First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons.

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4.

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.

Effect of spin-orbit interaction on a magnetic impurity in the vicinity of a surface.

We propose a new mechanism for surface-induced magnetic anisotropy to explain the thickness dependence of the Kondo resistivity of thin films of dilute magnetic alloys. The surface anisotropy energy, generated by spin-orbit coupling on the magnetic impurity itself, is an oscillating function of the distance d from the surface and decays as 1/d2. Numerical estimates based on simple models suggest that this mechanism, unlike its alternatives, gives rise to an effect of the desired order of magnitude.

Temperature dependent magnetic anisotropy in metallic magnets from an ab initio electronic structure theory: L1(0)-ordered FePt.

Using a first-principles, relativistic electronic structure theory of finite temperature metallic magnetism, we investigate the variation of magnetic anisotropy K with magnetization M in metallic ferromagnets. We apply the theory to the high uniaxial K material, L1(0)-ordered FePt, and find its magnetic easy axis perpendicular to the Fe/Pt layers for all M and K to be proportional to M2 for a broad range of values of M. For small M, near the Curie temperature, the calculations pick out the easy axis for the onset of magnetic order. Our ab initio results for this important magnetic material agree well with recent experimental measurements, whereas the single-ion anisotropy model fails to give the correct qualitative behavior.

Onset of magnetic order in fcc-Fe films on Cu(100).

On the basis of an ab initio theory of metallic magnetism in layered materials, we investigate the onset of magnetic order in thin (2-8 layers) fcc-Fe films on and embedded in Cu(100) substrates. In particular, we find an oscillatory dependence of the Curie temperatures on embedding depth, in excellent agreement with experimental data. The thermally induced spin fluctuations are treated within a mean-field disordered local moment picture and give rise to layer-dependent "local exchange splittings" in the electronic structure even in the paramagnetic phase. These features determine the magnetic intralayer and interlayer interactions which are strongly influenced by the presence and extent of the Cu cap.

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.