Time-dependent Spin-density Functional Theory Research Articles

Magnetization dynamics with time-dependent spin-density functional theory: Significance of exchange-correlation torques

In spin-density functional theory (SDFT) 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. Exact benchmark solutions for a five-site extended Hubbard lattice at half filling and in the presence of spin-orbit coupling are compared with SDFT results obtained using orbital-dependent exchange-only approximations. The magnetization dynamics following short-pulse excitations is found to be reasonably well described in the exchange-only approximation for weak to moderate interactions. For stronger interactions and near transitions between magnetically ordered and frustrated phases, exchange and correlation torques tend to compensate each other and must both be accounted for.

First-principles calculation of the parameters used by atomistic magnetic simulations

While the ground state of magnetic materials is in general well described on the basis of spin density functional theory (SDFT), the theoretical description of finite-temperature and non-equilibrium properties require an extension beyond the standard SDFT. Time-dependent SDFT (TD-SDFT), which give for example access to dynamical properties are computationally very demanding and can currently be hardly applied to complex solids. Here we focus on the alternative approach based on the combination of a parameterized phenomenological spin Hamiltonian and SDFT-based electronic structure calculations, giving access to the dynamical and finite-temperature properties for example via spin-dynamics simulations using the Landau–Lifshitz–Gilbert (LLG) equation or Monte Carlo simulations. We present an overview on the various methods to calculate the parameters of the various phenomenological Hamiltonians with an emphasis on the KKR Green function method as one of the most flexible band structure methods giving access to practically all relevant parameters. Concerning these, it is crucial to account for the spin–orbit coupling (SOC) by performing relativistic SDFT-based calculations as it plays a key role for magnetic anisotropy and chiral exchange interactions represented by the DMI parameters in the spin Hamiltonian. This concerns also the Gilbert damping parameters characterizing magnetization dissipation in the LLG equation, chiral multispin interaction parameters of the extended Heisenberg Hamiltonian, as well as spin–lattice interaction parameters describing the interplay of spin and lattice dynamics processes, for which an efficient computational scheme has been developed recently by the present authors.

Time-dependent spin-density-functional-theory description of He+ -He collisions

Theoretical total cross-section results for all ionization and capture processes in the ${\mathrm{He}}^{+}$-He collision system are presented in the approximate impact energy range of 10--1000 keV/amu. Calculations were performed within the framework of time-dependent spin-density functional theory. The Krieger-Li-Iafrate approximation was used to determine an accurate exchange-correlation potential in the exchange-only limit. The results of two models, one where electron translation factors in the orbitals used to calculate the potential are ignored and another where partial electron translation factors are included, are compared with available experimental data as well as a selection of previous theoretical calculations.

Ab initio dynamical exchange interactions in frustrated antiferromagnets

The ultrafast response to an optical pulse excitation of the spin-spin exchange interaction in transition metal anti-ferromagnets is studied within the framework of the time-dependent spin-density functional theory. We propose a formulation for the purely dynamical exchange interaction, which is non-local in space, and it is derived starting from {\it ab initio} arguments. Then, we investigate the effect of the laser pulse on the onset of the dynamical process. It is found that we can distinguish two types of excitations, both activated immediately after the action of the laser pulse. While the first one can be associated to a Stoner-like excitation and involves the transfer of spin from one site to another, the second one is related to the ultrafast modification of a Heisenberg-like exchange interaction and can trigger the formation of spin waves in the first few hundred femtoseconds of the time evolution.

Ultrafast demagnetizing fields from first principles

Starting from the continuity equation for the magnetization in time-dependent spin-density functional theory, we derive an expression for the effective time-dependent magnetic fields driving the out-of-equilibrium spin dynamics in magnetic systems. We evaluate these, so called, kinetic magnetic fields in the ultrafast demagnetization response to optical pulse excitations of ferromagnetic iron-based materials, namely Fe$_6$ cluster and bulk bcc Fe. We identify spatial "hot spots" where the demagnetization is particularly enhanced as a result of the increased kinetic torque.

Role of spin-orbit interaction in the ultrafast demagnetization of small iron clusters

The ultra-fast demagnetization of small iron clusters initiated by an intense optical excitation is studied with time-dependent spin density functional theory (TDSDFT). In particular we investigate the effect of the spin-orbit interaction on the onset of the demagnetization process. It is found that the initial rate of coherent spin loss is proportional to the square of the atomic spin-orbit coupling constant, $\lambda$. A simplified quantum spin model comprising spin-orbit interaction and a local time-dependent magnetic field is found to be the minimal model able to reproduce our {\it ab initio} results. The model predicts the $\lambda^2$ dependence of the onset rate of demagnetization when it is solved either numerically or analytically in the linear response limit. Our findings are supported by additional TDSDFT simulations of clusters made of Co and Ni.

