Spinors and c2x

Non collinear, or vector, spin in DFT has a reputation for poor convergence followed by difficulties in visualisation. So this page serves to illustrate a simple example of a frustrated spin state which does sometimes work.

The vector spin is visualised by using the part of an XSF file intended to record forces. This can either be done on a regular grid of dummy atoms, or on existing atoms. C2x can take point values, average over spheres of fixed radius, or integrate over spheres of fixed radius. Version 2.41 (or later) of c2x is required.

The system Mn₃Sn is chosen. Its unit cell is small, and it has frustrated anti-ferromagnetic spin states, with the spins being in-plane and pointing in directions which are multiples of 120°. But despite the small unit cell of just eight atoms, the calculations are still much larger than the other examples on this site.

An article in Nature Communications has a figure confirming the expected spin structure (fig 1b).

• Castep / XCrysden spinor example (this includes visualising spin on a grid as well as on atoms)
• Abinit / XCrysden spinor example
• Quantum Espresso / VESTA spinor example
• Siesta / XCrysden spinor example (of an Fe₃ linear trimer)
• VASP spinor example

There has been no attempt to converge the above calulations properly, as they exist merely to demonstrate visualisation. The initial spins used to break the symmetry and define the desired spin geometry had magnitudes of 0.5μ_e per atom. The calculated results per Mn atom were 3.0μ_e (VASP), 3.1μ_e (QE), 3.2μ_e (Castep) and 3.3μ_e (Abinit).

Wavefunctions

C2x has been able to extract spinor wavefunctions for visualisation from the output of Abinit, Castep and QE since version 2.30 (2.34c for Castep 18 and later).