Crystal Structure:

CIF Source:
Spedding F H, Daane A H, Herrmann K W
Acta Crystallographica 9 (1956) 559-563
The crystal structures and lattice parameters of high-purity scandium,
yttrium and the rare earth metals
Locality: synthetic
Note: sample 99.8% pure
_database_code_amcsd 0009175

http://rruff.geo.arizona.edu/AMS/download.php?id=10420.cif&down=cif

Simulated Powder XRD using VESTA:

X-Ray Wavelength: 1.54059 Angstrom

Simulation 1: GGA-Spin Polarized

Pseudopotential Used:

Dy.pbe-spdn-rrkjus_psl.1.0.0.UPF

PP Type: Ultrasoft
Exchange Correlation Functional: PBE-GGA Spin Polarized
Non-linear core corrections are used.

Wavefunction Energy Cutoff: 35 Ry
Charge Density Energy Cutoff: 385 Ry
k – mesh: 8x8x8
Run Type: GGA-PBE
Starting Magnetization: 0.4

Total Energy vs Cutoff:

Cutoff(Ry)       Total Energy(Ry)

10                    -247.31269578
15                   -249.39216615
20                   -249.80984740
25                   -249.88662023
30                   -249.89774501
35                   -249.89854612
37                   -249.89874195

In order to perform spin polarized calculations set the nspin parameter to 2.

Then as explained here, set a starting magnetization to break the symmetry. The calculation should find the lowest-energy spin state compatible with the given crystal structure and not orthogonal to initial conditions (e.g.: if you start
with a FM alignment, you will hardly find an AFM final state even if it exists). Perform several calculations at different starting magnetizations, choose the one with smaller energy as ground state. The system must be in all cases treated as a metal, whether it is or not. In principle, you should use pseudopotentials with the nonlinear core correction.

The following shows the total energy for different values of starting magnetization. NOTE: Starting magnetization is given in fractions, ranging between -1 (all spins down for the valence electrons of atom type ‘i’) to 1 (all spins up).

Total Energy vs Starting Magnetization:

SM               Total Energy (Ry)          Tot. Magnetic Mom/Abs. Mg. Mom. (Bohr Magneton)

0.1                 -249.89851578                 0.16/0.16
0.2                 -249.89854612                 0.10/0.10
0.3                 -249.89856050                 0.01/0.01
0.4                 -249.89856057                 0.01/0.01
0.5                 -249.89855980                 0.01/0.01
0.6                 -249.89855985                 0.01/0.01
0.7                 -249.89855995                 0.02/0.02
0.8                 -249.89855872                 0.03/0.03
0.9                 -249.89856010                 0.01/0.01
1.0                 -249.89853780                 0.12/0.12

Here we can see that the magnetic moments are pretty small, and therefore, a spin polarized calculation may or may not be necessary.

Clearly, a starting magnetization value of 0.4 gives the lowest energy.

Now, we perform optimization of geometry.

Optimized Coordinates and Lattice Parameters:

CELL_PARAMETERS {angstrom}

3.614257               0.000003               0.000000
-1.807126               3.130034               0.000000
0.000000               0.000000               5.618172

ATOMIC_POSITIONS {angstrom}

Dy              -0.000010              2.086705              1.404543
Dy              1.807122              1.043363              4.213629

Total magnetic moment for optimized system: 0.00 Bohr Magneton.

This shows the that GGA-DFT is insufficient to predict the correct experimental magnetic moment value of 7-10 B.M.

Magnetic moment per atom= 0.00 B.M.

Bandstructure:

Density of States(DOS):

Input Files:

 

 

Acknowledgements:

I acknowledge the use of the following tools and packages in order to produce the above simulations.
Quantum Espresso(for DFT based simulations): http://www.quantum-espresso.org/
BURAI(for visualization and as a GUI for QE): http://nisihara.wixsite.com/burai
VESTA(for visualization and XRD simulations): http://jp-minerals.org/vesta/en/

References and Resources

https://en.wikipedia.org/wiki/Dysprosium

http://www-rjn.physics.ox.ac.uk/lectures/magnetismnotes10.pdf

http://146.141.41.27/Lectures/Omololu-Wednesday-21-MetalsMagnetism2.pdf