BEXT
BEXT = [real array]
| Default: BEXT | = 0.0 | if ISPIN=2 |
| = 3*0.0 | if LNONCOLLINEAR=.TRUE. | |
| = N/A | else |
Description: Specifies an external magnetic field in eV.
BEXT tag sets an external magnetic field that acts on the electrons in a Zeeman-like manner. An additional potential of the following form carries this interaction:
- For spin-polarized calculations (ISPIN = 2):
- 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/":): {\displaystyle V^{\uparrow} = V^{\uparrow} + B_{\rm ext} }
- 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/":): {\displaystyle V^{\downarrow} = V^{\downarrow} - B_{\rm ext} }
- 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/":): {\displaystyle B_{\rm ext}} = BEXT (in eV).
- For noncollinear calculations (LNONCOLLINEAR = .TRUE.):
- 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/":): {\displaystyle V_{\alpha\beta} = V_{\alpha\beta} + \mathbf{B}_{\rm ext} \cdot \mathbf{\sigma}_{\alpha \beta} }
- 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/":): {\displaystyle \mathbf{B}_{\rm ext}=({B}^1_{\rm ext}, {B}^2_{\rm ext}, {B}^3_{\rm ext})^T} is given by
BEXT = B1 B2 B3 ! in eV
- 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/":): {\mathbf {\sigma }} is the vector of Pauli matrices (SAXIS).
The effect of the above is most easily understood for the collinear case (ISPIN=2): The eigenenergies of spin-up states are raised 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/":): {\displaystyle B_{\rm ext}} eV, whereas the eigenenergies of spin-down states are lowered by the same amount. The total energy changes 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/":): {\displaystyle \Delta E = (n^{\uparrow} - n^{\downarrow}) B_{\rm ext} } eV
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/":): {\displaystyle n^{\uparrow}} 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/":): {\displaystyle n^{\downarrow}} are the number of up- and down-spin electrons in the system.
BEXT is applied during the self-consistent electronic minimization and effectively shifts the eigenenergies of the spin-up and spin-down states w.r.t. each other at each step. Consequently, the electrons redistribute (changing the occupancies) and the density changes. The change in the density (,e.g., charge density and magnetization) also affects the scf potential and KS orbitals. For a rigid-band Zeeman splitting, converge the charge density with BEXT=0 and restart with BEXTFailed 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/":): {\displaystyle \neq} 0 and fixed charge density (ICHARG=11).
Units
For an applied magnetic field 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/":): {\displaystyle B_0} , the energy difference between two Zeeman-splitted electronic states 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/":): {\displaystyle \hbar \omega = g_e \mu_B B_0, }
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/":): {\displaystyle \mu_B} is the Bohr magneton 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/":): {\displaystyle g_e} is the electron spin g-factor.
For ISPIN=2, rigid-band Zeeman-splitted states imply:
- 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/":): {\displaystyle V^{\uparrow} - V^{\downarrow} = 2 B_{\rm ext} }
This leads to the following relationship between our definition of 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/":): {\displaystyle B_{\rm ext}} (in eV) and the magnetic field 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/":): {\displaystyle B_0} (in T):
- 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/":): {\displaystyle B_0 = \frac{2 B_{\rm ext}}{g_e \mu_B} }
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/":): {\displaystyle \mu_B} = 5.788 381 8060 x 10-5 eV T-1, 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/":): {\displaystyle g_e} = 2.002 319 304 362 56.