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):

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

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

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

where 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 $\langle S_{z}\rangle$ 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

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

In the equations above r=|r|, 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.

Units

The Fermi contact term $A$ is measured in following units

$[A]=\left[\mu _{0}\right]\times \left[g_{e}\mu _{e}\right]\times \left[g_{j}\mu _{j}\right]\times \left[|\psi (0)|^{2}\right]={\frac {T^{2}m^{3}}{J}}\times {\frac {J}{T}}\times {\frac {MHz}{T}}\times {\frac {1}{m^{3}}}=MHz$

with $\mu _{0}=4\pi \times 10^{-7}T^{2}m^{3}J^{-1}$, $g_{e}\mu _{e}=9.28476377\times 10^{-24}JT^{-1},|\psi (0)|^{2}=10^{30}m^{-3}$. NGYROMAG is given in units of MHz/T, see here for a table of different gyromagnetic ratios.

Related tags and articles

NGYROMAG

Examples that use this tag

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