Spin-spiral calculations

Spin-spiral calculations model continuously rotating magnetic structures without the need for large supercells. This page provides step-by-step instructions for setting up, running, and analyzing spin-spiral calculations in VASP. For the underlying formalism — the generalized Bloch condition, the modified Hamiltonian, and the basis-set requirements — see Spin spirals.

Prerequisites

Spin spirals are a noncollinear-magnetism feature. You need a VASP build that supports noncollinear magnetism (enabled with LNONCOLLINEAR), and it is helpful to be familiar with collinear magnetic calculations, the MAGMOM tag, and Setting up an electronic minimization before starting.

Step-by-step instructions

Step 1: Start from a converged ground 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 WAVECAR and CHGCAR as a starting point for the spin-spiral run.

Step 2: Set up the spin-spiral INCAR

Add the following tags to the INCAR:

LNONCOLLINEAR = .TRUE.
LSPIRAL       = .TRUE.
QSPIRAL       = q1 q2 q3
ISYM          = -1
ENINI         = 300
ENMAX         = 400

Here, q1 q2 q3 are the components of the spin-spiral propagation vector in direct (fractional) coordinates of the reciprocal lattice. Choose the remaining electronic-minimization tags (ALGO, EDIFF, NELM, ISMEAR) as described in Setting up an electronic minimization; frustrated or incommensurate magnets often need a larger NELM.

Mind: {{{2}}}

Tip: Set ENMAX at least 100 eV above ENINI. VASP prints a runtime warning if the value is too small for the chosen q vector, e.g.:

 -----------------------------------------------------------------------------
|      To represent the spin spiral you requested, with a kinetic              |
|      energy cutoff of ENINI=  300.00 eV, choose ENMAX >  331.21 eV           |
|      Currently ENMAX=  400.00 eV                                            |
 -----------------------------------------------------------------------------

Step 3: Initialize the magnetic subsystem

As for all magnetic calculations, initialize the magnetic subsystem with the MAGMOM tag, in the noncollinear (three-component-per-atom) format. If no initial moments are given, the initial order is ferromagnetic, which may trap the system in a local minimum even when the ground state is not ferromagnetic.

In a spin-spiral calculation the magnetic configuration is set both by the initial moments within the cell and by how the magnetization rotates between cells (the QSPIRAL vector). Worked examples are given in the Examples section below.

Step 4: Constrain to a planar spiral (optional)

To prevent the magnetization density from developing a z-component, set:

LZEROZ = .TRUE.

This forces [math]\displaystyle{ m_z({\bf r})=0 }[/math] at each step of the electronic minimization.

Step 5: Run the calculation

Run VASP as usual and monitor convergence in the OSZICAR file. A spin-spiral calculation has approximately the same cost as a standard noncollinear calculation of the primitive cell.

Step 6: Extract local magnetic moments

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:

The standard analysis via LORBIT (output in the PROCAR file and at the end of the OUTCAR file) does not account for this. As a workaround, use the constrained-moment infrastructure with a zero penalty potential:

I_CONSTRAINED_M = 1
LAMBDA          = 0.0
RWIGS           = <one radius per species>

This switches on the constrained-magnetic-moment approach but sets the penalty potential to zero (LAMBDA = 0.0). The magnetization density is then integrated inside site-centered spheres of radius RWIGS, and the resulting local moments are written under M_int in the OSZICAR file, e.g.:

 E_p =  0.00000E+00  lambda =  0.000E+00
<lVp>=  0.00000E+00
 DBL =  0.00000E+00
 ion        MW_int                 M_int
  1  1.178  0.000  0.000    1.573  0.000  0.000
RMM:   8    -0.819213822792E+01    0.53417E-07   -0.43965E-08  2542   0.310E-03

Here the local moment on ion 1 (after iteration 8) is [math]\displaystyle{ M=1.573\,\hat{x}\;\mu_{\rm B} }[/math].

Mind: Do not forget to set RWIGS for every species; without it the integration spheres are undefined.

