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 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):

{\displaystyle 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

{\displaystyle (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.^[1].

The dipolar contributions to the hyperfine tensor are given by

{\displaystyle (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: