BEXT

BEXT = [real array] 

Default: BEXT	= 0.0	if ISPIN=2
	= 3*0.0	if LNONCOLLINEAR=.TRUE.
	= N/A	else

Description: BEXT specifies an external magnetic field.

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By means of the BEXT one may specify an external magnetic field that acts on the electrons in a Zeeman-like manner. This interaction is carried by an additional potential of the following form:

• For ISPIN = 2:

$V^{\uparrow }=V^{\uparrow }+B_{\rm {ext}}$

$V^{\downarrow }=V^{\downarrow }-B_{\rm {ext}}$

and $B_{\rm {ext}}$ = BEXT (in eV).

• For LNONCOLLINEAR = .TRUE.:

$V_{\alpha \beta }=V_{\alpha \beta }+{\vec {B}}_{\rm {ext}}\cdot {\vec {\sigma }}_{\alpha \beta }$

where $({B}_{\rm {ext}}^{x},{B}_{\rm {ext}}^{y},{B}_{\rm {ext}}^{z})$ = BEXT (in eV), and ${\vec {\sigma }}$ is the vector of Pauli matrices.

Heuristically, the effect of the above is most easily understood for the collinear spinpolarized case (ISPIN=2):

• The eigenenergies of spin-up states are raised by $B_{\rm {ext}}$ eV, whereas the eigenenergies of spin-down states are lowered by the same amount.

• The total energy changes by:

$\Delta E=(n^{\uparrow }-n^{\downarrow })B_{\rm {ext}}$ eV

where $n^{\uparrow }$ 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.

• Shifting the eigenenergies of the spin-up and spin-down states w.r.t. each other may lead to a redistribution of the electrons over these states (changes in the occupancies) and hence to changes in the density with all subsequent consequences.

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 g-factor.

For ISPIN=2, for purely Zeeman splitted states, we have:

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.

Related tags and articles

ISPIN, LNONCOLLINEAR

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