Spin-spiral calculations - Revision history

Csheldon: Capitalize first letter of file/image link target (broken by wiki case-sensitivity change)

2026-07-22T14:50:49Z

Capitalize first letter of file/image link target (broken by wiki case-sensitivity change)

← Older revision		Revision as of 14:50, 22 July 2026
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	Analyzing site-resolved local moments is less straightforward than usual, because the spin-spiral period is generally incommensurate with the unit cell, so the magnetization density is not cell-periodic:		Analyzing site-resolved local moments is less straightforward than usual, because the spin-spiral period is generally incommensurate with the unit cell, so the magnetization density is not cell-periodic:

	:[[File:~~ss3~~.png\|300px]]		:[[File:Ss3.png\|300px]]

	The standard analysis via {{TAG\|LORBIT}} (output in the {{FILE\|PROCAR}} file and at the end of the {{FILE\|OUTCAR}} file) does not account for this. As a workaround, use the constrained-moment infrastructure with a zero penalty potential:		The standard analysis via {{TAG\|LORBIT}} (output in the {{FILE\|PROCAR}} file and at the end of the {{FILE\|OUTCAR}} file) does not account for this. As a workaround, use the constrained-moment infrastructure with a zero penalty potential:
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	{{TAGBL\|QSPIRAL}} = 0.0 0.0 0.5		{{TAGBL\|QSPIRAL}} = 0.0 0.0 0.5

	:[[File:~~ss1~~.png\|500px]]		:[[File:Ss1.png\|500px]]

	'''Flat spin spiral.''' Two magnetic atoms with initial moments ''M'' along ''y'' and ''x'', respectively, and <math>{\bf q}=(0,0,\tfrac{1}{2})</math>:		'''Flat spin spiral.''' Two magnetic atoms with initial moments ''M'' along ''y'' and ''x'', respectively, and <math>{\bf q}=(0,0,\tfrac{1}{2})</math>:
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	{{TAGBL\|QSPIRAL}} = 0.0 0.0 0.5		{{TAGBL\|QSPIRAL}} = 0.0 0.0 0.5

	:[[File:~~ss2~~.png\|500px]]		:[[File:Ss2.png\|500px]]
	{{NB\|tip\|Both configurations obey the same generalized Bloch condition, <math>{\bf q}=(0,0,0.5)</math>, and during the electronic minimization, one may transform into the other if that lowers the total energy. The Bloch condition fixes the change in magnetization density from one cell to the next, but does not constrain the magnetic order ''within'' a cell.}}		{{NB\|tip\|Both configurations obey the same generalized Bloch condition, <math>{\bf q}=(0,0,0.5)</math>, and during the electronic minimization, one may transform into the other if that lowers the total energy. The Bloch condition fixes the change in magnetization density from one cell to the next, but does not constrain the magnetic order ''within'' a cell.}}
	=== Example 2: Spin-spiral energy of a NiI<sub>2</sub> monolayer ===		=== Example 2: Spin-spiral energy of a NiI<sub>2</sub> monolayer ===

Huebsch: Huebsch moved page Construction:Spin-spiral calculations to Spin-spiral calculations without leaving a redirect

2026-06-22T08:18:23Z

Huebsch moved page Construction:Spin-spiral calculations to Spin-spiral calculations without leaving a redirect

← Older revision		Revision as of 08:18, 22 June 2026
(No difference)

Huebsch: Issue #16: proofreader fixes (Related-tags comma, Example 2 anchor, Step 1 paren, tt->code)

2026-06-22T08:13:56Z

Issue #16: proofreader fixes (Related-tags comma, Example 2 anchor, Step 1 paren, tt->code)

Huebsch: Issue #16: spin-spiral figure now single-panel; update caption

2026-06-19T11:55:48Z

Issue #16: spin-spiral figure now single-panel; update caption

← Older revision		Revision as of 11:55, 19 June 2026
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	This example uses a spin-spiral calculation to obtain the total energy of a flat spin spiral in a NiI<sub>2</sub> monolayer. The spin spiral is scanned along the {{TAG\|QSPIRAL}} path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.		This example uses a spin-spiral calculation to obtain the total energy of a flat spin spiral in a NiI<sub>2</sub> monolayer. The spin spiral is scanned along the {{TAG\|QSPIRAL}} path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.

