This mini-tutorial shows how to set up an atomic chain, and calculate the transmission spectrum. To make it a bit more interesting, we will do a spin-polarized calculation, and compare the transmission in the two cases where the electrodes have parallel and anti-parallel spin-polarizations.

We will use a chain of carbon atoms to make the calculations run fast. Carbon is not naturally magnetic, but when the atom spacing in the chain is large enough - but not too large - one can actually obtain a spin-polarization. The system is thus artificial, and only chosen for the purpose of illustrating the methodology.

This tutorial is a bit longer than some of the other mini-tutorials, and will take perhaps 15-30 minutes to complete. It will be assumed that you have already gone through some of the quicker and simpler tutorials, and so are familiar with the basic workflow in VNL, like how to set up and perform a calculation, and how to operate the Builder.

Setting up a one-dimensional carbon chain

1. Open the Builder
2. Switch the "Lattice type" from "Simple cubic" to "Simple tetragonal". Set lattice constants a=6 and c=2.9 Å.
   The large unit cell in the X/Y directions minimizes the electrostatic interactions between the repeated copies of the chain; remember there will be periodic boundary conditions in these directions.
   
3. Insert a carbon atom. Center it in the cell by setting its fractional coordinates to (0.5, 0.5, 0.5) - or use the menu Transform>Center.
4. From the menu choose Transform>Repetition and repeat the system 12 times in the C direction.
   Switch to device mode by clicking the icon
5. The automatically suggested electrode length 8.7 Å is a good value, and the setup of the two-probe system is complete.
   

Parallel calculation

We will now set up the calculation with parallel spin in the two electrodes.

1. Send the geometry to the Script Generator using the "Send to" icon in the lower right-hand corner of the Builder.
2. Set the "Default output file" to c_para.nc (use the browse button "..." to specify the precise location of the file, otherwise it will be saved in the directory where VNL was started from).
3. Insert a "New Calculator" and open it (double-click in the left-hand panel, then double-click in the right-hand panel).
4. The most important thing we need to do is to select a spin-polarized exchange-correlation functional. We will use LSDA.
5. Second, there are a number of steps we can take to speed up the calculations and reduce the memory consumption:
   • Reduce the mesh cut-off of 40 H
   • Increase the temperature to 1500 K
   • Change the LCAO basis set type to SingleZeta
   • Change the Poisson solver to FFT
     
6. Double-click "Initial State" to insert a block that defines the initial spin populations. We can leave all parameters in it at default (all atoms start out at maximum Up polarization) for the parallel electrode calculation.
7. Double-click "Analysis" and insert a "TransmissionSpectrum" block. Also here the default parameters are fine.
   
8. The script is now ready.

	Tip
	It is a good idea to save the script from the Script Generator, for future reference and use.

Parallel transmission spectrum

Run the script by sending it to the Job Manager and click "Process queue" there. (Don't close the Script Generator, we will need it soon again!) If you have followed the instructions above precisely, the calculation will just take a few minutes to run.

	Note
	By inspecting the log file, we note that the populations for the up/down (DM[U]/DM[D]) states are nearly the same on all atoms, as expected in an ideal system. (The small differences are primarily due to the low mesh cut-off.)

To view the transmission spectrum for the parallel spin, select the file c_para.nc in the main VNL window, and you will see in the right column of the window that the file contains two objects.

Click the TransmissionSpectrum object, and two actions will appear in the panel below. Click the Show button next to "Plot", and a plot of the transmission spectrum will appear.

It can be verified by running a simple band structure calculation that an atomic carbon chain has a spin-polarized electronic structure. Thus we expect to see a difference between the up (black) and down (red) spin components in the transmission spectrum, which indeed is the case.

Anti-parallel calculation

We will now set up the anti-parallel spin calculation. We will use the self-consistent state of the parallel configuration as initial state, to provide a good initial guess for the calculation. To set this up, return to the Script Generator tool and modify the script for the parallel spin calculation.

	Tip
	To go to the Script Generator, you may use the Windows menu, available in all VNL windows.

1. Change the "Default output file" to c_anti.nc.
2. Double-click the "Initial State" block and modify the following parameters:
   • Tick Enable spin, and also tick "Use old calculation".
   • Click the "..." browse button and locate the file c_para.nc containing the converged calculation for the parallel configuration.
   • Set the (scaled) initial spin on atoms 6 to 11 to -1.
     
3. We are done! Save the script under a new name (menu File>Save as), send it to the Job Manager and run it.

Anti-parallel transmission spectrum

When the calculation finishes, we can again plot the transmission spectrum contained in the file c_anti.nc. The two spin components have identical transmission spectra in this case, as expected.

On inspection of the log file for the anti-parallel calculation, you can see that the spin is indeed flipped in the right part of the system. Regarding the use of the parallel calculation as initial state, ATK will actually flip the density matrix if the initial spin (which we set in the "Initial state" block) is less than zero. Also, the spin of the right electrode is automatically set to match the spin configuration of the "right electrode copy" (cf. the discussion on the two-probe geometry in the Upgrade Guide).