BEXT: Difference between revisions

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{{DISPLAYTITLE:BEXT}}
{{DISPLAYTITLE:BEXT}}
{{TAGDEF|BEXT|[real array]}}
{{TAGDEF|BEXT|[real] ( [real] [real] )}}
{{DEF|BEXT|0.0|if {{TAG|ISPIN}}{{=}}2|3*0.0|if {{TAG|LNONCOLLINEAR}}{{=}}.TRUE.| N/A | else}}
{{DEF|BEXT|0.0|if {{TAG|ISPIN}}{{=}}2|3*0.0|if {{TAG|LNONCOLLINEAR}}{{=}}.TRUE.| N/A | else}}


Description: {{TAG|BEXT}} specifies an external magnetic field.
Description: Specifies an external magnetic field in eV.


----
----


By means of the {{TAG|BEXT}} one may specify an external magnetic field that acts on the electrons in a Zeeman-like manner.
{{TAG|BEXT}} tag sets 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:
An additional potential of the following form carries this interaction:


* For {{TAG|ISPIN}} = 2:
* For spin-polarized calculations ({{TAG|ISPIN}} = 2):
:<math>
:<math>
V^{\uparrow} = V^{\uparrow} + B_{\rm ext}
V^{\uparrow} = V^{\uparrow} + B_{\rm ext}
Line 19: Line 19:
:and <math>B_{\rm ext}</math> = {{TAG|BEXT}} (in eV).
:and <math>B_{\rm ext}</math> = {{TAG|BEXT}} (in eV).


* For {{TAG|LNONCOLLINEAR}} = .TRUE.:
* For noncollinear calculations ({{TAG|LNONCOLLINEAR}} = .TRUE.):
:<math>
:<math>
V_{\alpha\beta} = V_{\alpha\beta} + \vec{B}_{\rm ext} \cdot \vec{\sigma}_{\alpha \beta}
V_{\alpha\beta} = V_{\alpha\beta} + \mathbf{B}_{\rm ext} \cdot \mathbf{\sigma}_{\alpha \beta}
</math>
</math>


:where <math>({B}^x_{\rm ext}, {B}^y_{\rm ext}, {B}^z_{\rm ext})</math> = {{TAG|BEXT}} (in eV), and <math>\vec{\sigma}</math> is the vector of Pauli matrices.
:where <math>\mathbf{B}_{\rm ext}=({B}^1_{\rm ext}, {B}^2_{\rm ext}, {B}^3_{\rm ext})^T</math> is given by


Heuristically, the effect of the above is most easily understood for the collinear spinpolarized case ({{TAG|ISPIN}}=2):
{{CB|{{TAGBL|BEXT}} {{=}} B1 B2 B3 ! in eV|:}}


* The eigenenergies of spin-up states are raised by <math>B_{\rm ext}</math> eV, whereas the eigenenergies of spin-down states are lowered by the same amount.
:and <math>\mathbf{\sigma}</math> is the vector of Pauli matrices ({{TAG|SAXIS}}, default:  <math>\sigma_1=\hat x</math>, <math>\sigma_2 =\hat y</math>, <math>\sigma_3 = \hat z</math>).


* The total energy changes by:
The effect of the above is most easily understood for the collinear case ({{TAG|ISPIN}}=2):
The eigenenergies of spin-up states are raised by <math>B_{\rm ext}</math> eV, whereas the eigenenergies of spin-down states are lowered by the same amount. The total energy changes by:
::<math>\Delta E = (n^{\uparrow} - n^{\downarrow}) B_{\rm ext}
::<math>\Delta E = (n^{\uparrow} - n^{\downarrow}) B_{\rm ext}
</math> eV
</math> eV
:where <math>n^{\uparrow}</math> and <math>n^{\downarrow}</math> are the number of up- and down-spin electrons in the system.  
where <math>n^{\uparrow}</math> and <math>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.
{{TAG|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 {{TAG|BEXT}}=0 and restart with {{TAG|BEXT}}<math>\neq</math>0 and fixed charge density ({{TAG|ICHARG}}=11).


The energy difference between two Zeeman-splitted electronic states is given by:
== Units ==
 
For an applied magnetic field <math>B_0</math>, the energy difference between two Zeeman-splitted electronic states is given by:
:<math>
:<math>
\hbar \omega = g_e \mu_B B_0
\hbar \omega = g_e \mu_B B_0,
</math>
</math>
where <math>\mu_B</math> is the Bohr magneton and <math>g_e</math> is the electron ''g''-factor.
where <math>\mu_B</math> is the Bohr magneton and <math>g_e</math> is the electron spin ''g''-factor.


For {{TAG|ISPIN}}=2, for purely Zeeman splitted states, we have:
For {{TAG|ISPIN}}=2, rigid-band Zeeman-splitted states imply:
:<math>
:<math>
V^{\uparrow} - V^{\downarrow}  = 2 B_{\rm ext}
V^{\uparrow} - V^{\downarrow}  = 2 B_{\rm ext}
Line 52: Line 55:
</math>
</math>
where <math>\mu_B</math>= 5.788 381 8060 x 10<sup>-5</sup> eV T<sup>-1</sup>, and <math>g_e</math>= 2.002 319 304 362 56.
where <math>\mu_B</math>= 5.788 381 8060 x 10<sup>-5</sup> eV T<sup>-1</sup>, and <math>g_e</math>= 2.002 319 304 362 56.


== Related tags and articles ==
== Related tags and articles ==


{{TAG|ISPIN}},
{{TAG|ISPIN}},
{{TAG|LNONCOLLINEAR}}
{{TAG|LNONCOLLINEAR}},
{{TAG|SAXIS}}


----
----


[[Category:INCAR tag]] [[Category:Magnetism]]
[[Category:INCAR tag]] [[Category:Magnetism]]

Latest revision as of 13:45, 27 June 2024

BEXT = [real] ( [real] [real] ) 

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):
and = BEXT (in eV).
where is given by
BEXT = B1 B2 B3 ! in eV
and is the vector of Pauli matrices (SAXIS, default: , , ).

The effect of the above is most easily understood for the collinear case (ISPIN=2): The eigenenergies of spin-up states are raised by eV, whereas the eigenenergies of spin-down states are lowered by the same amount. The total energy changes by:

eV

where and 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 BEXT0 and fixed charge density (ICHARG=11).

Units

For an applied magnetic field , the energy difference between two Zeeman-splitted electronic states is given by:

where is the Bohr magneton and is the electron spin g-factor.

For ISPIN=2, rigid-band Zeeman-splitted states imply:

This leads to the following relationship between our definition of (in eV) and the magnetic field (in T):

where = 5.788 381 8060 x 10-5 eV T-1, and = 2.002 319 304 362 56.

Related tags and articles

ISPIN, LNONCOLLINEAR, SAXIS