	[[File:NiI2_spinspiral_structure.png\|thumb\|center\|~~650px~~\|~~Left: the 1T NiI<sub>2</sub> monolayer unit cell. Right: the~~ flat in-plane spin spiral at the computed Γ–M minimum '''Q''' = (0.214, 0, 0); the Ni moments rotate in the plane with period ''λ'' = 1/''Q'' ≈ 4.7 ''a~~'' along '''Q'~~''.]]		[[File:NiI2_spinspiral_structure.png\|thumb\|center\|600px\|The flat in-plane spin spiral at the computed Γ–M minimum '''Q''' = (0.214, 0, 0): the Ni moments rotate in the plane along '''Q''' with period ''λ'' = 1/''Q'' ≈ 4.7 ''a''.]]

	'''Structure''': A 1T (CdI<sub>2</sub>-type) NiI<sub>2</sub> monolayer, hexagonal ''a'' = 3.97 Å with ≈8 Å of vacuum ({{FILE\|POSCAR}}):		'''Structure''': A 1T (CdI<sub>2</sub>-type) NiI<sub>2</sub> monolayer, hexagonal ''a'' = 3.97 Å with ≈8 Å of vacuum ({{FILE\|POSCAR}}):

Huebsch: Issue #16: embed NiI2 structure + spin-spiral figure in Example 2

2026-06-19T11:49:48Z

Issue #16: embed NiI2 structure + spin-spiral figure in Example 2

← Older revision		Revision as of 11:49, 19 June 2026
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	=== Example 2: Spin-spiral energy of a NiI<sub>2</sub> monolayer ===		=== Example 2: Spin-spiral energy of a NiI<sub>2</sub> monolayer ===
	This example uses a spin-spiral calculation to obtain the total energy of a flat spin spiral in a NiI<sub>2</sub> monolayer. The spin spiral is scanned along the {{TAG\|QSPIRAL}} path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.		This example uses a spin-spiral calculation to obtain the total energy of a flat spin spiral in a NiI<sub>2</sub> monolayer. The spin spiral is scanned along the {{TAG\|QSPIRAL}} path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.

			[[File:NiI2_spinspiral_structure.png\|thumb\|center\|650px\|Left: the 1T NiI<sub>2</sub> monolayer unit cell. Right: the flat in-plane spin spiral at the computed Γ–M minimum '''Q''' = (0.214, 0, 0); the Ni moments rotate in the plane with period ''λ'' = 1/''Q'' ≈ 4.7 ''a'' along '''Q'''.]]

	'''Structure''': A 1T (CdI<sub>2</sub>-type) NiI<sub>2</sub> monolayer, hexagonal ''a'' = 3.97 Å with ≈8 Å of vacuum ({{FILE\|POSCAR}}):		'''Structure''': A 1T (CdI<sub>2</sub>-type) NiI<sub>2</sub> monolayer, hexagonal ''a'' = 3.97 Å with ≈8 Å of vacuum ({{FILE\|POSCAR}}):

Huebsch: Issue #16: embed spin-spiral energy figure in Example 2

2026-06-19T09:52:19Z

Issue #16: embed spin-spiral energy figure in Example 2

← Older revision		Revision as of 09:52, 19 June 2026
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	\| (0.133, 0.133, 0) \|\| Γ→K (minimum) \|\| −15.9		\| (0.133, 0.133, 0) \|\| Γ→K (minimum) \|\| −15.9
	\|}		\|}

			[[File:NiI2_spinspiral_energy.png\|thumb\|center\|500px\|Spin-spiral energy ''E''('''q''') − ''E''(Γ) of a monolayer NiI<sub>2</sub> along the Γ–M–K–Γ path (PBE). The minima at incommensurate '''q''' indicate a spin-spiral ground state; the Γ–M minimum near '''q''' ≈ (0.21, 0, 0) matches the experimental helimagnetic vector.]]

