I CONSTRAINED M - Revision history

Huebsch: /* Related tags and articles */

2026-03-16T10:37:07Z

Singraber at 15:46, 2 October 2023

2023-10-02T15:46:11Z

← Older revision		Revision as of 15:46, 2 October 2023
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	::<math>V_I (\mathbf{r})=2\lambda \left( \vec{M}_I-\vec{M}^0_I \right)\cdot \vec{\sigma} F_I(\|\mathbf{r}\|)</math>		::<math>V_I (\mathbf{r})=2\lambda \left( \vec{M}_I-\vec{M}^0_I \right)\cdot \vec{\sigma} F_I(\|\mathbf{r}\|)</math>

	*{{TAG\|I_CONSTRAINED_M}}=4: Constrain the ''direction and sign'' of the magnetic moments{{cite\|ma:prb:15}}.		*{{TAG\|I_CONSTRAINED_M}}=4: Constrain the ''direction and sign'' of the magnetic moments{{cite\|ma:prb:15}}, available since VASP.6.4.0.
	:The total energy is given by		:The total energy is given by

Singraber at 15:21, 2 October 2023

2023-10-02T15:21:13Z

← Older revision		Revision as of 15:21, 2 October 2023
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	{{DISPLAYTITLE:I_CONSTRAINED_M}}		{{DISPLAYTITLE:I_CONSTRAINED_M}}
	{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}		{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2 {{!}} 4\|none}}

	Description: {{TAG\|I_CONSTRAINED_M}} switches on the constrained local moments approach ~~{{cite\|ma:prb:15}}~~.		Description: {{TAG\|I_CONSTRAINED_M}} switches on the constrained local moments approach.
	----		----
	VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius {{TAG\|RWIGS}}) into a direction given by the {{TAG\|M_CONSTR}}-tag.		VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius {{TAG\|RWIGS}}) into a direction given by the {{TAG\|M_CONSTR}}-tag.
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	:The total energy is given by		:The total energy is given by

	::<math>E=E_0+ \sum_I\lambda \left[ \vec{M}_I-\hat{M}^0_I \left( \hat{M}^0_I \cdot \vec{~~M_I~~}\right)\right]^2</math>		::<math>E=E_0+ \sum_I\lambda \left[ \vec{M}_I-\hat{M}^0_I \left( \hat{M}^0_I \cdot \vec{M}_I\right)\right]^2</math>

	:where ''E''<sub>0</sub> is the usual DFT energy, and the second term on the right-hand-side represents the penalty. The sum is taken over all atomic sites ''I'', <math>\hat{M}^0_I</math> is the desired direction of the magnetic moment at site ''I'' (as specified using {{TAG\|M_CONSTR}}), and <math>\vec{M}_I</math> is the integrated magnetic moment inside a sphere Ω<sub>''I''</sub> (the radius '''must''' be specified by means of {{TAG\|RWIGS}}) around the position of atom ''I'',		:where ''E''<sub>0</sub> is the usual DFT energy, and the second term on the right-hand-side represents the penalty. The sum is taken over all atomic sites ''I'', <math>\hat{M}^0_I</math> is the desired direction (unit vector) of the magnetic moment at site ''I'' (as specified using {{TAG\|M_CONSTR}}), and <math>\vec{M}_I</math> is the integrated magnetic moment inside a sphere Ω<sub>''I''</sub> (the radius '''must''' be specified by means of {{TAG\|RWIGS}}) around the position of atom ''I'',

	<span id="MWint">		<span id="MWint">
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	:The additional potential that arises from the penalty contribution to the total energy is given by		:The additional potential that arises from the penalty contribution to the total energy is given by
	::<math>V_I (\mathbf{r})=2\lambda \left( \vec{M}_I-\vec{M}^0_I \right)\cdot \vec{\sigma} F_I(\|\mathbf{r}\|)</math>		::<math>V_I (\mathbf{r})=2\lambda \left( \vec{M}_I-\vec{M}^0_I \right)\cdot \vec{\sigma} F_I(\|\mathbf{r}\|)</math>

