Category:Spin-orbit coupling

Spin-orbit coupling (SOC) is the relativistic interaction between the spin of an electron and its orbital motion. It is one of the relativistic corrections that become important for systems containing heavy elements, where it lifts spin degeneracies, splits energy bands, and couples the magnetic moments to the crystal lattice. Capturing this interaction is essential for properties such as magnetic anisotropy, orbital magnetic moments, the Rashba and Dresselhaus effects, and the spin texture of electronic states. In VASP, spin-orbit coupling is treated within the noncollinear framework, so that the wavefunction is described by two-component spinors rather than scalar orbitals.

Enabling spin-orbit coupling

Spin-orbit coupling is switched on with a single tag, which automatically activates the noncollinear framework. It is implemented for the projector-augmented-wave (PAW) method only and must be run with the noncollinear VASP executable vasp_ncl. Because the calculation now uses two-component spinors, the magnetic configuration is specified by three Cartesian components per atom.

LSORBIT, LNONCOLLINEAR, Noncollinear magnetism

When to include spin-orbit coupling

Even when you are not after a property that intrinsically requires spin-orbit coupling, it can still change your results. For heavy elements the effect on total energies, equilibrium geometries, and band energies may be far from negligible. Rather than assuming the interaction can be ignored, test its influence explicitly: run the property of interest once without and once with spin-orbit coupling and compare. If the difference is within your target accuracy, you may safely neglect it for that system; if not, keep it switched on. As a rule of thumb, the heavier the elements in your structure, the more likely spin-orbit coupling matters.

LSORBIT

Spin-quantization axis and magnetic properties

With spin-orbit coupling the energy is no longer invariant under a global rotation of the spins, so it depends on the orientation of the spins relative to the crystal axes. Total-energy differences between calculations with different spin-quantization axes therefore yield the magnetic anisotropy energy, and orbital magnetic moments become nonzero and can be written to the output. Spin-orbit coupling is built on the noncollinear-magnetism machinery and shares its conventions for the spin-quantization axis and the magnetic configuration. For the details, see Noncollinear magnetism.

SAXIS, LORBMOM, Noncollinear magnetism

Band structure and spin texture

Spin-orbit coupling splits bands that would otherwise be degenerate and gives each Bloch state a spin expectation value that varies across the Brillouin zone, the spin texture seen in Rashba and topological systems. After a self-consistent calculation with spin-orbit coupling, the spin-resolved band structure is obtained from a non-self-consistent run along a k-point path, and the site- and orbital-projected spin components are written with the projection tag. A step-by-step workflow for computing and visualizing the spin texture is given in the how-to Construction:Computing the spin texture.

LORBIT