Category:Magnetism - Revision history

Csheldon at 09:09, 12 January 2026

2026-01-12T09:09:40Z

← Older revision		Revision as of 09:09, 12 January 2026
Line 58:		Line 58:

	Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}		Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}

			== Additional resources ==

			=== Tutorials ===
			*Tutorial for [https://www.vasp.at/tutorials/latest/magnetism/part1/ spin-polarized calculations].
			*Tutorial for [https://www.vasp.at/tutorials/latest/magnetism/part2/ noncollinear calculations].

	== References ==		== References ==

Csheldon: /* Nuclear magnetic resonance */

2025-03-21T15:29:43Z

Nuclear magnetic resonance

← Older revision		Revision as of 15:29, 21 March 2025
Line 53:		Line 53:

	=== Nuclear magnetic resonance ===		=== Nuclear magnetic resonance ===
			The chemical shielding can be calculated using {{TAG\|LCHIMAG}}. The hyperfine coupling constant can also be calculated using {{TAG\|LHYPERFINE}}. Further options are listed in the [[:Category:NMR\|NMR category page]].
	~~See~~ {{TAG\|LCHIMAG}} ~~and~~ [[:Category:NMR\|NMR category page]].

	=== External magnetic field ===		=== External magnetic field ===

Csheldon: /* Nuclear magnetic resonance */

2025-03-21T15:26:36Z

Nuclear magnetic resonance

← Older revision		Revision as of 15:26, 21 March 2025
Line 54:		Line 54:
	=== Nuclear magnetic resonance ===		=== Nuclear magnetic resonance ===

	See {{TAG\|LCHIMAG}}.		See {{TAG\|LCHIMAG}} and [[:Category:NMR\|NMR category page]].

	=== External magnetic field ===		=== External magnetic field ===

Csheldon: /* Nuclear magnetic resonance */

2025-03-21T15:25:46Z

Nuclear magnetic resonance

← Older revision		Revision as of 15:25, 21 March 2025
Line 54:		Line 54:
	=== Nuclear magnetic resonance ===		=== Nuclear magnetic resonance ===

	See {{TAG\|LCHIMAG~~}} and {{:Category:NMR\|NMR cateogry page~~}}.		See {{TAG\|LCHIMAG}}.

	=== External magnetic field ===		=== External magnetic field ===

Csheldon: /* Nuclear magnetic resonance */

2025-03-21T15:25:33Z

Nuclear magnetic resonance

← Older revision		Revision as of 15:25, 21 March 2025
Line 54:		Line 54:
	=== Nuclear magnetic resonance ===		=== Nuclear magnetic resonance ===

	See {{TAG\|LCHIMAG}} and {{:Category:NMR}}.		See {{TAG\|LCHIMAG}} and {{:Category:NMR\|NMR cateogry page}}.

	=== External magnetic field ===		=== External magnetic field ===

Csheldon: /* Nuclear magnetic resonance */

2025-03-21T15:25:08Z

Nuclear magnetic resonance

← Older revision		Revision as of 15:25, 21 March 2025
Line 54:		Line 54:
	=== Nuclear magnetic resonance ===		=== Nuclear magnetic resonance ===

	See {{TAG\|LCHIMAG}}.		See {{TAG\|LCHIMAG}} and {{:Category:NMR}}.

	=== External magnetic field ===		=== External magnetic field ===

Csheldon at 14:03, 12 February 2025

2025-02-12T14:03:34Z

← Older revision		Revision as of 14:03, 12 February 2025
Line 63:		Line 63:


	[[Category:VASP]][[Category:Electronic ground-state properties]]		[[Category:VASP]][[Category:Electronic ground-state properties]][[Category:NMR]]

Huebsch at 12:16, 14 October 2024

2024-10-14T12:16:59Z

← Older revision		Revision as of 12:16, 14 October 2024
Line 6:		Line 6:

