Spin with CASTEP

An example of visualising antiferromagnetic spin in FeO, continuing from the previous page on crystals.

FeO.cell

%BLOCK LATTICE_CART
 0.000 4.332 4.332
 2.166 0.000 2.166
 2.166 2.166 0.000
%ENDBLOCK LATTICE_CART

%BLOCK POSITIONS_FRAC
  O   0.25 0.50 0.50
  O   0.75 0.50 0.50
 Fe   0.00 0.00 0.00   SPIN 2
 Fe   0.50 0.00 0.00   SPIN -2
%ENDBLOCK POSITIONS_FRAC

kpoints_mp_grid 1 3 3
kpoints_mp_offset 0.25 0 0

FeO.param

cut_off_energy  = 45 ry
iprint          = 1
opt_strategy : speed
spin_polarized : true

(This calculation will take longer to run than the previous examples, but still under a minute on a single core of a Haswell.)

To see the spin density in a single cell, simply run:

$ c2x -s FeO.check FeO.spin.xsf

The spin density is sharply concentrated close to the iron atoms, which are displayed as largish spheres, so one must set the isosurface value at a surprisingly small fraction of the peak values in the dataset. Here the isovalue is 0.06, and the peak is 8.6. Two unit cells are shown, with the repetition being in the y direction. As oxygen and iron are both shown as red, Display, Atomic Symbols has been turned on.

FeO and spin density

The alternating spins in the layers of Fe are clearly seen.

An estimation of the magnetic moment per Fe atom can be obtained by specifying -v on the command line:

$ c2x -vs --null FeO.check
Found 3D data for Spin
  min=-8.21808  max=8.45235  sum=1.10894  int=0.00173903  int|s|=6.99979
  (integral is e per cell for charge and spin densities)

The net spin per cell in this antiferromagnetic state is, of course, zero, to which 0.0017μ_B is a fair approximation. The integral of the modulus of the magnetic moment is 7.00μ_B per cell, or 3.50μ_B per Fe. This is within the range of published values - a 2016 JCTC paper quotes an experimental range of 3.3 to 4.2μ_B, and a calculated range of 3.4 to 4.3μ_B.