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

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

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

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

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:

Related Tags and Sections

NGYROMAG

References

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