Intraband and interband spin-orbit torques in non-centrosymmetric ferromagnets

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 ${\bf T}_{\rm FL}= \tau_{\rm FL}{\bf m}\times{\bf u}_{\rm so}$ (${\bf u}_{\rm so}$ 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 ${\bf T}_{\rm DL}= \tau_{\rm DL}{\bf m}\times({\bf u}_{\rm so}\times{\bf m})$. 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.Comment: 10 pages, 5 figure

Theoretical Modeling of Magnesium Ion Imprints in the Raman Scattering of Water

Hydration envelopes of metallic ions significantly influence their chemical properties and biological functioning. Previous computational studies, nuclear magnetic resonance (NMR), and vibrational spectra indicated a strong affinity of the Mg2+ Cation to water. We find it interesting that, although monatomic ions do not vibrate themselves, they cause notable changes in the water Raman signal. Therefore, in this Study, We used a combination of Raman spectroscopy and computer modeling to analyze the magnesium hydration shell and origin of the signal. In the measured spectra of several salts (LiCl, NaCl, KCl, MgCl2, CaCl2 MgBr2, and MgI2 Water Solutions), only the spectroscopic imprint of the hydrated Mg2+ Cation Could clearly be identified as an exceptionally distinct peak at similar to 355 cm(-1). The assignment of this band to the Mg-O stretching motion could be confirmed oil the basis of several models involving quantum chemical computations on metal/water clusters. Minor Raman spectral features could also be explained. Ab initio and Fourier transform (FT) techniques Coupled with the Car-Parrinello molecular dynamics were adapted to provide the spectra from dynamical trajectories. The results Suggest that even in concentrated Solutions magnesium preferentially forms a [Mg(H2O)(6)](2+) complex of a nearly octahedral symmetry; nevertheless, the Raman signal is primarily associated with the relatively strong metal-H2O bond. Partially covalent character of the Mg-O bond was confirmed by a natural bond orbital analysis. Computations oil hydrated chlorine anion did not provide a specific signal. The FT techniques gave good spectral profiles in the high-frequency region, whereas the lowest-wavenumber vibrations were better reproduced by the cluster models. Both dynamical and cluster computational models provided a useful link between spectral shapes and specific ion-water interactions