include on equal footing skew scattering and side-jump from electron-impurity collisions. As a demonstration of the strength and usefulness of the theory we apply it to the study of several effects of current experimental interest: the inverse Edelstein effect, the spin-current swapping effect, and the partial conversion of an electron-hole density wave to a spin density wave in a two-dimensional electron gas with Rashba and Dresselhaus spin-orbit couplings, subject to an electric field.
The Wiedemann-Franz law, connecting the electronic thermal conductivity to the electrical conductivity of a disordered metal, is generally found to be well satisfied even when electron-electron (e-e) interactions are strong. In ultra-clean conductors
, however, large deviations from the standard form of the law are expected, due to the fact that e-e interactions affect the two conductivities in radically different ways. Thus, the standard Wiedemann-Franz ratio between the thermal and the electric conductivity is reduced by a factor $1+tau/tau_{rm th}^{rm ee}$, where $1/tau$ is the momentum relaxation rate, and $1/tau_{rm th}^{rm ee}$ is the relaxation time of the thermal current due to e-e collisions. Here we study the density and temperature dependence of $1/tau_{rm th}^{rm ee}$ in the important case of doped, clean single layers of graphene, which exhibit record-high thermal conductivities. We show that at low temperature $1/tau_{rm th}^{rm ee}$ is $8/5$ of the quasiparticle decay rate. We also show that the many-body renormalization of the thermal Drude weight coincides with that of the Fermi velocity.
