### Crystal Structure:

Co (Hexagonal Closed Pack) |

About/Help |

**CIF Source:**

Taylor A, Floyd R W

Acta Crystallographica 3 (1950) 285-289

Precision measurements of lattice parameters of non-cubic crystals

Locality: synthetic

Sample: at T < 450 C

_database_code_amcsd 0009140

http://rruff.geo.arizona.edu/AMS/download.php?id=10374.cif&down=cif

### Simulated Powder XRD using VESTA:

X-Ray Wavelength: 1.54059 Angstrom

## Simulation 1: GGA-Spin Polarized

**Pseudopotential Used:**

Co.pbe-n-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**: 47 Ry

**Charge Density Energy Cutoff:** 517 Ry

**k – mesh**: 8x8x8

**Run Type**: GGA-PBE Spin Polarized

**Starting Magnetization**: 0.8

**Total Energy vs Cutoff:**

Cutoff(Ry) Total Energy(Ry)

25 -152.10091494

30 -152.25971773

35 -152.27675576

40 -152.27775041

45 -152.28072344

47 -152.28215106

50 -152.28389648

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 -152.24120855 0/0

0.2 -152.28215106 3.28/3.64

0.3 -152.28215155 3.28/3.64

0.4 -152.28215149 3.28/3.64

0.5 -152.28215153 3.28/6.64

0.6 -152.28215146 3.28/3.64

0.7 -152.28215147 3.28/3.64

0.8 -152.28215157 3.28/3.64

0.9 -152.28215131 3.28/3.64

1.0 -152.28215119 3.28/3.65

Clearly, a starting magnetization value of 0.8 gives the lowest energy.

Now, we perform optimization of geometry.

### Optimized Coordinates and Lattice Parameters:

**CELL_PARAMETERS {angstrom}**

2.491858 0.000001 -0.000000

-1.245928 2.158011 0.000000

-0.000000 0.000000 4.014676

**ATOMIC_POSITIONS {angstrom}**

Co -0.000009 1.438683 1.003669

Co 1.245927 0.719351 3.011007

Total magnetic moment for optimized system: 3.25 Bohr Magneton.

Since there are 2 Co atoms in our HCP lattice, therefore, the total magnetization per atom is 3.25/2=1.625 Bohr. Magnt. which is astoundingly very close to the experimental value.

**Magnetic moment per atom**= 1.625 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/Cobalt

http://www.materialsdesign.com/appnote/magnetic-moment-iron

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

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