7.3 Spin–orbit coupling and noncollinear states
7.3.1 Distinguish spin representation from relativity
Spin–orbit coupling (SOC) connects electronic spin with orbital motion in the ionic potential. Noncollinearity describes a magnetization direction that cannot be represented by one common spin-up/down axis. Either concept can appear without the other: a nonmagnetic crystal can have SOC, while a magnetic texture can be studied without SOC. This distinction prevents the common mistake of interpreting every four-component spin calculation as evidence of a magnetic ground state.
This unexecuted, fixed-geometry case is pinned to ABACUS 3.9.0. Complete collinear magnetism and bands from fixed density. Start with a verified scalar-relativistic silicon benchmark, then prepare compatible fully relativistic pseudopotentials. Silicon is a modest educational SOC example; a resolved splitting may demand substantially tighter numerical precision than a coarse band plot suggests. No splitting value is promised here.
There is a documentation boundary to notice: the 3.9.0 spin page contains an older statement that SOC forces/stress are unavailable, while the current FAQ describes support since 3.9. This lesson therefore restricts itself to SCF/NSCF at fixed geometry. Before SOC relaxation or cell optimization, check the exact installed release, supported basis/solver path and a finite-difference force/stress benchmark. Do not resolve conflicting documentation by silently assuming the more convenient statement applies to every build.
7.3.2 The spinor and a trustworthy comparison
For a spinor state,
The local spin-density matrix contains information beyond two diagonal populations. An SOC comparison should retain the same physical geometry, functional, valence treatment and numerical resolution. Simply replacing a scalar pseudopotential with an unrelated fully relativistic file changes more than SOC. Different semicore choices or cutoff requirements can dominate the apparent difference.
Use the same verified fully relativistic potential for the SOC-on and SOC-off comparison when the documented conversion path supports that choice. ABACUS can reduce such a potential for a non-SOC calculation. Matching numerical orbitals remain essential for LCAO; their functions are spin-independent, but that does not authorize pairing them with an unrelated potential.
The figure explains representations. The drawn splitting is schematic, not a silicon prediction or an experimental fit.
7.3.3 Conditional INPUT and STRU changes
Copy the converged parent into separate directories and substitute the fully relativistic species assets as one documented step. Inspect the UPF header for full-relativistic/SOC information, commonly relativistic="full" and has_so; inspect the accepted channels in the startup log as well. Filename suffixes alone are insufficient.
# ABACUS 3.9.0; fixed-geometry SOC SCF delta
suffix Si_SOC_fixed
nspin 4
lspinorb 1
noncolin 0
out_chg 1
Retain the parent's basis, solver, cutoff, occupations, STRU and KPT after the compatible potential substitution. nspin 4 selects the spinor representation, not four independent scalar spin populations. lspinorb enables SOC; do not expect a scalar-relativistic UPF to acquire missing spin–orbit channels because this flag is present.
For a separate noncollinear magnetic study, change noncolin according to the release guide and provide documented STRU moment directions. The 3.9.0 STRU manual describes per-atom magnetic information and angular conventions. This lesson deliberately does not invent a generic magnetic vector line that might be parsed differently by another version. Start from the official noncollinear example, map its atom ordering to your cell, and vary one initial direction at a time. A magnetically noncollinear initialization is not needed merely to demonstrate nonmagnetic silicon SOC.
7.3.4 Workflow and outputs
First reproduce the no-SOC result with the chosen fully relativistic assets in the supported reduced mode. Then enable SOC and converge the electronic state. Check electron count, accepted spin mode, SCF residuals and symmetry treatment. A changed symmetry reduction changes the list of irreducible k points; compare the physical mesh rather than demanding the same printed k-point count.
Read OUT.<suffix>/running_scf.log for the calculation state and preserve all emitted charge components. A scalar SPIN1_CHG.cube alone is not a complete reusable spinor density. For band comparison, use an independently converged density for each Hamiltonian, the same physical k path and the documented SOC NSCF workflow. Do not initialize a spinor NSCF job from an arbitrary collinear two-channel output directory and assume the conversion is harmless.
To study magnetic anisotropy later, compare self-consistent states with carefully controlled directions and verify the exact constraints supported by your binary. Merely changing the starting direction does not hold a moment fixed during SCF. If the states relax to one orientation, their energy difference is not an anisotropy measurement between constrained orientations.
7.3.5 Convergence and interpretation
| Potential / orbital hashes | SOC setting | Physical k mesh | Basis / grid | SCF accepted? | Selected splitting (eV) | Moment direction / magnitude | Symmetry treatment |
|---|---|---|---|---|---|---|---|
| same FR assets | off | ||||||
| same FR assets | on | ||||||
| same FR assets | on, tighter |
Specify where and between which states a splitting is measured. Resolve it against the numerical error of the eigenvalues, not only the total-energy convergence. Degeneracy can depend on time-reversal and crystal symmetries: SOC does not universally split every pair of bands. Track the band character through crossings instead of subtracting fixed column numbers without checking their meaning. For magnetic energy differences, independently test basis, k mesh, occupations and electronic tolerances until the uncertainty is smaller than the requested difference.
7.3.6 Pitfalls, exercises and answers
Pitfalls. A fully relativistic potential with the wrong exchange-correlation construction changes the comparison. Setting nspin 4 while retaining only a two-channel restart discards representation information. Guessing degree-versus-radian conventions for moment angles produces a different spin texture. Combining U, HSE and SOC without checking their supported joint path is outside the validated recipe. Plotting a smooth band spline does not establish a resolved SOC splitting.
Exercise 1. Nonmagnetic SOC silicon has zero net moment. Did the calculation fail? Answer: not necessarily. SOC can change the spectrum without generating magnetization; validate accepted spinor mode, relativistic assets and symmetry before deciding.
Exercise 2. Two initial magnetic directions converge to the same final direction. Can their final energy difference be called anisotropy? Answer: no. The intended distinct orientation states were not maintained. Establish a supported constraint strategy and its physical meaning before constructing that comparison.
7.3.7 Sources
- ABACUS 3.9.0 spin and SOC guide.
- ABACUS 3.9.0 STRU specification.
- Current official FAQ: check the force/stress version qualification against your build.