			*{{TAG\|I_CONSTRAINED_M}}=4: Constrain the ''direction and sign'' of the magnetic moments{{cite\|ma:prb:15}}.
			:The total energy is given by

			::<math>E=E_0+ \sum_I\lambda \left( \|\vec{M}_I\| - \hat{M}^0_I \cdot \vec{M}_I\right)</math>

			:where <math>\hat{M}^0_I</math> is the desired magnetic moment at site ''I'' (as specified using {{TAG\|M_CONSTR}}).
			:The additional potential that arises from the penalty contribution to the total energy is given by
			::<math>V_I (\mathbf{r})=\lambda \left( \hat{M}_I-\hat{M}^0_I \right)\cdot \vec{\sigma} F_I(\|\mathbf{r}\|)</math>
			:where <math>\hat{M}_I</math> denotes the unit vector in <math>\vec{M}_I</math> direction.

	The weight λ, with which the penalty terms enter into the total energy expression and the Hamiltonian in the above is specified through the {{TAG\|LAMBDA}} tag.		The weight λ, with which the penalty terms enter into the total energy expression and the Hamiltonian in the above is specified through the {{TAG\|LAMBDA}} tag.

Singraber at 09:23, 2 October 2023

2023-10-02T09:23:06Z

← Older revision		Revision as of 09:23, 2 October 2023
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	{{sc\|I_CONSTRAINED_M\|Examples\|Examples that use this tag}}		{{sc\|I_CONSTRAINED_M\|Examples\|Examples that use this tag}}
	----		----
	~~[[The_VASP_Manual\|Contents]]~~

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

	== References ==		== References ==

Singraber at 09:17, 2 October 2023

2023-10-02T09:17:51Z

← Older revision		Revision as of 09:17, 2 October 2023
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	{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}		{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}

	Description: {{TAG\|I_CONSTRAINED_M}} switches on the constrained local moments approach~~<ref name="~~ma:prb:15~~"/>~~.		Description: {{TAG\|I_CONSTRAINED_M}} switches on the constrained local moments approach {{cite\|ma:prb:15}}.
	----		----
	VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius {{TAG\|RWIGS}}) into a direction given by the {{TAG\|M_CONSTR}}-tag.		VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius {{TAG\|RWIGS}}) into a direction given by the {{TAG\|M_CONSTR}}-tag.
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	The weight λ, with which the penalty terms enter into the total energy expression and the Hamiltonian in the above is specified through the {{TAG\|LAMBDA}} tag.		The weight λ, with which the penalty terms enter into the total energy expression and the Hamiltonian in the above is specified through the {{TAG\|LAMBDA}} tag.

	As is probably clear from the above, applying constraints by means of a penalty functional contributes to the total energy. This contribution, however, decreases with increasing {{TAG\|LAMBDA}} and can in principle be made vanishingly small. Increasing {{TAG\|LAMBDA}} stepwise, from one run to another (slowly so the solution remains stable) one thus converges towards the DFT total energy for a given magnetic configuration.		As is probably clear from the above, applying constraints by means of a penalty functional contributes to the total energy. This contribution, however, decreases with increasing {{TAG\|LAMBDA}} and can in principle be made vanishingly small {{cite\|ma:prb:15}}. Increasing {{TAG\|LAMBDA}} stepwise, from one run to another (slowly so the solution remains stable) one thus converges towards the DFT total energy for a given magnetic configuration.
	----		----

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

			== References ==

Singraber at 09:13, 2 October 2023

2023-10-02T09:13:41Z

← Older revision		Revision as of 09:13, 2 October 2023
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	{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}		{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}

	Description: {{TAG\|I_CONSTRAINED_M}} switches on the constrained local moments approach.		Description: {{TAG\|I_CONSTRAINED_M}} switches on the constrained local moments approach<ref name="ma:prb:15"/>.
	----		----
	VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius {{TAG\|RWIGS}}) into a direction given by the {{TAG\|M_CONSTR}}-tag.		VASP offers the possibility to add a penalty contribution to the total energy expression (and consequently a penalty functional to the Hamiltonian) that drives the local magnetic moment (integral of the magnetization in a site centered sphere of radius {{TAG\|RWIGS}}) into a direction given by the {{TAG\|M_CONSTR}}-tag.