	The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the high-symmetry M and K points, reflecting the frustration of the triangular Ni sublattice. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈1 meV, and the spiral is stabilized by ≈16 meV per formula unit relative to the ferromagnet. The Γ–M minimum at '''q''' ≈ (0.21, 0, 0) is in good agreement with the helimagnetic propagation vector '''q''' = (0.220, 0, 0) measured for monolayer NiI<sub>2</sub> by spin-polarized scanning tunneling microscopy.{{cite\|miao:pnas:25}}		The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the high-symmetry M and K points, reflecting the frustration of the triangular Ni sublattice. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈1 meV, and the spiral is stabilized by ≈16 meV per formula unit relative to the ferromagnet. The Γ–M minimum at '''q''' ≈ (0.21, 0, 0) is in good agreement with the helimagnetic propagation vector '''q''' = (0.220, 0, 0) measured for monolayer NiI<sub>2</sub> by spin-polarized scanning tunneling microscopy.{{cite\|miao:pnas:25}}

Huebsch at 09:45, 19 June 2026

2026-06-19T09:45:00Z

Huebsch: Issue #16: Example 2 -> PBE results, experimental q comparison (Miao 2025), GPAW reference removed

2026-06-18T15:57:14Z

Issue #16: Example 2 -> PBE results, experimental q comparison (Miao 2025), GPAW reference removed

← Older revision		Revision as of 15:57, 18 June 2026
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	{{TAGBL\|MAGMOM}} = 2 0 0 0 0 0 0 0 0		{{TAGBL\|MAGMOM}} = 2 0 0 0 0 0 0 0 0

	A Γ-centered 12×12×1 k-mesh and Ni_pv and I PAW potentials were used. The total energy ''E''('''q''') is read from the {{FILE\|OUTCAR}}.		A Γ-centered 12×12×1 k-mesh and PBE Ni_pv and I PAW potentials were used. The total energy ''E''('''q''') is read from the {{FILE\|OUTCAR}}.

	'''Result''' — spin-spiral energy relative to the ferromagnetic state ('''q''' = Γ):		'''Result''' — spin-spiral energy relative to the ferromagnetic state ('''q''' = Γ):
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	\| (0, 0, 0) \|\| Γ (ferromagnetic) \|\| 0.0		\| (0, 0, 0) \|\| Γ (ferromagnetic) \|\| 0.0
	\|-		\|-
	\| (0.143, 0, 0) \|\| Γ→M \|\| ~~−22~~.7		\| (0.143, 0, 0) \|\| Γ→M \|\| −12.4
	\|-		\|-
	\| (0.214, 0, 0) \|\| Γ→M (minimum) \|\| ~~−29~~.7		\| (0.214, 0, 0) \|\| Γ→M (minimum) \|\| −14.5
	\|-		\|-
	\| (0.5, 0, 0) \|\| M \|\| +36.3		\| (0.5, 0, 0) \|\| M \|\| +40.2
	\|-		\|-
	\| (1/3, 1/3, 0) \|\| K \|\| ~~−12~~.5		\| (1/3, 1/3, 0) \|\| K \|\| +8.2
	\|-		\|-
	\| (0.133, 0.133, 0) \|\| Γ→K (minimum) \|\| ~~−32~~.9		\| (0.133, 0.133, 0) \|\| Γ→K (minimum) \|\| −15.9
	\|}		\|}

	The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the M~~-point antiferromagnet~~. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈3 meV, and the spiral is stabilized by ~~≈30~~ meV per formula unit relative to the ferromagnet. ~~This reproduces~~ the ~~qualitative result of the GPAW tutorial: a frustration-driven incommensurate ground state with two near~~-~~degenerate minima~~.		The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the high-symmetry M and K points, reflecting the frustration of the triangular Ni sublattice. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈1 meV, and the spiral is stabilized by ≈16 meV per formula unit relative to the ferromagnet. The Γ–M minimum at '''q''' ≈ (0.21, 0, 0) is in good agreement with the helimagnetic propagation vector '''q''' = (0.220, 0, 0) measured for monolayer NiI<sub>2</sub> by spin-polarized scanning tunneling microscopy.{{cite\|miao:pnas:25}}
	{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}		{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}
	== Magnon dispersion and exchange interactions ==		== Magnon dispersion and exchange interactions ==