Examples

Example 1: initializing the magnetic configuration

The initial moments within the cell, together with the QSPIRAL vector, determine which magnetic configuration the calculation starts from.

Double-layer antiferromagnet. Two magnetic atoms with initial moments M along y, and [math]\displaystyle{ {\bf q}=(0,0,\tfrac{1}{2}) }[/math]:

MAGMOM  = 0 M 0  0 M 0
QSPIRAL = 0.0 0.0 0.5

Flat spin spiral. Two magnetic atoms with initial moments M along y and x, respectively, and [math]\displaystyle{ {\bf q}=(0,0,\tfrac{1}{2}) }[/math]:

MAGMOM  = 0 M 0  M 0 0
QSPIRAL = 0.0 0.0 0.5

Tip: Both configurations obey the same generalized Bloch condition, [math]\displaystyle{ {\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 NiI₂ monolayer

This example reproduces the spin-spiral calculation from the GPAW spin-spiral tutorial with VASP: the total energy of a flat spin spiral in a NiI₂ monolayer is scanned along the QSPIRAL path Γ–M–K–Γ to find the magnetic ground state. The triangular Ni sublattice is magnetically frustrated, which stabilizes an incommensurate spiral.

Structure — a 1T (CdI₂-type) NiI₂ monolayer, hexagonal a = 3.97 Å with ≈8 Å of vacuum (POSCAR):

NiI2 1T monolayer
1.0
   3.9697   0.0000    0.0000
  -1.9849   3.4379    0.0000
   0.0000   0.0000   11.0271
Ni I
1 2
Direct
  0.0000 0.0000 0.5000
  0.3333 0.6667 0.6373
  0.6667 0.3333 0.3627

INCAR — one self-consistent calculation per q, changing only QSPIRAL. The Ni moment is initialized in the xy-plane and iodine is nonmagnetic; LDA is used to match the tutorial:

LNONCOLLINEAR = .TRUE.
LSPIRAL       = .TRUE.
QSPIRAL       = q1 q2 0.0
ISYM          = -1
ENINI         = 600
ENCUT         = 700
ISMEAR        = 0
SIGMA         = 0.05
MAGMOM        = 2 0 0  0 0 0  0 0 0

A Γ-centered 12×12×1 k-mesh and LDA Ni_pv and I PAW potentials were used. The total energy E(q) is read from the OUTCAR.

Result — spin-spiral energy relative to the ferromagnetic state (q = Γ):

q (fractional)	point / direction	E(q) − E(Γ) (meV)
(0, 0, 0)	Γ (ferromagnetic)	0.0
(0.143, 0, 0)	Γ→M	−22.7
(0.214, 0, 0)	Γ→M (minimum)	−29.7
(0.5, 0, 0)	M	+36.3
(1/3, 1/3, 0)	K	−12.5
(0.133, 0.133, 0)	Γ→K (minimum)	−32.9

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.

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

Scanning the spin-spiral energy E(q) as in Example 2 is the basis of the frozen-magnon method for extracting magnetic interactions.^[1] Mapping the computed energies onto a classical Heisenberg model,

[math]\displaystyle{ E({\bf q}) = E_0 - \sum_{\bf R} J({\bf R})\, \cos({\bf q}\cdot{\bf R}), }[/math]

gives the interatomic exchange constants [math]\displaystyle{ J({\bf R}) }[/math] as a Fourier transform of E(q). If the ferromagnetic state is the ground state, the adiabatic magnon dispersion follows from the same energies, [math]\displaystyle{ \hbar\omega({\bf q}) \propto [E({\bf q}) - E(0)]/M }[/math], with M the local moment. If instead the minimum of E(q) lies at a finite q — as for NiI₂ — the system is predicted to order as an incommensurate spin spiral with that propagation vector.

Practical notes:

Use a fixed k-mesh and the same ENINI/ENMAX for every q, since the relevant energy differences are only a few meV.
Restart each point from the same converged charge density (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).