Nonadiabatic time-dependent spin-density functional theory for strongly correlated systems

We propose a nonadiabatic time-dependent spin-density functional theory (TDSDFT) approach for studying single-electron excited states and the ultrafast response of systems with strong electron correlations. The correlation part of the nonadiabatic exchange–correlation (XC) kernel is constructed by using exact results for the Hubbard model of strongly correlated electrons. We demonstrate that the corresponding nonadiabatic XC kernel reproduces the main features of the spectrum of the Hubbard dimer and the 2D, 3D and infinite-dimensional Hubbard models, some of which are impossible to obtain within the adiabatic approach. The formalism may be applied for ab initio examination of strongly correlated electron systems in- and out-of-equilibrium within the TDSDFT, extending it beyond the metallic and semiconductor structures with plasmons, excitons and other excitations.

Dynamical exchange interaction from time-dependent spin density functional theory

We report on {\it ab initio} time-dependent spin dynamics simulations for a two-center magnetic molecular complex based on time-dependent non-collinear spin density functional theory. In particular, we discuss how the dynamical behavior of the {\it ab initio} spin-density in the time-domain can be mapped onto a model Hamiltonian based on the classical Heisenberg spin-spin interaction $J\vcr{S}_1\cdot \vcr{S}_2$. By analyzing individual localized-spin trajectories, extracted from the spin-density evolution, we demonstrate a novel method for evaluating the effective Heisenberg exchange coupling constant, $J$, from first principles simulations. We find that $J$, extracted in such a new dynamical way, agrees quantitatively to that calculated by the standard density functional theory broken-symmetry scheme.

Spin-drag relaxation time in one-dimensional spin-polarized Fermi gases

Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed ``spin drag'' relaxation time ${\ensuremath{\tau}}_{\mathrm{sd}}$. In this paper we present both numerical and analytical calculations of ${\ensuremath{\tau}}_{\mathrm{sd}}$ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for ${\ensuremath{\tau}}_{\mathrm{sd}}$, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in one-dimensional inhomogeneous systems of interacting fermions.

Correlation effects and the high-frequency spin susceptibility of an electron liquid: Exact limits

Spin correlations in an interacting electron liquid are studied in the high-frequency limit and in both two and three dimensions. The third-moment sum rule is evaluated and is used to derive exact limiting forms (at both long and short wavelengths) for the spin-antisymmetric local-field factor, ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega}).$ In two dimensions ${limop}_{\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\omega}}\ensuremath{\infty}}{G}_{\ensuremath{-}}(\mathbf{q},\ensuremath{\omega})$ is found to diverge as $1/q$ at long wavelengths, and the spin-antisymmetric exchange-correlation kernel of time-dependent spin density functional theory diverges as ${1/q}^{2}$ in both two and three dimensions. These signal a failure of the local-density approximation, one that can be redressed by alternative approaches.

Solving the ultranonlocality problem in time-dependent spin-density-functional theory.

It has been known for some time that the exchange-correlation potential in time-dependent density-functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin-density functional theory. We show how the use of the spin current density as a basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents.

Spin dynamics from time-dependent spin-density-functional theory.

We derive the spin-wave dynamics of a magnetic material from the time-dependent spin-density-functional theory in the linear response regime. The equation of motion for the magnetization includes, besides the static spin stiffness, a "Berry curvature" correction and a damping term. A gradient expansion scheme based on the homogeneous spin-polarized electron gas is proposed for the latter two quantities, and the first few coefficients of the expansion are calculated to second order in the Coulomb interaction.

Spin currents and spin dynamics in time-dependent density-functional theory.

We derive and analyze the equation of motion for the spin degrees of freedom within time-dependent spin-density-functional theory (TD-SDFT). The results are (i) a prescription for obtaining many-body corrections to the single-particle spin currents from the Kohn-Sham equation of TD-SDFT, (ii) the existence of an exchange-correlation (xc) torque within TD-SDFT, (iii) a prescription for calculating, from TD-SDFT, the torque exerted by spin currents on the spin magnetization, (iv) a novel exact constraint on approximate xc functionals, and (v) the discovery of serious deficiencies of popular approximations to TD-SDFT when applied to spin dynamics.

Collective Excitations in Quantum Dots: Calculated Raman Spectra

Electronic Raman scattering provides information on excited states, whose collective character as being related to the charge or spin density can be distinguished by using different polarization configurations. We employ time-dependent spin-density functional theory to calculate Raman spectra for circular semiconductor quantum dots with up to 10 electrons for the polarized and depolarized configuration and in dependence on an external magnetic field and the momentum transfer. Our results demonstrate an increase of the collective (or many-particle) character of the excitations with increasing momentum transfer and a mixing of spin- and charge-density modes for excitations from ground states with finite spin density. These results have predictive character, because corresponding experiments on few-electron dots have not yet been performed.

Collective Excitations in Quantum Dots: Calculated Raman Spectra

Electronic Raman scattering provides information on excited states, whose collective character as being related to the charge or spin density can be distinguished by using different polarization configurations. We employ time-dependent spin-density functional theory to calculate Raman spectra for circular semiconductor quantum dots with up to 10 electrons for the polarized and depolarized configuration and in dependence on an external magnetic field and the momentum transfer. Our results demonstrate an increase of the collective (or many-particle) character of the excitations with increasing momentum transfer and a mixing of spin- and charge-density modes for excitations from ground states with finite spin density. These results have predictive character, because corresponding experiments on few-electron dots have not yet been performed.