Huebsch: /* Magnon dispersion and exchange interactions */

2026-06-18T13:39:00Z

Magnon dispersion and exchange interactions

← Older revision		Revision as of 13:39, 18 June 2026
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	* Restart each point from the same converged charge density ({{TAG\|ICHARG}} = 1) for consistency across the scan.		* Restart each point from the same converged charge density ({{TAG\|ICHARG}} = 1) for consistency across the scan.
	* The mapping assumes rigid local moments; verify that the local moment is roughly '''q'''-independent (in Example 2 it varies by only a few percent).		* The mapping assumes rigid local moments; verify that the local moment is roughly '''q'''-independent (in Example 2 it varies by only a few percent).
	{{NB\|mind\|The spin-spiral approach is incompatible with [[~~spin–orbit~~ coupling]] ({{TAG\|LSORBIT\|TRUE}}), because ~~spin–orbit~~ coupling breaks the spin-rotational symmetry that the generalized Bloch condition relies on.}}		{{NB\|mind\|The [[spin spirals\|spin-spiral approach]] is incompatible with [[spin-orbit coupling]] ({{TAG\|LSORBIT\|TRUE}}), because spin-orbit coupling breaks the spin-rotational symmetry that the generalized Bloch condition relies on.}}

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

Huebsch at 13:38, 18 June 2026

2026-06-18T13:38:00Z

← Older revision		Revision as of 13:38, 18 June 2026
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	The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the M-point antiferromagnet. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈3 meV, and the spiral is stabilized by ≈30 meV per formula unit relative to the ferromagnet. This reproduces the qualitative result of the GPAW tutorial: a frustration-driven incommensurate ground state with two near-degenerate minima.		The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the M-point antiferromagnet. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈3 meV, and the spiral is stabilized by ≈30 meV per formula unit relative to the ferromagnet. This reproduces the qualitative result of the GPAW tutorial: a frustration-driven incommensurate ground state with two near-degenerate minima.
			{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}
	{{NB\|tip\|The exact position of the incommensurate minimum depends on the functional, PAW potentials, k-mesh, and cutoff, so the numbers above reproduce the ''physics'' of the GPAW tutorial rather than identical values. Determining the orientation of the spiral plane additionally requires a non-self-consistent spin–orbit-coupling step, which is not covered here.}}

	== Magnon dispersion and exchange interactions ==		== Magnon dispersion and exchange interactions ==
	Scanning the spin-spiral energy ''E''('''q''') as in [[#Example 2: spin-spiral energy of a NiI2 monolayer\|Example 2]] is the basis of the ''frozen-magnon'' method for extracting magnetic interactions.{{cite\|marsman:prb:02}} Mapping the computed energies onto a classical Heisenberg model,		Scanning the spin-spiral energy ''E''('''q''') as in [[#Example 2: spin-spiral energy of a NiI2 monolayer\|Example 2]] is the basis of the ''frozen-magnon'' method for extracting magnetic interactions.{{cite\|marsman:prb:02}} Mapping the computed energies onto a classical Heisenberg model,

← Older revision		Revision as of 11:55, 19 June 2026
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	This example uses a spin-spiral calculation to obtain the total energy of a flat spin spiral in a NiI<sub>2</sub> monolayer. The spin spiral is scanned along the {{TAG\|QSPIRAL}} path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.		This example uses a spin-spiral calculation to obtain the total energy of a flat spin spiral in a NiI<sub>2</sub> monolayer. The spin spiral is scanned along the {{TAG\|QSPIRAL}} path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.