	In VASP, the electronic spin can be treated either within a so-called ''spin-polarized calculation'' ({{TAG\|ISPIN}}=2) or a ''noncollinear calculation'' ({{TAG\|LNONCOLLINEAR}}=T){{Cite\|hobbs:prb:00}}. The aim is to solve the Kohn-Sham (KS) equations including the spin degree of freedom to yield spin-dependent KS orbitals, thus fulfilling quantum mechanical statistics. In this context it is important to choose the [[pseudopotential]] such that the electrons that give rise to magnetism are treated as valence electrons. The electron–electron interaction is included based on the selected [[exchange-correlation functional]]. For a general introduction to magnetism in the context of density-functional theory (DFT), we recommend the book ''Theory of itinerant electron magnetism'' by Jürgen Kübler {{Cite\|kuebler2000:book}}.		In VASP, the electronic spin can be treated either within a so-called ''spin-polarized calculation'' ({{TAG\|ISPIN}}=2) or a ''noncollinear calculation'' ({{TAG\|LNONCOLLINEAR}}=T){{Cite\|hobbs:prb:00}}. The aim is to solve the Kohn-Sham (KS) equations including the spin degree of freedom to yield spin-dependent KS orbitals, thus fulfilling quantum mechanical statistics. In this context it is important to choose the [[pseudopotential]] such that the electrons that give rise to magnetism are treated as valence electrons. The electron–electron interaction is included based on the selected [[exchange-correlation functional]]. For a general introduction to magnetism in the context of density-functional theory (DFT), we recommend the book ''Theory of itinerant electron magnetism'' by Jürgen Kübler {{Cite\|kuebler2000:book}}.
			{{NB\|tip\|In magnetic systems the [[electronic minimization]] is often hard to converge, see [[troubleshooting electronic convergence]] for help.}}
	== Spin-polarized calculation ==		== Spin-polarized calculation ==
	In spin-polarized calculations, there is a distinct spin-up and spin-down charge density		In spin-polarized calculations, there is a distinct spin-up and spin-down charge density
Line 32:		Line 32:
	Note that in the noncollinear case, the KS equations do not decouple for spin-up and spin-down because the potential has off-diagonal elements that couple the two spin species. This is the SCF loop of noncollinear spin-density functional theory (SDFT).		Note that in the noncollinear case, the KS equations do not decouple for spin-up and spin-down because the potential has off-diagonal elements that couple the two spin species. This is the SCF loop of noncollinear spin-density functional theory (SDFT).

	As VASP needs to treat many quantities as matrices instead of arrays, you need to use the '''vasp_ncl''' executable for these calculations in addition to setting {{TAG\|LNONCOLLINEAR}}=T and/or {{TAG\|LSORBIT}}=T for spin-orbit coupling. The magnetization ({{FILE\|CHGCAR}}, {{FILE\|PROCAR}}) and on-site magnetic moments (see {{TAG\|MAGMOM}}, {{TAG\|LORBIT}}) live in spinor space as defined by {{TAG\|SAXIS}}.		As VASP needs to treat many quantities as matrices instead of arrays, you need to use the '''vasp_ncl''' executable for these calculations in addition to setting {{TAG\|LNONCOLLINEAR}}=T and/or {{TAG\|LSORBIT}}=T for spin-orbit coupling. The magnetization ({{FILE\|CHGCAR}}, {{FILE\|PROCAR}}) and on-site magnetic moments (see {{TAG\|MAGMOM}}, {{TAG\|LORBIT}}) live in spinor space as defined by {{TAG\|SAXIS}}.

	== Advanced methods ==		== Advanced methods ==
Line 60:		Line 60:
	Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}		Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}

	~~<!---~~

	~~What can one do when convergence is bad:~~
	*Start from charge density of non-spin-polarized calculation using {{TAG\|ISTART}}=0 (or remove the {{TAG\|WAVECAR}} file) and {{TAG\|ICHARG}}=1.
	*Use linear mixing by setting {{TAG\|BMIX}}=0.0001 and {{TAG\|BMIX_MAG}}=0.0001.
	*Mix slowly, i.e., reduce {{TAG\|AMIX}} and {{TAG\|AMIX_MAG}}.
	*REDUCE {{TAG\|MAXMIX}}, the number of steps stored in the Broyden mixer (default {{TAG\|MAXMIX}}=45).
	*Restart from partially converged results (stop a calculation after say 20 steps and restart from the {{TAG\|WAVECAR}} file).
	*Use constraints to stabilize the magnetic configuration.
	*Pray.

	~~-->~~
	== References ==		== References ==


	[[Category:VASP]][[Category:Electronic ground-state properties]]		[[Category:VASP]][[Category:Electronic ground-state properties]]

Huebsch at 10:08, 14 October 2024

2024-10-14T10:08:32Z

← Older revision		Revision as of 10:08, 14 October 2024
Line 1:		Line 1:
	There are three ingredients to obtain '''magnetism'''.		There are three ingredients to obtain '''magnetism''':
	* The first is the electronic spin. The origin of spin is explained by Dirac theory, that is the relativistic quantum theory of an electron.		* The first is the ''electronic spin''. The origin of spin is explained by Dirac theory, that is the relativistic quantum theory of an electron.
	* The second ingredient is quantum mechanical statistics. The Bohr–Van Leeuwen theorem states that a classical particle that follows Boltzmann statistics can never give rise to magnetism, even if the particle carries charge and spin. Therefore, in addition to spin, proper quantum mechanical statistics are necessary to explain magnetism.		* The second ingredient is ''quantum mechanical statistics''. The Bohr–Van Leeuwen theorem states that a classical particle that follows Boltzmann statistics can never give rise to magnetism, even if the particle carries charge and spin. Therefore, in addition to spin, proper quantum mechanical statistics are necessary to explain magnetism.
	* And finally, there is one more necessary ingredient: electron–electron interaction. Only the specific details of the interaction between electrons leads to a finite magnetization, otherwise any material would be magnetic.		* And finally, there is one more necessary ingredient: ''electron–electron interaction''. Only the specific details of the interaction between electrons leads to a finite magnetization, otherwise any material would be magnetic.
	In summary, magnetism is a collective, quantum electrodynamic phenomenon.		In summary, magnetism is a ''collective, quantum electrodynamic phenomenon''. The challenge is now to describe magnetism from first principles using ab-initio simulations.

	In VASP, the spin ~~degrees of freedom~~ can be treated either within a so-called spin-polarized calculation ({{TAG\|ISPIN}}=2) or a noncollinear calculation ({{TAG\|LNONCOLLINEAR}}=T).		In VASP, the electronic spin can be treated either within a so-called ''spin-polarized calculation'' ({{TAG\|ISPIN}}=2) or a ''noncollinear calculation'' ({{TAG\|LNONCOLLINEAR}}=T){{Cite\|hobbs:prb:00}}. The aim is to solve the Kohn-Sham (KS) equations including the spin degree of freedom to yield spin-dependent KS orbitals, thus fulfilling quantum mechanical statistics. In this context it is important to choose the [[pseudopotential]] such that the electrons that give rise to magnetism are treated as valence electrons. The electron–electron interaction is included based on the selected [[exchange-correlation functional]]. For a general introduction to magnetism in the context of density-functional theory (DFT), we recommend the book ''Theory of itinerant electron magnetism'' by Jürgen Kübler {{Cite\|kuebler2000:book}}.

	== Spin-polarized calculation ==		== Spin-polarized calculation ==
	~~Similar to the Stoner model~~, there is a distinct spin-up and spin-down charge density		In spin-polarized calculations, there is a distinct spin-up and spin-down charge density
	:<math>n_\sigma(\mathbf{r}) = \sum_{n=1}^N \|\psi_{\sigma n}(\mathbf{r})\|^2. </math>		:<math>n_\sigma(\mathbf{r}) = \sum_{n=1}^N \|\psi_{\sigma n}(\mathbf{r})\|^2, </math>
	As in standard DFT, one electron moves in an effective potential, but the effective potential of a spin-polarized calculation ({{TAG\|ISPIN}}=2) has an additional spin index		similar to the well-known Stoner model.
			As in standard DFT, one electron moves in an effective potential, but the effective potential <math>v_\sigma^{eff}({\bf r})</math> of a spin-polarized calculation ({{TAG\|ISPIN}}=2) has an additional spin index
	:<math>v_\sigma^{eff}({\bf r})=v^{ext}({\bf r}) + v^{H}({\bf r}) + v_\sigma^{xc}({\bf r}).</math>		:<math>v_\sigma^{eff}({\bf r})=v^{ext}({\bf r}) + v^{H}({\bf r}) + v_\sigma^{xc}({\bf r}).</math>
	The [[XC functional\|exchange-correlation potential]] is		The [[XC functional\|exchange-correlation potential]] is
	:<math>v_\sigma^{xc}=\frac{\delta E_{xc}[n_\uparrow,n_\downarrow]}{\delta n_{\sigma}}.</math>		:<math>v_\sigma^{xc}=\frac{\delta E_{xc}[n_\uparrow,n_\downarrow]}{\delta n_{\sigma}}.</math>
	The spin-dependent effective potential enters the ~~Kohn-Sham (~~KS) equations		The spin-dependent effective potential enters the KS equations
	:<math>\left[-{\mathbf \nabla}^2_n + v^{eff}_\uparrow({\mathbf r}_n)\right]\psi_{\uparrow n}= \varepsilon_{n} \psi_{\uparrow n}</math>		:<math>\left[-{\mathbf \nabla}^2_n + v^{eff}_\uparrow({\mathbf r}_n)\right]\psi_{\uparrow n}= \varepsilon_{n} \psi_{\uparrow n}</math>
	:<math>\left[-{\mathbf \nabla}^2_n + v^{eff}_\downarrow({\mathbf r}_n)\right]\psi_{\downarrow n}= \varepsilon_{n} \psi_{\downarrow n}</math>		:<math>\left[-{\mathbf \nabla}^2_n + v^{eff}_\downarrow({\mathbf r}_n)\right]\psi_{\downarrow n}= \varepsilon_{n} \psi_{\downarrow n}</math>
	and leads to spin-dependent solutions for the KS orbitals. Finally, the spin-up and spin-down KS orbitals are used to update the spin-up and spin-down charge densities until self-consistency is reached. Note that, the spin species only couple to one another through the exchange-correlation potential where both, the spin-up and spin-down charge densities enter as an argument.		and leads to spin-dependent solutions for the KS orbitals <math>\psi_{\uparrow n}</math>. Finally, the spin-up and spin-down KS orbitals are used to update the spin-up and spin-down charge densities until self-consistency is reached. Note that, the spin species only couple to one another through the [[XC functional\|exchange-correlation potential]] where both, the spin-up and spin-down charge densities enter as an argument.

	Spin-polarized calculations are enabled by setting {{TAG\|ISPIN}}=2 in the {{FILE\|INCAR}} file and executing '''vasp_std'''.		Spin-polarized calculations are enabled by setting {{TAG\|ISPIN}}=2 in the {{FILE\|INCAR}} file and executing '''vasp_std'''. It is useful in order to describe collinear magnetic systems without spin-orbit coupling. Also see {{TAG\|MAGMOM}}, {{TAG\|LORBIT}}.

	== Noncollinear calculation ==		== Noncollinear calculation ==
Line 31:		Line 32:
	Note that in the noncollinear case, the KS equations do not decouple for spin-up and spin-down because the potential has off-diagonal elements that couple the two spin species. This is the SCF loop of noncollinear spin-density functional theory (SDFT).		Note that in the noncollinear case, the KS equations do not decouple for spin-up and spin-down because the potential has off-diagonal elements that couple the two spin species. This is the SCF loop of noncollinear spin-density functional theory (SDFT).

	As VASP needs to treat many quantities as matrices instead of arrays, you need to use the '''vasp_ncl''' executable for these calculations in addition to setting {{TAG\|LNONCOLLINEAR}}=T and/or {{TAG\|LSORBIT}}=T for spin-orbit coupling.		As VASP needs to treat many quantities as matrices instead of arrays, you need to use the '''vasp_ncl''' executable for these calculations in addition to setting {{TAG\|LNONCOLLINEAR}}=T and/or {{TAG\|LSORBIT}}=T for spin-orbit coupling. The magnetization ({{FILE\|CHGCAR}}, {{FILE\|PROCAR}}) and on-site magnetic moments (see {{TAG\|MAGMOM}}, {{TAG\|LORBIT}}) live in spinor space as defined by {{TAG\|SAXIS}}.

	== ~~How to~~ ==		== Advanced methods ==
	* Spin-orbit coupling: {{TAG\|LSORBIT}}.
	* Noncollinear magnetism: {{TAG\|LNONCOLLINEAR}}.
	* Spin spirals: {{TAG\|Spin spirals}}.
	* Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}

			Some methods below can be applied in the context of both spin-polarized and noncollinear calculations.

