CHAPTER 12 · ADVANCED · MAGNETISM

Spin polarization and magnetism

nspin and starting_magnetization, setting up AFM order with atom labels, and measured runs on bcc Fe and FeO.

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This is the gateway to transition-metal oxides. Collinear spin polarization is switched on by nspin = 2; the real problem is which magnetic solution the SCF converges to.

Basic setup

&SYSTEM
  nspin = 2
  starting_magnetization(1) =  0.6   ! Fe1 (up)
  starting_magnetization(2) = -0.6   ! Fe2 (down), AFM
  starting_magnetization(3) =  0.0   ! O
  occupations = 'smearing'
  smearing    = 'mv'
  degauss     = 0.01
/
&ELECTRONS
  mixing_beta = 0.2                  ! keep it low for magnets
  mixing_mode = 'local-TF'
/

ATOMIC_SPECIES
  Fe1  55.845  Fe.pbe-spn-kjpaw_psl.1.0.0.UPF
  Fe2  55.845  Fe.pbe-spn-kjpaw_psl.1.0.0.UPF   ! same file, different label
  O    15.999  O.pbe-n-kjpaw_psl.1.0.0.UPF
  • starting_magnetization is a dimensionless ratio between −1 and 1 (not μB), and it is only an initial guess. The SCF is free to change it.
  • To constrain the total magnetization, use tot_magnetization (separate Fermi levels for up and down). The O₂ triplet in Example E4 does exactly this.

AFM order is built with labels

The key trick for antiferromagnetic order: register the same pseudopotential under two labels (Fe1, Fe2) and give them opposite initial magnetizations. Without the label split, QE treats the two Fe atoms as symmetry-equivalent and cannot form an AFM state at all. The same label split is needed later by DFT+U and hp.x.

Classify the converged state from two output lines:

Order total magnetization absolute magnetization
FM Large About equal to total
AFM ≈ 0 Large
Collapsed (nonmagnetic) ≈ 0 ≈ 0

Measured: bcc Fe and FeO

Example E9 (ferromagnetic metal) and Example E10 (antiferromagnetic oxide) are this chapter in practice.

bcc Fe spin-resolved DOS
Measured spin-resolved DOS of bcc Fe (QE 7.5, PBE). Exchange splits the up and down d bands; the occupation difference is the ferromagnetic moment (measured 2.19 μB per atom, experiment 2.22).

When a magnet will not converge

It is common for the magnetization to collapse to zero during the SCF. In order:

  1. mixing_beta 0.7 → 0.3 → 0.1
  2. mixing_mode = 'local-TF'
  3. Larger starting_magnetization (0.4–0.9)
  4. Smaller degauss (excess smearing erases moments). If the SCF itself fails, temporarily raise it, converge, then restart with startingpot='file' while lowering it
  5. diagonalization = 'cg' or 'ppcg'

And the fundamental caution:

Magnets have multiple local minima

Every magnetic ordering is its own metastable solution. One converged answer is not evidence of the ground state. The standard practice is to start from several initial magnetizations (FM, AFM, nonmagnetic), converge each, and pick the lowest energy.

Noncollinear magnetism and spin-orbit coupling exist behind noncolin=.true. and lspinorb=.true. (with fully relativistic pseudopotentials), at a much higher cost. Learn them when you need them.