### Crystal Structure:

Dy (Hexagonal Closed Pack) |

About/Help |

**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