I CONSTRAINED M
I_CONSTRAINED_M = 1 | 2
Default: I_CONSTRAINED_M = none
Description: I_CONSTRAINED_M switches on the constrained local moments approach.
VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius r=RWIGS) into a direction given by the M_CONSTR-tag.
- Constrain the direction of the magnetic moments. The total energy is given by
- [math]\displaystyle{ E=E_0+ \sum_I\lambda \left[ \vec{M}_I-\hat{M}^0_I \left( \hat{M}^0_I \cdot \vec{M_I}\right)\right]^2 }[/math]
- where E0 is the usual DFT energy, and the second term on the right-hand-side represents the penalty. The sum is taken over all atomic sites I, [math]\displaystyle{ \hat{M}^0_I }[/math] is the desired direction of the magnetic moment at site I (as specified using M_CONSTR), and [math]\displaystyle{ \vec{M}_I }[/math] is the integrated magnetic moment inside a sphere ΩI (the radius must be specified by means of RWIGS) around the position of atom I,
- [math]\displaystyle{ \vec{M}_I=\int_{\Omega_I} \vec{m}(\mathbf{r}) F_I(|\mathbf{r}|) d\mathbf{r} }[/math]
- where FI(|r|) is a function of norm 1 inside ΩI, that smoothly goes to zero towards the boundary of ΩI.
- The penalty term in the total energy introduces an additional potential inside the aforementioned spheres centered at the atomic sites I, given by
- [math]\displaystyle{ V_I (\mathbf{r})=2\lambda \left[ \vec{M}_I-\hat{M}^0_I \left( \hat{M}^0_I \cdot \vec{M_I}\right)\right] \cdot \vec{\sigma} F_I(|\mathbf{r}|) }[/math]
- where [math]\displaystyle{ \vec{\sigma}=(\sigma_x,\sigma_y,\sigma_z) }[/math] are the Pauli spin-matrices.
Related Tags and Sections
M_CONSTR, LAMBDA, RWIGS, LNONCOLLINEAR