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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 AI describes the interaction between a nuclear spin SI (located at site RI) and the electronic spin distribution Se (in most cases associated with a paramagnetic defect state):

${\displaystyle E=\sum _{{ij}}S_{i}^{e}A_{{ij}}^{I}S_{j}^{I}}$

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

${\displaystyle (A_{{{\mathrm {iso}}}}^{I})_{{ij}}={\frac {2}{3}}{\frac {\mu _{0}\gamma _{e}\gamma _{I}}{\langle S_{z}\rangle }}\delta _{{ij}}\int \delta _{T}({\mathbf {r}})\rho _{s}({\mathbf {r}}+{\mathbf {R}}_{I})d{\mathbf {r}}}$

where ρs is the spin density, μ0 is the magnetic susceptibility of free space, γe the electron gyromagnetic ratio, γI the nuclear gyromagnetic ratio of the nucleus at RI, and ${\displaystyle \langle S_{z}\rangle }$ the expectation value of the z-component of the total electronic spin.

δT(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

${\displaystyle (A_{{{\mathrm {ani}}}}^{I})_{{ij}}={\frac {\mu _{0}}{4\pi }}{\frac {\gamma _{e}\gamma _{I}}{\langle S_{z}\rangle }}\int {\frac {\rho _{s}({\mathbf {r}}+{\mathbf {R}}_{I})}{r^{3}}}{\frac {3r_{i}r_{j}-\delta _{{ij}}r^{2}}{r^{2}}}d{\mathbf {r}}}$

In the equations above r=|r|, ri the i-th component of r, and r is taken relative to the position of the nucleus RI.

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. Apw, A1PS, A1AE, and A1c 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 Atot. Beware: for the moment we have chosen NOT to include the core contributions A1c in Atot. If you so want, you should add them by hand to Atot. 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 A1AE. 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.