	[[File:NiI2_spinspiral_structure.png\|thumb\|center\|~~650px~~\|~~Left: the 1T NiI<sub>2</sub> monolayer unit cell. Right: the~~ flat in-plane spin spiral at the computed Γ–M minimum '''Q''' = (0.214, 0, 0); the Ni moments rotate in the plane with period ''λ'' = 1/''Q'' ≈ 4.7 ''a~~'' along '''Q'~~''.]]		[[File:NiI2_spinspiral_structure.png\|thumb\|center\|600px\|The flat in-plane spin spiral at the computed Γ–M minimum '''Q''' = (0.214, 0, 0): the Ni moments rotate in the plane along '''Q''' with period ''λ'' = 1/''Q'' ≈ 4.7 ''a''.]]

	'''Structure''': A 1T (CdI<sub>2</sub>-type) NiI<sub>2</sub> monolayer, hexagonal ''a'' = 3.97 Å with ≈8 Å of vacuum ({{FILE\|POSCAR}}):		'''Structure''': A 1T (CdI<sub>2</sub>-type) NiI<sub>2</sub> monolayer, hexagonal ''a'' = 3.97 Å with ≈8 Å of vacuum ({{FILE\|POSCAR}}):

← Older revision		Revision as of 08:13, 22 June 2026
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	{{NB\|mind\| Symmetry:		{{NB\|mind\| Symmetry:

	The introduction of a spin spiral will lower the symmetry of the system. At present, VASP cannot correctly account for the presence of a spin spiral in its symmetry analysis. Therefore, the use of symmetry must be switched off in the subsequent steps by setting {{TAG\|ISYM\|-1}}. Generally, the number of irreducible '''k''' points changes for different symmetry settings ({{TAG\|ISYM}} and thus restarting from {{FILE\|CHGCAR}} should be preferred over restarting from {{FILE\|WAVECAR}}. You may set {{TAG\|LWAVE\|False}} to avoid writing the {{FILE\|WAVECAR}}. It is not advantageous to switch off symmetry from the get-go, as using symmetry reduces the computational effort and hence saves substantial computational cost during the course of convergence studies.}}		The introduction of a spin spiral will lower the symmetry of the system. At present, VASP cannot correctly account for the presence of a spin spiral in its symmetry analysis. Therefore, the use of symmetry must be switched off in the subsequent steps by setting {{TAG\|ISYM\|-1}}. Generally, the number of irreducible '''k''' points changes for different symmetry settings ({{TAG\|ISYM}}), and thus restarting from {{FILE\|CHGCAR}} should be preferred over restarting from {{FILE\|WAVECAR}}. You may set {{TAG\|LWAVE\|False}} to avoid writing the {{FILE\|WAVECAR}}. It is not advantageous to switch off symmetry from the get-go, as using symmetry reduces the computational effort and hence saves substantial computational cost during the course of convergence studies.}}
	{{NB\|tip\|Magnetism usually arises in d-electron and f-electron bands. To write the augmentation charges of those bands, set {{TAG\|LMAXMIX\|4}} (d electrons) or <code>6</code>.}}		{{NB\|tip\|Magnetism usually arises in d-electron and f-electron bands. To write the augmentation charges of those bands, set {{TAG\|LMAXMIX\|4}} (d electrons) or <code>6</code>.}}
	Choose the remaining electronic-minimization tags ({{TAG\|ALGO}}, {{TAG\|EDIFF}}, {{TAG\|NELM}}, {{TAG\|ISMEAR}}) as described in [[Setting up an electronic minimization]]; frustrated or incommensurate magnets often need a larger {{TAG\|NELM}} and {{TAG\|ALGO\|Conjugate}} is often most reliable.		Choose the remaining electronic-minimization tags ({{TAG\|ALGO}}, {{TAG\|EDIFF}}, {{TAG\|NELM}}, {{TAG\|ISMEAR}}) as described in [[Setting up an electronic minimization]]; frustrated or incommensurate magnets often need a larger {{TAG\|NELM}} and {{TAG\|ALGO\|Conjugate}} is often most reliable.
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	{{TAGBL\|ENCUT}} = 400		{{TAGBL\|ENCUT}} = 400

