Spin Polarization and Magnetic Systems in QE code

Up till now we have been assuming that we always had some set of bands which could each fit two identical electrons. Essentially we have been ignoring the electron spin. If you want to examine, for example, a magnetic system then the spin of the electrons is important. It can also be important in modelling atomic or molecular systems. We’ll cover several examples of this in this lab.

The Hydrogen Atom and electron spin

As a first example, let’s look again at hydrogen. In the molecule we have two hydrogen atoms bonded together, and two electrons in total, and we can do this with a standard calculation.
But if we instead want to find the energy of an isolated H atom accurately it’s a little more tricky. A hydrogen atom has one electron, which means if we treat it with doubly-degenerate bands, we would have a single half occupied band. To calculate it like this we can treat it as a metal, and use some small smearing, so that we allow partial occupation of bands. This is equivalent to assuming that we have half an electron in each spin state. If we however restrict it to being in one spin state or another, we may find a slightly different energy (coming primarily from differences in how the DFT exchange term is calculated in each case, with the latter being more physical).
To perform a spin-polarized calculation in quantum espresso with the pw.x code, there are two additional variables you’ll need to set.

• nspin: this is 1 by default so no spin polarization is taken into account. To perform a spin polarized calculation it should be set to 2.
• tot_magnetization: this is difference between the number of spin-up and spin-down electrons in the cell. If we want a single spin up electron we can set this to 1.0.

The directory 01_H1_metal has an input file for a single H atom using a small smearing, while the directory 01_H1_spin has the same calculation, but with no smearing, and we have used the two input variables above to enable a spin polarized calculation.

• Run the input files in these two folders.
• Compare the total energy obtained in each case. In which case is the energy lower?
• Compare the energies of the lowest energy calculated bands.
  • Enabling smearing for the “metal” calculation will automatically add extra bands, but only the lowest energy band will be occupied in this calculation.
  • In the spin polarized calculation if you check the output you will see two sections for the band energies. One listing the energies of the “spin up” bands, and the other listing “spin down” bands. Since we have said we want 1 spin up electron in the calculation, the spin up band will be occupied and should be lower in energy than the unoccupied spin down band.
• Slightly above the band energies in the output of the spin polarized calculation, you’ll see that quantum espresso also outputs the magnetic moment associated with each atom in the system. And slightly below the final total energy output, it will list the total magnetization of the system in Bohr magnetons per cell. The measured value for hydrogen is 1. How close are you here?

To continue reading click on the following link:

https://eamonnmurray.gitlab.io/modelling_materials/lab08/