The Landau-Lifshitz equation reliably describes magnetization dynamics using a phenomenological treatment of damping. This Letter presents first-principles calculations of the damping parameters for Fe, Co, and Ni that quantitatively agree with existing ferromagnetic resonance measurements. This agreement establishes the dominant damping mechanism for these systems and takes a significant step toward predicting and tailoring the damping constants of new materials.
We present an efficient implementation of the Bethe-Salpeter equation (BSE) method for obtaining core-level spectra including x-ray absorption (XAS), x-ray emission (XES), and both resonant and non-resonant inelastic x-ray scattering spectra (N/RIXS). Calculations are based on density functional theory (DFT) electronic structures generated either by abinit or Quantumespresso, both plane-wave basis, pseudopotential codes. This electronic structure is improved through the inclusion of a GW self energy. The projector augmented wave technique is used to evaluate transition matrix elements between core-level and band states. Final two-particle scattering states are obtained with the NIST core-level BSE solver (NBSE). We have previously reported this implementation, which we refer to as ocean (Obtaining Core Excitations from Ab initio electronic structure and NBSE) [Phys. Rev. B 83, 115106 (2011)]. Here, we present additional efficiencies that enable us to evaluate spectra for systems ten times larger than previously possible; containing up to a few thousand electrons. These improvements include the implementation of optimal basis functions that reduce the cost of the initial DFT calculations, more complete parallelization of the screening calculation and of the action of the BSE Hamiltonian, and various memory reductions. Scaling is demonstrated on supercells of SrTiO 3 and example spectra for the organic light emitting molecule Tris-(8-hydroxyquinoline)aluminum (Alq 3 ) are presented. The ability to perform large-scale spectral calculations is particularly advantageous for investigating dilute or non-periodic systems such as doped materials, amorphous systems, or complex nano-structures.
The motion of simple domain walls and of more complex magnetic textures in the presence of a transport current is described by the Landau-Lifshitz-Slonczewski (LLS) equations. Predictions of the LLS equations depend sensitively on the ratio between the dimensionless material parameter β which characterizes non-adiabatic spin-transfer torques and the Gilbert damping parameter α. This ratio has been variously estimated to be close to 0, close to 1, and large compared to 1. By identifying β as the influence of a transport current on α, we derive a concise, explicit and relatively simple expression which relates β to the band structure and Bloch state lifetimes of a magnetic metal. Using this expression we demonstrate that intrinsic spin-orbit interactions lead to intraband contributions to β which are often dominant and can be (i) estimated with some confidence and (ii) interpreted using the "breathing Fermi surface" model.
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