SiestaStudio

Magnetism (and DFT+U): ferromagnetic iron

Iron is ferromagnetic: each atom carries a magnetic moment of about 2.2 Bohr magnetons. In this tutorial you build bcc iron in the structure builder, run a spin-polarized calculation, read the moment, look at how the spin-up and spin-down electrons differ in the DOS and band structure, and see what a Hubbard U on the Fe 3d shell (DFT+U) does to the moment.

It takes about 20 minutes; each SIESTA run takes under a minute.

1. Build bcc iron

Create a project named Fe magnetism and open the studio in it. In Atomic Structure, click Edit Structure to open the Crystal Structure Builder. In Generate Structure:

  • Crystal System: Body-Centered Cubic
  • Lattice Constant a (Å): 2.87 (the measured value for iron)
  • Elements: Fe

and click Generate Structure. The builder makes the conventional cubic cell with 2 atoms. Open Symmetry and click Primitive Cell: the cell becomes the 1-atom primitive cell of bcc iron, half the work for SIESTA.

Builder

Primitive cell

Click Apply to Studio, and set System Name to Fe.

2. Set up a spin-polarized calculation

Open the Calculation Setup Wizard and choose Bulk Crystal, Magnetic, Band structure and Standard. On Optional features:

tick Spin-polarized (marked "Recommended" for a magnetic material) and Compute DOS.

Wizard options

Click Next and Apply All. In Spin & Magnetism the Spin Type is now polarized. Leave Initial Spin Configuration empty: SIESTA then starts with all spins parallel, which is what you want for a ferromagnet.

Spin settings

3. The k-path and the charges

In DOS & Band Structure, click Open BZ Editor. It recognises the Body-Centered Cubic cell and loads the standard path Γ-H-N-Γ-P-H-P-N. Click Apply.

Brillouin zone editor

In Chemical Analysis, set Mulliken Population Analysis to Atomic and orbital charges.

4. Check, download and save

Check Diagnostics, download the two input files and the pseudopotentials, and save the calculation as Fe.

5. A second calculation with DFT+U

To compare, make a second calculation that adds a Hubbard U on the Fe 3d electrons. Saving again in the studio would overwrite Fe, so make a copy first:

  1. Open Calculations in the sidebar, find Fe and click Duplicate. A copy, Fe (copy), appears. Click Load on it.

    Duplicate

  2. In DFT+U Correction, switch on Enable DFT+U Correction and type in DFTU.Proj Block:

    Fe    1
  n=3 2
    2.00  0.00
    0.00  0.00

    The lines say: one shell for Fe; the shell n = 3, l = 2 (3d); U = 2.00 eV and J = 0.00 eV; and a projector radius of 0, which lets SIESTA choose it.

    DFT+U

  3. Download the two input files into another folder, and save the calculation: in the dialog, change the name to Fe DFT+U. The copy is already in the project Fe magnetism.

6. Run SIESTA

Run each calculation in its own folder, with Fe.psml next to the input files:

siesta < siesta.fdf > siesta.out

7. The magnetic moment

The moment of iron comes out at 2.29 μB, close to the measured 2.22 μB (you read it in the studio in the next section, or in the last spin moment line of siesta.out). With U = 2 eV on the 3d shell it rises to about 2.74 μB: the Hubbard U pushes the d electrons towards being localized, which favours a larger moment.

This second run is a demonstration of how DFT+U is set up and what it does. For a metal like iron, where the d electrons are not localized, plain GGA is already the better description: the moment with U moves away from the measured value. DFT+U is meant for materials with localized d or f electrons, such as transition-metal oxides.

8. The output in the studio

Open Analyze File and drop in the siesta.out of the plain calculation: it converged. Properties shows the magnetic moment under Magnetic Properties, 2.294 μB in total and per atom (Fe #1), and the Fermi energy, -3.368 eV. The siesta.out of the DFT+U run shows 2.743 μB.

Properties

Charges shows the Mulliken population of the Fe atom: 16 electrons in total (the valence of this pseudopotential), counting both spins.

Charges

The Properties tab also shows a pressure of -16.6 GPa. A negative pressure (tension) is expected here: 2.87 Å is the measured lattice constant, larger than the PBE equilibrium of about 2.83 Å, so the cell would like to shrink. Part of it can also come from the modest Standard settings: converge the basis, mesh cutoff and k-points before you trust a pressure.

9. Spin-up and spin-down electrons

Open siesta.DOS, type the Fermi energy, -3.368, into Set Fermi Energy (E_f) (or click from .out and choose siesta.out), and click Plot Density of States. The spin-up DOS is drawn above the axis, the spin-down DOS below it.

Spin-resolved DOS

The d states of the two spins are shifted apart: the spin-up d band is almost full (below E_F), the spin-down d band is partly empty. This exchange splitting is what gives iron its moment: there are more spin-up than spin-down electrons.

Open siesta.PDOS, tick the d orbitals under By Orbital and click Plot Selected Projections: the d states, drawn solid for spin up and dashed for spin down, make up most of the DOS near E_F.

Fe d PDOS

10. Spin-split bands

Open siesta.bands, click Plot Band Structure, set the vertical range to -10 to 5 eV, and switch on Split Spin Channels: the spin-up and spin-down bands are drawn side by side. The same bands appear in both, shifted against each other by the exchange splitting.

Spin-split bands

11. Save the analysis

Click Save Analysis, choose the project and save.

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