4.4 Test collinear magnetic states
These educational templates have not been executed and contain no fabricated numerical results. Inputs and filenames follow ABACUS 3.9.0 documentation; recheck every interface when changing version.
4.4.1 Question and declared model
Does a chosen periodic iron model converge to different self-consistent magnetic states when initialized differently? Build a two-atom conventional bcc Fe cell, compare nonmagnetic and several collinear seeds, and separate initial guesses from physical constraints. The goal is a reproducible magnetic-state search for one specified Hamiltonian, not an assumed experimental ground state.
4.4.2 Physical interpretation
In collinear spin DFT the up and down densities share a global quantization axis. The total electron density is their sum, while their difference determines spin magnetization. A seed encourages a basin; it does not constrain the converged moment. Competing states must use the same geometry, PP, basis and occupation treatment before their energy difference is interpreted.
Two Fe sites allow same-sign and opposite-sign starting moments. The latter is a pedagogical commensurate seed in this particular cell, not a declaration of the true antiferromagnetic ordering vector. A zero total moment may conceal opposite local moments, so examine both integrated spin channels and spatial or orbital-resolved information. Larger cells may be necessary to represent another ordering pattern.
Original course illustration; conceptual geometry and curves, not calculated results.
4.4.3 Worked input and file changes
INPUT
INPUT_PARAMETERS
suffix iron_seed
calculation scf
basis_type pw
ks_solver cg
ntype 1
nspin 2
dft_functional PBE
pseudo_dir ./data/
ecutwfc 100
nbands 24
scf_thr 1e-9
scf_nmax 200
mixing_beta 0.2
symmetry 0
smearing_method gaussian
smearing_sigma 0.01
out_chg 1 10
STRU
ATOMIC_SPECIES
Fe 55.845 Fe_PBE_VERIFIED.upf
LATTICE_CONSTANT
1.889726125457828
LATTICE_VECTORS
2.86 0 0
0 2.86 0
0 0 2.86
ATOMIC_POSITIONS
Direct
Fe
0.0
2
0.0 0.0 0.0 m 0 0 0 mag 2.0
0.5 0.5 0.5 m 0 0 0 mag 2.0
KPT
Save INPUT, STRU and KPT separately. Fe_PBE_VERIFIED.upf is a required local verified norm-conserving PBE file, not a downloadable promise. Inspect its valence count, semicore treatment and relativistic metadata; twenty-four bands may need expansion for your PP. This PW model has no NUMERICAL_ORBITAL block. The lattice constant converts the displayed 2.86 vectors into Angstrom; 2.86 Angstrom is a model starting value, not a computed optimum. Per-atom mag 2.0 seeds 2 Bohr magnetons. Make additional separate seeds +1/+1, +3/+3 and +2/-2. For a non-spin-polarized reference set nspin 1 and remove magnetic interpretation of those seeds. Do not add nupdown unless you intentionally want a fixed spin-population constraint.
4.4.4 Run and inspect the evidence
Run each seed from atomic density rather than silently reusing a common converged magnetic density. Inspect OUT.iron_seed/running_scf.log and screen output for energy, SCF residual and reported magnetic indicators. The stable spin guide names TMAG and AMAG; retain their labels and documented definitions, and independently integrate the spin-density difference if a specific total moment is required. Export SPIN1_CHG.cube and SPIN2_CHG.cube with matched grids. Use different suffixes so no seed overwrites another. Once candidate states are identified, restart each from its own density with identical stricter numerical settings and check that it remains in the same basin. If using LCAO in a later extension, out_mul provides mulliken.txt, whose local moments depend on the chosen basis; it is not requested in this PW template.
4.4.5 Observable-specific convergence
Converge the energy difference between candidate states, not just each absolute energy. Cross meshes 8, 10 and 12 with smaller occupation widths, retaining enough empty bands. smearing_sigma is in Ry; 0.01 Ry is about 0.136 eV and is not a temperature declared in Kelvin. A proposed teaching target is state-energy ordering stable within 1 meV per atom and moment changes below 0.02 Bohr magnetons per cell under tighter controls. Establish that both spin channels are converged and electron totals agree with the PP count. Different initial seeds reaching the same state support basin robustness, but do not prove a global minimum over all magnetic patterns or structural phases.
4.4.6 Acceptance worksheet and provenance
The magnetic worksheet records per-atom initial moments, final total spin moment, spatial compensation pattern, energy per atom, SCF status and occupation width. Separate the initialization columns from the final-state columns. Two different seeds that reach the same final density are repeats of one basin, not two distinct physical states. Conversely, a compensated state needs local evidence even when its total moment is zero.
For a density integration use the same cube grid for up and down spin, sum their difference times the Bohr-cubed voxel volume, and multiply the electron-number imbalance by the Bohr magneton. Compare this with the code's total-magnetization report after verifying labels and units. The sum of spin channels must reproduce the PP electron total. When comparing energies, divide by the same atom count and retain the same finite-smearing convention. If the energy ordering is smaller than the observed mesh/width sensitivity, mark it unresolved rather than rounding one state into a preferred result.
| Initial site moments (Bohr magnetons) | Final total / local pattern | Energy difference (meV/atom) | Numerical ordering resolved? |
|---|---|---|---|
| +1 / +1, +2 / +2, +3 / +3 | — | — | — |
| +2 / -2 | — | — | — |
| nspin 1 reference | — | — | — |
Store separate density identities for every converged basin. A later restart must use its own state's density, otherwise the nominal seed comparison becomes a test of one common restart.
4.4.7 Pitfalls and limits
Zero seed and nspin 1 are not identical to a deliberately searched spin-polarized state. A zero total moment does not exclude local magnetism. Comparing relaxed ferromagnetic and fixed-geometry antiferromagnetic energies mixes structural and magnetic effects. A scalar-relativistic PP is adequate only for this declared no-SOC collinear model; adding SOC later needs separate version and PP checks. Do not copy MAGMOM into INPUT. A larger mixing_beta is not a guaranteed cure for coupled charge-spin oscillations; inspect the residual history first.
4.4.8 Exercises with answer guidance
- Two opposite local moments give a total close to zero. May the result be called nonmagnetic? Guidance: no; inspect local/spatial spin density and distinguish compensation from absence of polarization.
- Two seeds differ by 0.5 meV per atom, but changing the mesh shifts their difference by 3 meV. Which is lower? Guidance: ordering is unresolved within numerical error. Improve convergence before reporting a preferred state.
4.4.9 Versioned references
The university-authored guide provides teaching context; older pages can predate 3.9. Use the linked official version for exact syntax. This is original instructional synthesis, and reference outputs are not presented as results of this course.