	Here, <tt>q1 q2 q3</tt> are the components of the spin-spiral propagation vector in direct (fractional) coordinates of the reciprocal lattice. In a spin-spiral calculation, the magnetic configuration is set both by the initial moments ''within'' the cell using the {{TAG\|MAGMOM}} tag, in the noncollinear (three-component-per-atom) format, and by how the magnetization rotates ''between'' cells (the {{TAG\|QSPIRAL}} vector). Worked examples are given in the [[#Examples\|Examples]] section below. Choose the remaining electronic-minimization tags as in step 1.		Here, <code>q1 q2 q3</code> are the components of the spin-spiral propagation vector in direct (fractional) coordinates of the reciprocal lattice. In a spin-spiral calculation, the magnetic configuration is set both by the initial moments ''within'' the cell using the {{TAG\|MAGMOM}} tag, in the noncollinear (three-component-per-atom) format, and by how the magnetization rotates ''between'' cells (the {{TAG\|QSPIRAL}} vector). Worked examples are given in the [[#Examples\|Examples]] section below. Choose the remaining electronic-minimization tags as in step 1.
	{{NB\|mind\|Symmetry must be switched off completely ({{TAG\|ISYM\|-1}}). VASP cannot account for the symmetry reduction introduced by a spin spiral, so leaving symmetry on produces incorrect results.}}		{{NB\|mind\|Symmetry must be switched off completely ({{TAG\|ISYM\|-1}}). VASP cannot account for the symmetry reduction introduced by a spin spiral, so leaving symmetry on produces incorrect results.}}
	{{NB\|tip\|Set {{TAG\|ENCUT}} (or equivalently {{TAG\|ENMAX}}) at least 100 eV above {{TAG\|ENINI}}. VASP prints a runtime warning if the value is too small for the chosen '''q''' vector, ''e.g.'':}}		{{NB\|tip\|Set {{TAG\|ENCUT}} (or equivalently {{TAG\|ENMAX}}) at least 100 eV above {{TAG\|ENINI}}. VASP prints a runtime warning if the value is too small for the chosen '''q''' vector, ''e.g.'':}}
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	{{TAGBL\|RWIGS}} = <one radius per species>		{{TAGBL\|RWIGS}} = <one radius per species>

	This switches on the [[I_CONSTRAINED_M\|constrained-magnetic-moment approach]] but sets the penalty potential to zero ({{TAG\|LAMBDA}} = 0.0). The magnetization density is then integrated inside site-centered spheres of radius {{TAG\|RWIGS}}, and the resulting local moments are written under <tt>M_int</tt> in the {{FILE\|OSZICAR}} file, ''e.g.'':		This switches on the [[I_CONSTRAINED_M\|constrained-magnetic-moment approach]] but sets the penalty potential to zero ({{TAG\|LAMBDA}} = 0.0). The magnetization density is then integrated inside site-centered spheres of radius {{TAG\|RWIGS}}, and the resulting local moments are written under <code>M_int</code> in the {{FILE\|OSZICAR}} file, ''e.g.'':

	E_p = 0.00000E+00 lambda = 0.000E+00		E_p = 0.00000E+00 lambda = 0.000E+00
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	{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[Choosing pseudopotentials\|PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}		{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[Choosing pseudopotentials\|PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}
	== Magnon dispersion and exchange interactions ==		== Magnon dispersion and exchange interactions ==
	Scanning the spin-spiral energy ''E''('''q''') as in [[#Example 2: ~~spin~~-spiral energy of a NiI2 monolayer\|Example 2]] is the basis of the ''frozen-magnon'' method for extracting magnetic interactions.{{cite\|marsman:prb:02}} Mapping the computed energies onto a classical Heisenberg model,		Scanning the spin-spiral energy ''E''('''q''') as in [[#Example 2: Spin-spiral energy of a NiI2 monolayer\|Example 2]] is the basis of the ''frozen-magnon'' method for extracting magnetic interactions.{{cite\|marsman:prb:02}} Mapping the computed energies onto a classical Heisenberg model,

