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):
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): 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
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): (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 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 \<Sz\> 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
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://www.vasp.at/wiki/restbase/vasp.at/v1/":): (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|, 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: