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.
- I_CONSTRAINED_M=1: Constrain the direction of the magnetic moments.
- The total energy 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/":): 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, 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/":): {\hat {M}}_{I}^{0} is the desired direction of the magnetic moment at site I (as specified using M_CONSTR), and 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/":): {\vec {M}}_{I} is the integrated magnetic moment inside a sphere ΩI (the radius must be specified by means of RWIGS) around the position of atom I,
- 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/":): {\vec {M}}_{I}=\int _{{\Omega _{I}}}{\vec {m}}({\mathbf {r}})F_{I}(|{\mathbf {r}}|)d{\mathbf {r}}
- 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
- 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/":): 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 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/":): {\vec {\sigma }}=(\sigma _{x},\sigma _{y},\sigma _{z}) are the Pauli spin-matrices.
- I_CONSTRAINED_M=2: Constrain the size and direction of the magnetic moments.
- The total energy 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/":): E=E_{0}+\sum _{I}\lambda \left({\vec {M}}_{I}-{\vec {M}}_{I}^{0}\right)^{2}
- where 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/":): {\vec {M}}_{I}^{0} is the desired magnetic moment at site I (as specified using M_CONSTR).
- The additional potential that arises from the penalty contribution to the total energy 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/":): V_{I}({\mathbf {r}})=2\lambda \left({\vec {M}}_{I}-{\vec {M}}_{I}^{0}\right)\cdot {\vec {\sigma }}F_{I}(|{\mathbf {r}}|)
Related Tags and Sections
M_CONSTR, LAMBDA, RWIGS, LNONCOLLINEAR