	:<math> E({\bf q}) = E_0 - \sum_{\bf R} J({\bf R})\, \cos({\bf q}\cdot{\bf R}), </math>		:<math> E({\bf q}) = E_0 - \sum_{\bf R} J({\bf R})\, \cos({\bf q}\cdot{\bf R}), </math>
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	{{TAG\|LNONCOLLINEAR}}, {{TAG\|MAGMOM}}, {{TAG\|ISYM}}, {{TAG\|I_CONSTRAINED_M}}, {{TAG\|LAMBDA}}, {{TAG\|RWIGS}}, {{TAG\|LORBIT}}		{{TAG\|LNONCOLLINEAR}}, {{TAG\|MAGMOM}}, {{TAG\|ISYM}}, {{TAG\|I_CONSTRAINED_M}}, {{TAG\|LAMBDA}}, {{TAG\|RWIGS}}, {{TAG\|LORBIT}}

	{{TAG\|LSPIRAL}}, {{TAG\|QSPIRAL}}, {{TAG\|LZEROZ}}, , {{TAG\|ENINI}}		{{TAG\|LSPIRAL}}, {{TAG\|QSPIRAL}}, {{TAG\|LZEROZ}}, {{TAG\|ENINI}}

	== References ==		== References ==

← Older revision		Revision as of 09:45, 19 June 2026
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	=== Step 1: Start from a converged magnetic state ===		=== Step 1: Start from a converged magnetic state ===
	Begin with a converged collinear or noncollinear ground-state calculation of the primitive cell, following [[Setting up an electronic minimization]], and keep the resulting {{FILE\|CHGCAR}} as a starting point for the spin-spiral run. The total energy and on-site magnetic moments ({{TAG\|LORBIT}}) should be converged with respect to '''k'''-mesh density and energy cutoff ({{TAG\|ENCUT}}).		Begin with a converged collinear or noncollinear ground-state calculation of the primitive cell, following [[Setting up an electronic minimization]], and keep the resulting {{FILE\|CHGCAR}} as a starting point for the spin-spiral run. The total energy and on-site magnetic moments ({{TAG\|LORBIT}}) should be converged with respect to '''k'''-mesh density and energy cutoff ({{TAG\|ENCUT}}).
			{{NB\|mind\| Symmetry:

	The introduction of a spin spiral will lower the symmetry of the system. At present, VASP cannot correctly account for the presence of a spin spiral in its symmetry analysis. Therefore, the use of symmetry must be switched off in the subsequent steps by setting {{TAG\|ISYM\|-1}}. Generally, the number of irreducible '''k''' points changes for different symmetry settings ({{TAG\|ISYM}} and thus restarting from {{FILE\|CHGCAR}} should be preferred over restarting from {{FILE\|WAVECAR}}. You may set {{TAG\|LWAVE\|False}} to avoid writing the {{FILE\|WAVECAR}}. It is not advantageous to switch off symmetry from the get-go, as using symmetry reduces the computational effort and hence saves ~~substential~~ computational cost during the course of convergence studies.		The introduction of a spin spiral will lower the symmetry of the system. At present, VASP cannot correctly account for the presence of a spin spiral in its symmetry analysis. Therefore, the use of symmetry must be switched off in the subsequent steps by setting {{TAG\|ISYM\|-1}}. Generally, the number of irreducible '''k''' points changes for different symmetry settings ({{TAG\|ISYM}} and thus restarting from {{FILE\|CHGCAR}} should be preferred over restarting from {{FILE\|WAVECAR}}. You may set {{TAG\|LWAVE\|False}} to avoid writing the {{FILE\|WAVECAR}}. It is not advantageous to switch off symmetry from the get-go, as using symmetry reduces the computational effort and hence saves substantial computational cost during the course of convergence studies.}}
			{{NB\|tip\|Magnetism usually arises in d-electron and f-electron bands. To write the augmentation charges of those bands, set {{TAG\|LMAXMIX\|4}} (d electrons) or <code>6</code>.}}
	Magnetism usually arises in d-electron and f-electron bands. To write the augmentation charges of those bands, set {{TAG\|LMAXMIX\|4}} (d electrons) or <code>6</code>.

