Ferromagnetic bcc Fe

Goal

Your first magnetic calculation. Converge the ferromagnetic ground state of bcc Fe with a spin-polarized SCF (nspin=2) and compare the moment with experiment. This is the hands-on version of the metal-plus- magnetism convergence craft of Chapter 12.

New cards and variables

Item	Role
`nspin=2` + `starting_magnetization`	Collinear polarization with an initial guess (a ratio, −1 to 1)
`mixing_beta=0.3` + `mixing_mode='local-TF'`	The mixing prescription for magnetic metals
`ecutrho = 10×ecutwfc`	The heavy density cutoff Fe PAW demands

Input file

Download fe.scf.in

! E09: ferromagnetic bcc iron. Metal + magnetism, the convergence
! combination that transition-metal oxides are made of.

&CONTROL
  calculation = 'scf'
  prefix      = 'fe'
  outdir      = './tmp/'
  pseudo_dir  = './pseudo/'
  verbosity   = 'high'
/
&SYSTEM
  ibrav       = 3               ! bcc
  celldm(1)   = 5.42            ! bohr (= 2.87 Angstrom, experimental)
  nat         = 1
  ntyp        = 1
  ecutwfc     = 70              ! Fe semicore PAW is demanding
  ecutrho     = 700             ! 10x, not 8x: Fe needs it
  occupations = 'smearing'
  smearing    = 'mv'
  degauss     = 0.02
  nspin       = 2               ! collinear spin polarization
  starting_magnetization(1) = 0.7   ! INITIAL GUESS, a dimensionless ratio in [-1,1]
                                    ! (not Bohr magnetons); the SCF refines it
/
&ELECTRONS
  conv_thr    = 1.0d-8
  mixing_beta = 0.3             ! magnetic metals need gentle mixing
  mixing_mode = 'local-TF'      ! and the local-TF preconditioner
  electron_maxstep = 200        ! allow more iterations than the default 100
/

ATOMIC_SPECIES
  Fe  55.845  Fe.pbe-spn-kjpaw_psl.1.0.0.UPF

ATOMIC_POSITIONS (alat)
  Fe  0.00  0.00  0.00

! a dense grid: the Fermi surface of a magnetic metal needs resolution
K_POINTS (automatic)
  16 16 16  0 0 0

Run

mpirun -np 6 pw.x -nk 6 -in fe.scf.in > fe.scf.out

What to check: measured

Item	Measured (QE 7.5, PAW)	Note
Total energy	−329.26290531 Ry
total magnetization	2.19 μB/cell	Experiment 2.22 μB: PBE nearly nails it
absolute magnetization	2.32 μB/cell	Close to total, so FM
Fermi level	17.4481 eV	A metal

Total ≈ absolute is the badge of ferromagnetism. For AFM the total is near zero while the absolute stays large; that case is E10.

Spin-resolved DOS: an extra measurement

On top of the same density we ran an nscf (20³, tetrahedra) plus dos.x to get the spin-resolved DOS (dos.x prints up and down columns for polarized runs).

bcc Fe spin-resolved DOS — Measured spin-resolved DOS of bcc Fe (QE 7.5, PBE). Exchange splitting pushes the majority (up) d band down to near-full occupation while the minority (down) d band straddles the Fermi level. The occupation difference is exactly the 2.2 μB moment.

Exercises

Set starting_magnetization = 0.0. Does the run collapse to the nonmagnetic solution?
Compare with a nspin=1 run and extract the magnetic stabilization energy.
Run the PDOS pipeline of E7, observe the exchange splitting of the up/down d bands, read the local moment from the Löwdin charges, and compare with the cell magnetization.
Raise degauss to 0.05. What happens to the moment?

Common mistakes

Declaring the first converged solution the ground state. Magnets hold several metastable solutions; converge from several initial magnetizations (0.3 / 0.7 / −0.7) and compare energies. And remember, starting_magnetization is a ratio, not μB (Chapter 03).

12 Spin polarization and magnetism · 07 Controlling SCF convergence