Intraband and interband contributions to the current-driven spin-orbit torque in magnetic materials lacking inversion symmetry are theoretically studied using Kubo formula. In addition to the current-driven field-like torque TFL = τFLm × uso (uso being a unit vector determined by the symmetry of the spin-orbit coupling), we explore the intrinsic contribution arising from impurity-independent interband transitions and producing an anti-damping-like torque of the form TDL = τDLm × (uso × m). Analytical expressions are obtained in the model case of a magnetic Rashba two-dimensional electron gas, while numerical calculations have been performed on a dilute magnetic semiconductor (Ga,Mn)As modeled by the Kohn-Luttinger Hamiltonian exchanged coupled to the Mn moments. Parametric dependences of the different torque components and similarities to the analytical results of the Rashba two-dimensional electron gas in the weak disorder limit are described.

A quantitative description of specific ion effects is an essential and focused topic in colloidal and biological science. In this work, the dynamic light scattering technique was employed to study the aggregation kinetics of colloidal particles in the various alkali ion solutions with a wide range of concentrations. It indicated that the activation energies could be used to quantitatively characterize specific ion effects, which was supported by the results of effective hydrodynamic diameters, aggregation rates and critical coagulation concentrations. At a given concentration of 25 mmol L(-1), the activation energies for Li(+) are 1.2, 5.7, 28, and 126 times as much for Na(+), K(+), Rb(+), and Cs(+), respectively. Most importantly, the activation energy differences between two alkali cation species increase sharply with decrease of electrolyte concentrations, implying the more pronounced specific ion effects at lower concentrations. The dominant role of electrolyte cations during the aggregation of negatively charged colloidal particles was confirmed by alternative anions. Among the various theories, only the polarization effect can give a rational interpretation of the above specific ion effects, and this is substantially supported by the presence of strong electric fields from montmorillonite surfaces and its association mainly with electrolyte cations and montmorillonite particles. The classical induction theory, although with inclusion of electric field, requires significant corrections because it predicts an opposite trend to the experimentally observed specific ion effects.

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The Hofmeister or specific ion effects are not involved in the existing ion exchange equilibrium theories. In this study, a new cation exchange model considering the specific ion effects was established. The relative adsorption ability was quantified through relative adsorption energy or selectivity coefficients of ions. The quantificational sequence of relative adsorption ratio ((relative adsorption energe for i ion)/(relative adsorption energy for j ion)) calculated from the new model was obtained: Ca > Mg ((Ca 2+ )/(Mg 2+ ) = 1.407) > K ((Mg 2+ )/ K 2+ = 1.467) > Na (K + /(Na 2+ ) = 1.646) > Li ((Na 2+ )/(Li 2+ ) = 1.110). It provided a new theory for quantificational description of ionic exchange adsorption selectivity for any ion pairs. The experimental data on various materials (montmorillonite, Illite, and Altamont soil) with very different charge densities agree well with each other. Thus we presume that the new model may apply to all charged surfaces.

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