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.

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 }=2V^{\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

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:

\hbar \omega =g_{e}\mu _{B}B_{0}

where $\mu _{B}$ is the Bohr magneton and $g_{e}$ is the electron g-factor.

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

V^{\uparrow }-V^{\downarrow }=2B_{\rm {ext}}

This leads to the following relationship between our definition of $B_{\rm {ext}}$ (in eV) and the magnetic field $B_{0}$ (in T):

B_{0}={\frac {2B_{\rm {ext}}}{g_{e}\mu _{B}}}

where $\mu _{B}$ = 5.788 381 8060 x 10^-5 eV T^-1, and $g_{e}$ = 2.002 319 304 362 56.

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