I CONSTRAINED M

I_CONSTRAINED_M = 1 | 2
Default: I_CONSTRAINED_M = none 

Description: I_CONSTRAINED_M switches on the constrained local moments approach.

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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.

• I_CONSTRAINED_M=1

Constrain the direction of the magnetic moments. The total energy is given by

$E=E_{0}+\sum _{I}\lambda \left[{\vec {M}}_{I}-{\hat {M}}_{I}^{0}\left({\hat {M}}_{I}^{0}\cdot {\vec {M_{I}}}\right)\right]^{2}$

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, ${\hat {M}}_{I}^{0}$ is the desired direction of the magnetic moment at site I (as specified using M_CONSTR), and ${\vec {M}}_{I}$ is the integrated magnetic moment inside a sphere Ω_I (the radius must be specified by means of RWIGS) around the position of atom I,

${\vec {M}}_{I}=\int _{\Omega _{I}}{\vec {m}}(\mathbf {r} )F_{I}(|\mathbf {r} |)d\mathbf {r}$

where F_I(|r|) is a function of norm 1 inside Ω_I, that smoothly goes to zero towards the boundary of Ω_I.

The penalty term in the total energy introduces an additional potential inside the aforementioned spheres centered at the atomic sites I, given by

$V_{I}(\mathbf {r} )=2\lambda \left[{\vec {M}}_{I}-{\hat {M}}_{I}^{0}\left({\hat {M}}_{I}^{0}\cdot {\vec {M_{I}}}\right)\right]\cdot {\vec {\sigma }}F_{I}(|\mathbf {r} |)$

where ${\vec {\sigma }}=(\sigma _{x},\sigma _{y},\sigma _{z})$ are the Pauli spin-matrices.

• I_CONSTRAINED_M=2

Related Tags and Sections

M_CONSTR, LAMBDA, RWIGS, LNONCOLLINEAR

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