LHYPERFINE

LHYPERFINE = .TRUE. | .FALSE.
Default: LHYPERFINE = .FALSE. 

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

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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):

$E=\sum_{ij} S^e_i A^I_{ij} S^I_j$

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

$(A^I_{\mathrm{iso}})_{ij}= \frac{2}{3}\frac{\mu_0\gamma_e\gamma_I}{<S_z>}\delta_{ij}\int \delta_T(\mathbf{r})\rho_s(\mathbf{r}+\mathbf{R}_I)d\mathbf{r}$

where ρ_s is the spin density, μ₀ 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 \<S_z\> 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..

The dipolar contributions to the hyperfine tensor are given by

$(A^I_{\mathrm{ani}})_{ij}=\frac{\mu_0}{4\pi}\frac{\gamma_e\gamma_I}{<S_z>} \int \frac{\rho_s(\mathbf{r}+\mathbf{R}_I)}{r^3}\frac{3r_ir_j-\delta_{ij}r^2}{r^2} d\mathbf{r}$

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.

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

NGYROMAG

References

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