	Choose the remaining electronic-minimization tags ({{TAG\|ALGO}}, {{TAG\|EDIFF}}, {{TAG\|NELM}}, {{TAG\|ISMEAR}}) as described in [[Setting up an electronic minimization]]; frustrated or incommensurate magnets often need a larger {{TAG\|NELM}} and {{TAG\|ALGO\|Conjugate}} is often most reliable.		Choose the remaining electronic-minimization tags ({{TAG\|ALGO}}, {{TAG\|EDIFF}}, {{TAG\|NELM}}, {{TAG\|ISMEAR}}) as described in [[Setting up an electronic minimization]]; frustrated or incommensurate magnets often need a larger {{TAG\|NELM}} and {{TAG\|ALGO\|Conjugate}} is often most reliable.

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	The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the high-symmetry M and K points, reflecting the frustration of the triangular Ni sublattice. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈1 meV, and the spiral is stabilized by ≈16 meV per formula unit relative to the ferromagnet. The Γ–M minimum at '''q''' ≈ (0.21, 0, 0) is in good agreement with the helimagnetic propagation vector '''q''' = (0.220, 0, 0) measured for monolayer NiI<sub>2</sub> by spin-polarized scanning tunneling microscopy.{{cite\|miao:pnas:25}}		The energy is lowest for an incommensurate spin spiral, not for the ferromagnet (Γ) or the high-symmetry M and K points, reflecting the frustration of the triangular Ni sublattice. Two shallow minima appear along inequivalent in-plane directions — near '''q''' ≈ (0.21, 0, 0) along Γ–M and '''q''' ≈ (0.13, 0.13, 0) along Γ–K — separated by a barrier of only ≈1 meV, and the spiral is stabilized by ≈16 meV per formula unit relative to the ferromagnet. The Γ–M minimum at '''q''' ≈ (0.21, 0, 0) is in good agreement with the helimagnetic propagation vector '''q''' = (0.220, 0, 0) measured for monolayer NiI<sub>2</sub> by spin-polarized scanning tunneling microscopy.{{cite\|miao:pnas:25}}
	{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}		{{NB\|tip\|The exact position of the incommensurate minimum depends on the [[XC functional]], [[Choosing pseudopotentials\|PAW potentials]], and proper convergence of k-mesh density, and cutoff energy.}}
	== Magnon dispersion and exchange interactions ==		== Magnon dispersion and exchange interactions ==
	Scanning the spin-spiral energy ''E''('''q''') as in [[#Example 2: spin-spiral energy of a NiI2 monolayer\|Example 2]] is the basis of the ''frozen-magnon'' method for extracting magnetic interactions.{{cite\|marsman:prb:02}} Mapping the computed energies onto a classical Heisenberg model,		Scanning the spin-spiral energy ''E''('''q''') as in [[#Example 2: spin-spiral energy of a NiI2 monolayer\|Example 2]] is the basis of the ''frozen-magnon'' method for extracting magnetic interactions.{{cite\|marsman:prb:02}} Mapping the computed energies onto a classical Heisenberg model,
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	== Related tags and articles ==		== Related tags and articles ==
	[[Spin spirals]], [[Setting up an electronic minimization]]		[[Spin spirals]] (Theory), [[Setting up an electronic minimization]]

	{{TAG\|LNONCOLLINEAR}}, {{TAG\|MAGMOM}}, {{TAG\|ISYM}}, {{TAG\|I_CONSTRAINED_M}}, {{TAG\|LAMBDA}}, {{TAG\|RWIGS}}, {{TAG\|LORBIT}}		{{TAG\|LNONCOLLINEAR}}, {{TAG\|MAGMOM}}, {{TAG\|ISYM}}, {{TAG\|I_CONSTRAINED_M}}, {{TAG\|LAMBDA}}, {{TAG\|RWIGS}}, {{TAG\|LORBIT}}