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:

[math]\displaystyle{ V^{\uparrow} = V^{\uparrow} + B_{\rm ext} }[/math]

[math]\displaystyle{ V^{\downarrow} = V^{\downarrow} - B_{\rm ext} }[/math]

and [math]\displaystyle{ B_{\rm ext} }[/math] = BEXT (in eV).

• For LNONCOLLINEAR = .TRUE.:

[math]\displaystyle{ V_{\alpha\beta} = V_{\alpha\beta} + \vec{B}_{\rm ext} \cdot \vec{\sigma}_{\alpha \beta} }[/math]

where [math]\displaystyle{ ({B}^x_{\rm ext}, {B}^y_{\rm ext}, {B}^z_{\rm ext}) }[/math] = BEXT (in eV), and [math]\displaystyle{ \vec{\sigma} }[/math] 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 [math]\displaystyle{ B_{\rm ext} }[/math] eV, whereas the eigenenergies of spin-down states are lowered by the same amount.

• The total energy changes by:

[math]\displaystyle{ \Delta E = (n^{\uparrow} - n^{\downarrow}) B_{\rm ext} }[/math] eV

where [math]\displaystyle{ n^{\uparrow} }[/math] and [math]\displaystyle{ n^{\downarrow} }[/math] 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:

[math]\displaystyle{ \hbar \omega = g_e \mu_B B_0 }[/math]

where [math]\displaystyle{ \mu_B }[/math] is the Bohr magneton and [math]\displaystyle{ g_e }[/math] is the electron g-factor.

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

[math]\displaystyle{ V^{\uparrow} - V^{\downarrow} = 2 B_{\rm ext} }[/math]

This leads to the following relationship between our definition of [math]\displaystyle{ B_{\rm ext} }[/math] (in eV) and the magnetic field [math]\displaystyle{ B_0 }[/math] (in T):

[math]\displaystyle{ B_0 = \frac{2 B_{\rm ext}}{g_e \mu_B} }[/math]

where [math]\displaystyle{ \mu_B }[/math]= 5.788 381 8060 x 10^-5 eV T^-1, and [math]\displaystyle{ g_e }[/math]= 2.002 319 304 362 56.

Related tags and articles

ISPIN, LNONCOLLINEAR

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