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Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is know about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single particle calculations tend to overestimate spin gaps while they underestimate charge gaps.
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In spin-density-functional theory for noncollinear magnetic materials, the Kohn-Sham system features exchange-correlation (xc) scalar potentials and magnetic fields. The significance of the xc magnetic fields is not very well explored; in particular, they can give rise to local torques on the magnetization, which are absent in standard local and semilocal approximations. We obtain exact benchmark solutions for two electrons on four-site extended Hubbard lattices over a wide range of interaction strengths, and compare exact xc potentials and magnetic fields with approximations obtained from orbital-dependent xc functionals. The xc magnetic fields turn out to play an increasingly important role as systems becomes more and more correlated and the electrons begin to localize; the effects of the xc torques, however, remain relatively minor. The approximate xc functionals perform overall quite well, but tend to favor symmetry-broken solutions for strong interactions.
We performed non-local electrical measurements of a series of Py/Cu lateral spin valve devices with different Cu thicknesses. We show that both the spin diffusion length of Cu and the apparent spin polarization of Py increase with Cu thickness. By fitting the results to a modified spin-diffusion model, we show that the spin diffusion length of Cu is dominated by spin-flip scattering at the surface. In addition, the dependence of spin polarization of Py on Cu thickness is due to a strong spin-flip scattering at the Py/Cu interface.
These lecture notes contain a brief practical introduction to doing density functional theory calculations for crystals using the open source Quantum Espresso software. The level is aimed at graduate students who are studying condensed matter or solid state physics, either theoretical or experimental.
The ferroelectricity of the spiral magnets LiCu2O2 and LiCuVO4 was examined by calculating the electric polarizations of their spin spiral states on the basis of density functional theory with spin-orbit coupling. Our work unambiguously reveals that spin-orbit coupling is responsible for the ferroelectricity with the primary contribution from the spin-orbit coupling on the Cu sites, but the asymmetric density distribution responsible for the electric polarization occurs mainly around the O atoms. The electric polarization is calculated to be much greater for the ab- than for the bc-plane spin spiral. The observed spin-spiral plane is found to be consistent with the observed direction of the electric polarization for LiCuVO4, but inconsistent for LiCu2O2.
Accurate calculations of electrostatic potentials and treatment of substrate polarizability are critical for predicting the permeation of ions inside water-filled nanopores. The {it ab initio} molecular dynamics method (AIMD), based on Density Functional Theory (DFT), accounts for the polarizability of materials, water, and solutes, and it should be the method of choice for predicting accurate electrostatic energies of ions. In practice, DFT coupled with the use of periodic boundary conditions in a charged system leads to large energy shifts. Results obtained using different DFT packages may vary because of the way pseudopotentials and long-range electrostatics are implemented. Using maximally localized Wannier functions, we apply robust corrections that yield relatively unambiguous ion energies in select molecular and aqueous systems and inside carbon nanotubes. Large binding energies are predicted for ions in metallic carbon nanotube arrays, while with consistent definitions Na$^+$ and Cl$^-$ energies are found to exhibit asymmetries comparable with those computed using non-polarizable water force fields.
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