Spin Currents and Spin Dynamics in Time-Dependent Density-Functional Theory

Abstract

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. DOI: 10.1103/PhysRevLett.87.206403 PACS numbers: 71.15.Mb, 72.25. -b, 73.40. -c, 75.40.Gb The dynamics of the spin degrees of freedom is responsible for such diverse phenomena as spin wave excitations, Bloch wall motion, spin-polarized currents, spin injection, and spin filtering; concepts and phenomena which are important, e.g., in the growing field of spintronics [1]. The calculation of spin dynamics within density-functional theory (DFT) has consequently received much attention [2]. The most popular DFT method for a first-principles treatment of the spin degrees of freedom is spin-densityfunctional theory (SDFT, see Refs. [3,4] for reviews.) SDFT has led to versatile and powerful schemes for the calculation of, e.g., total energies, spin densities, and spin-resolved single-particle band structures, but its traditional (i.e., ground state) formulation is applicable only to static situations. This situation has changed with the advent of time-dependent DFT (TD-DFT) [5], which has brought dynamical phenomena within reach of DFT.In this Letter, we first derive the equation of motion for the spin magnetization from TD-SDFT, including exchange-correlation (xc) effects. We then show how this equation can be used to obtain information on the manybody spin current. Although one might think that a calculation of spin currents would require the more complex formalism of time-dependent current-density-functional theory (CDFT), we find that this is not entirely true: as a consequence of the continuity equation TD-SDFT suffices to calculate the spin currents in several cases of great practical interest.Numerical applications of TD-SDFT, as of any other DFT, require knowledge of the xc potentials, which contain all many-body effects beyond the Hartree approximation. In traditional DFT many exact properties of these xc potentials are known, and greatly aid the construction of good approximations [3,4], but the same is not true in the time-dependent case, where properties of the xc potentials are just beginning to be explored [6]. As a by-product, our analysis reveals a previously unknown exact property of the xc potentials of TD-SDFT, which strongly constrains suitable approximations.In TD-SDFT the fundamental variables are the timedependent particle density,and the time-dependent magnetization (or spin) densitywhere C C͑r 1 , . . . , r N , t͒ is the many-body wave function (spin ...

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