Noncollinear magnetism in density functional calculations

Abstract

We generalize the treatment of the electronic spin degrees of freedom in density functional calculations to the case where the spin vector variables employed in the definition of the energy functional can vary in any direction in space. The expression for the generalized exchange-correlation potential matrix elements is derived for general functionals which among their ingredients include the electron density, its gradient and Laplacian, the kinetic energy density, and non-local Hartree-Fock type exchange. We present calculations on planar Cr clusters that exhibit ground states with noncollinear spin densities due to geometrically frustrated antiferromagnetic interactions.

Noncollinear density functional theory having proper invariance and local torque properties

“…16. In analogy to previous studies, 14,18 we find that the magnetization tends to be highly collinear in the core region, with rather strongly accented boundaries where it changes orientation. These boundaries coincide with the domains where the calculated exchange-correlation magnetic field deviates the most from the collinear alignment with respect to m. It is clear that the exchange-correlation magnetic torque is non-negligible and exhibits rich structure.…”

“…This, obviously, cannot be captured by previous generalizations of GGA functionals to noncollinear SDFT, in which B xc was still constrained to be parallel to m everywhere. [13][14][15] …”

“…These approximations include the generalized gradient approximations (GGAs), 13 meta-GGAs, and hybrid functionals. 14,15 However, many of these extensions that directly rely on the local reference frame for density derivatives can suffer from numerical instabilities 14,16 or lead to an exchange-correlation magnetic field that is always parallel to the magnetization.…”

“…Moreover, it does not suffer from the numerical instabilities that proved to be problematic in our previous formulation of noncollinear DFT. 14 The purpose of this work is to provide a generalization of our formalism for periodic systems. It is well established that many properties of solids, such as band gaps and lattice parameters, are much more accurate when described in terms of screened hybrid functionals.…”

Relativistic effects and fully spin-polarized Fermi surface at the Tl/Si(111) surface

“…23 The exchange-correlation energy has been approximated within the PBE-GGA parametrization. 24,25 We used norm-conserving fully relativistic pseudopotentials as illustrated in Refs. 26 and 27.…”