Karsai at 15:55, 7 April 2022

2022-04-07T15:55:26Z

← Older revision		Revision as of 15:55, 7 April 2022
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	{{DISPLAYTITLE:I_CONSTRAINED_M}}		{{DISPLAYTITLE:I_CONSTRAINED_M}}

	{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}		{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}

Karsai: /* Related tags and articles */

2022-04-07T06:48:02Z

Karsai at 16:42, 6 April 2022

2022-04-06T16:42:39Z

← Older revision		Revision as of 16:42, 6 April 2022
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			{{DISPLAYTITLE:I_CONSTRAINED_M}}

	{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}		{{TAGDEF\|I_CONSTRAINED_M\|1 {{!}} 2\|none}}

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	Under <tt>lambda*MW_perp</tt> the constraining "magnetic field" at each atomic site is listed. It shows which magnetic field is added to the DFT Hamiltonian to stabilize the magnetic configuration.		Under <tt>lambda*MW_perp</tt> the constraining "magnetic field" at each atomic site is listed. It shows which magnetic field is added to the DFT Hamiltonian to stabilize the magnetic configuration.

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|M_CONSTR}},		{{TAG\|M_CONSTR}},
	{{TAG\|LAMBDA}},		{{TAG\|LAMBDA}},
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	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:INCAR]][[Category:Magnetism]]		[[Category:INCAR tags]][[Category:Magnetism]]

Vaspmaster at 10:13, 20 September 2021

2021-09-20T10:13:44Z

← Older revision		Revision as of 10:13, 20 September 2021
Line 38:		Line 38:
	The weight λ, with which the penalty terms enter into the total energy expression and the Hamiltonian in the above is specified through the {{TAG\|LAMBDA}} tag.		The weight λ, with which the penalty terms enter into the total energy expression and the Hamiltonian in the above is specified through the {{TAG\|LAMBDA}} tag.

	As is probably clear from the above, applying constraints by means of a penalty functional contributes to the total energy. This contribution, however, decreases with ~~decreasing~~ {{TAG\|LAMBDA}} and can in principle be made vanishingly small. ~~Decreasing~~ {{TAG\|LAMBDA}} stepwise, from one run to another (slowly so the solution remains stable) one thus converges towards the DFT total energy for a given magnetic configuration.		As is probably clear from the above, applying constraints by means of a penalty functional contributes to the total energy. This contribution, however, decreases with increasing {{TAG\|LAMBDA}} and can in principle be made vanishingly small. Increasing {{TAG\|LAMBDA}} stepwise, from one run to another (slowly so the solution remains stable) one thus converges towards the DFT total energy for a given magnetic configuration.
	----		----

← Older revision		Revision as of 10:37, 16 March 2026
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	{{TAG\|LNONCOLLINEAR}}		{{TAG\|LNONCOLLINEAR}}

	{{sc\|I_CONSTRAINED_M\|~~Examples~~\|~~Examples~~ that use this tag}}		{{sc\|I_CONSTRAINED_M\|HowTo\|Workflows that use this tag}}
	~~----~~

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

	== References ==		== References ==

← Older revision		Revision as of 06:48, 7 April 2022
Line 79:		Line 79:
	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:INCAR ~~tags~~]][[Category:Magnetism]]		[[Category:INCAR tag]][[Category:Magnetism]]