			=== Constrained magnetic moments ===

			See {{TAG\|I_CONSTRAINED_M}}.

			=== Spin spirals ===

			[[Spin spirals]], or spin waves, are a magnetic order that can be described in terms of the generalized Bloch theorem. It states that the spin-up and spin-down components, and thus the magnetization, are rotated based on a certain spin-spiral propagation vector <math>\mathbf{q}</math>. If the corresponding wavelength is a multiple of the lattice vector of the crystal unit cell, the spin wave is commensurate. While the method can be used for both commensurate and incommensurable spin spirals, in practice it is more useful in case of incommensurable spin spirals. This is because spin spirals cannot be combined with spin orbit coupling and often systems with commensurate spin waves exhibit strong SOC, while in many compounds with incommensurable spin spirals SOC can be neglected. The main tag is {{TAG\|LSPIRAL}}.

			To learn how to apply the method read more on [[spin spirals]].

			=== Spin-orbit coupling ===

			Spin-orbit coupling (SOC) is supported as of VASP.4.5 and later described in Ref. {{cite\|Steiner:2016}}. The main tag is {{TAG\|LSORBIT}}, which automatically sets {{TAG\|LNONCOLLINEAR}} and requires using <code>vasp_ncl</code>. SOC couples the spin degrees of freedom with the lattice degrees of freedom, see {{TAG\|SAXIS}}.

			=== Nuclear magnetic resonance ===

			See {{TAG\|LCHIMAG}}.

			=== External magnetic field ===

			Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}

			<!---

	What can one do when convergence is bad:		What can one do when convergence is bad:
Line 48:		Line 70:
	*Use constraints to stabilize the magnetic configuration.		*Use constraints to stabilize the magnetic configuration.
	*Pray.		*Pray.
	----
			-->
			== References ==


	[[Category:VASP]][[Category:Electronic ground-state properties]]		[[Category:VASP]][[Category:Electronic ground-state properties]]

Huebsch: /* How to */

2024-06-12T13:58:04Z

How to

← Older revision		Revision as of 13:58, 12 June 2024
Line 39:		Line 39:
	* Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}		* Apply a constant external magnetic field (Zeeman-like term): {{TAG\|BEXT}}

	*What can one do when convergence is bad:
	**Start from charge density of non-spin-polarized calculation using {{TAG\|ISTART}}=0 (or remove the {{TAG\|WAVECAR}} file) and {{TAG\|ICHARG}}=1.		What can one do when convergence is bad:
	**Use linear mixing by setting {{TAG\|BMIX}}=0.0001 and {{TAG\|BMIX_MAG}}=0.0001.		*Start from charge density of non-spin-polarized calculation using {{TAG\|ISTART}}=0 (or remove the {{TAG\|WAVECAR}} file) and {{TAG\|ICHARG}}=1.
	**Mix slowly, i.e., reduce {{TAG\|AMIX}} and {{TAG\|AMIX_MAG}}.		*Use linear mixing by setting {{TAG\|BMIX}}=0.0001 and {{TAG\|BMIX_MAG}}=0.0001.
	**REDUCE {{TAG\|MAXMIX}}, the number of steps stored in the Broyden mixer (default {{TAG\|MAXMIX}}=45).		*Mix slowly, i.e., reduce {{TAG\|AMIX}} and {{TAG\|AMIX_MAG}}.
	**Restart from partially converged results (stop a calculation after say 20 steps and restart from the {{TAG\|WAVECAR}} file).		*REDUCE {{TAG\|MAXMIX}}, the number of steps stored in the Broyden mixer (default {{TAG\|MAXMIX}}=45).
	**Use constraints to stabilize the magnetic configuration.		*Restart from partially converged results (stop a calculation after say 20 steps and restart from the {{TAG\|WAVECAR}} file).
	**Pray.		*Use constraints to stabilize the magnetic configuration.
			*Pray.
	----		----

	[[Category:VASP]][[Category:Electronic ground-state properties]]		[[Category:VASP]][[Category:Electronic ground-state properties]]