Hyperfine Parameters

LHYPERFINE = .TRUE.

The hyperfine tensor describes the interaction between a nuclear spin (located at site ) and the electronic spin distribution (in most cases associated with a paramagnetic defect state):

The Fermi contact term is given by

The dipolar contributions to the hyperfine tensor are given by

In the equations above , the i-th component of , and is taken relative to the position of the nucleus .

The nuclear gyromagnetic ratios should be specified (in MHz, for T) by means of the `NGYROMAG`-tag:

NGYROMAG = gamma_1 gamma_2 ... gamma_Nwhere one should specify one number for each of the species on the POSCAR file. If one does not set

As usual, all output is written to the OUTCAR file. VASP writes three blocks of data, that look something like:

Fermi contact (isotropic) hyperfine coupling parameter (MHz) ------------------------------------------------------------- ion A_pw A_1PS A_1AE A_1c A_tot ------------------------------------------------------------- 1 ... ... ... ... ... .. ... ... ... ... ... -------------------------------------------------------------with an entry for each ion on the POSCAR file. , , , and are the plane wave, pseudo one-center, all-electron one-center, and one-center core contributions to the Fermi contact term, respectively. The total Fermi contact term is given by . Beware: for the moment we have chosen NOT to include the core contributions in . If you so want, you should add them by hand to . Core electronic contributions to the Fermi contact term are calculated in the manner proposed in Ref. [153].

The dipolar constributions are listed next:

Dipolar hyperfine coupling parameters (MHz) --------------------------------------------------------------------- ion A_xx A_yy A_zz A_xy A_xz A_yz --------------------------------------------------------------------- 1 ... ... ... ... ... ... .. ... ... ... ... ... ... ---------------------------------------------------------------------Again one line per ion in the POSCAR file.

The total hyperfine tensors are written as:

Total hyperfine coupling parameters after diagonalization (MHz) (convention: |A_zz| > |A_xx| > |A_yy|) ---------------------------------------------------------------------- ion A_xx A_yy A_zz asymmetry (A_yy - A_xx)/ A_zz ---------------------------------------------------------------------- 1 ... ... ... ... .. ... ... ... ... ----------------------------------------------------------------------i.e., the tensors have been diagonalized and rearranged.

N.B.: The Fermi contact term is strongly dominated by the all-electron one-center contribution
.
Unfortunately, this particular term is quite sensitive to the number and eigenenergy of the all-electron partial waves that
make up the one-center basis set, *i.e.*, to the particulars of the PAW dataset you are using.
As a result the Fermi contact term may strongly depend on the choice of PAW dataset.