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# LHYPERFINE

**LHYPERFINE** = .TRUE. | .FALSE.

Default: **LHYPERFINE** = .FALSE.

Description: compute the hyperfine tensors at the atomic sites (available as of vasp.5.3.2).

To have VASP compute the hyperfine tensors at the atomic sites, set

LHYPERFINE = .TRUE.

The hyperfine tensor A^{I} describes the interaction between a nuclear spin S^{I} (located at site **R**_{I}) and the electronic spin distribution S^{e} (in most cases associated with a paramagnetic defect state):

In general it is written as the sum of an isotropic part, the so-called Fermi contact term, and an anisotropic (dipolar) part.

The Fermi contact term is given by

where ρ_{s} is the spin density, μ_{0} is the magnetic susceptibility of free space,
γ_{e} the electron gyromagnetic ratio, γ_{I} the nuclear gyromagnetic ratio of the nucleus at **R**_{I}, and the expectation value of the
*z*-component of the total electronic spin.

δ_{T}(**r**) is a smeared out δ function, as described in
the Appendix of Ref.^{[1]}.

The dipolar contributions to the hyperfine tensor are given by

In the equations above *r*=|**r**|, *r*_{i} the i-th component of **r**, and **r** is
taken relative to the position of the nucleus **R**_{I}.

The nuclear gyromagnetic ratios should be specified by means of the NGYROMAG-tag:

NGYROMAG = gamma_1 gamma_2 ... gamma_N

where one should specify one number for each of the *N* species on the POSCAR file.
If one does not set NGYROMAG in the INCAR file, VASP assumes a factor of 1 for each species.

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.
A_{pw}, A_{1PS}, A_{1AE}, and A_{1c} 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 A_{tot}. Beware: for the moment we
have chosen **NOT** to include the core contributions A_{1c} in A_{tot}.
If you so want, you should add them by hand to A_{tot}.
Core electronic contributions to the Fermi contact term are calculated in the frozen valence approximation as proposed by Yazyev *et al.*^{[2]}

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 A_{1AE}.
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.

## Related Tags and Sections

## References

- ↑ P. E. Blöchl, Phys. Rev. B 62, 6158 (2000).
- ↑ O. V. Yazyev, I. Tavernelli, L. Helm, and U. R. Röthlisberger, Phys. Rev. B 71, 115110 (2006).