The Magnetic Tunnel Junction Builder tool is used in VNL for setting up calculations for a special type of two-probe systems: A magnetic tunnel junction.

Magnetic tunnel junctions are devices that can be modeled as an insulating thin layer sandwiched between magnetic metal electrodes.

In this tutorial we will:

We will guide you through some of the steps that you typically will do when you are working with magnetic tunnel junctions. Even though the tutorial takes you through everything step-by-step, it is assumed that you know the basics of how to work with VNL.

To launch the Magnetic Tunnel Junction Builder tool, double-click the icon in the Virtual NanoLab Toolbar. The tool will open up, displaying the magnetic tunnel junction initialized with default settings:

Using this tool, we will create a series of systems to model iron-magnesium oxide-iron interfaces, Fe-MgO-Fe, where the depth of the insulating magnesium oxide layer is of just a few atomic layers.

We will first adjust a few geometrical parameters to make the structures closer to the relaxed one: the minimum of the total potential energy. Note that this tutorial does not aim to fully relax the structure by finely adjusting all lattice constants and geometrical parameters, but to give a general scope of how to work with magnetic tunnel junctions. Define your system by taking the following steps.

Now, all parameters have been set to produce the first magnetic tunnel junction (with 2 layers of MgO between Fe electrodes). Next, create the configuration with these settings by left-clicking the button labeled Save/Save As. This will create a file called Fe-MgO-Fe.py, in your working folder. Rename it to Fe-MgO_2Layers-Fe.py.

Next, return to the Magnetic Tunnel Junction Builder tool, and change the Number of Layers to 3 in the Scattering region group box. Then create the corresponding NanoLanguage script and name this Fe-MgO_3Layers-Fe.py.

Analogously, create the configurations and associated files for systems with 4 and 5 MgO layers.

Now, you should have the following files in your working directory: “Fe-MgO_2Layers-Fe.py”, “Fe-MgO_3Layers-Fe.py”, “Fe-MgO_4Layers-Fe.py”, “Fe-MgO_5Layers-Fe.py”. The files should contain the configuration for magnetic tunnel junctions with, respectively, 2, 3, 4 and 5 layers of MgO between Fe electrodes.

The next step is to set up NanoLanguage scripts using the NanoLanguage Scripter tool to calculate the spin polarized transport properties (i.e. the transmission spectrum) for all the magnetic tunnel junction configurations you have just built. This you do by

Open the NanoLanguage Scripter tool by double-clicking the icon.

Loading a configuration

Once you have opened the NanoLanguage Scripter, add one of the configurations you created by drag-and-dropping the configuration file “Fe-MgO_2Layers-Fe.py” from your file browser onto the open NanoLanguage Scripter window. The system is now loaded into the NanoLanguage Scripter, and the Configuration tab shows the structure. You can also open and load the NanoLanguage Scripter directly by drag-and-drop the configuration directly from the Magnetic Tunnel Junction Builder 3D-window to the Scripter icon on the toolbar.

Setting calculation parameters

The next step is to specify the parameters for the calculation. It is far from trivial to select an optimal set of parameters, but the general rule of thumb is to select something that is reasonable (typically, the default initial guesses will), and then vary some of the most pertinent parameters to see if the result changes. In this tutorial, we have chosen to change quite a few parameters from their default values in order to increase the convergence and accuracy of the calculation.

Start by left-clicking the Method tab. This opens the first of the method dialog windows:

The parameters regulating how to solve the SCF equation is divided into groups that are displayed on different dialog windows. These can be navigated through using the top-level drop-down list of the Method tab, and is set to Basis set in Figure 38.

In this tutorial, we leave most parameters to their default values, but find that changing some of the parameters increase accuracy and convergence.

Setting the checkpoint file

After you have set up all the calculation parameters in the Method tab, left-click on the Self-Consistent Calculation tab. Type Fe-MgO_2Layers-Fe.nc in the Checkpoint Filename input field to specify the name of the checkpoint file. The scripter window now looks like this

Setting properties

Now that we have set up all the parameters to calculate and store the electron density, we also need to specify which properties to calculate for the system. This is done from the Analysis tab. Left-click the Analysis tab. Figure 40 shows the Analysis tab when you are done setting up the properties in this tutorial.

First, make sure the Store Results in VNL File is checked, and specify the name of the VNLFile by typing Fe-MgO_2Layers-Fe.vnl in the VNLFile Name input field.

Second, select Total energy from the Available Quantities list and press the > button to calculate and print out the total energy. Total energy now appears in the Selected Quantities list to the right.

Similarly, select Transmission spectrum from the Available Quantities list and press the > button. Transmission spectrum appears now in the Selected Quantities list to the right. Left-click the Transmission spectrum in the Selected Quantities list; a Calculate Transmission Spectrum panel appears. Specify that the transmission spectrum is calculated for 41 energies equally distributed from -0.2 to 0.2 eV by typing 41, -0.2, and 0.2 in the three Energies input fields. Change the number of k-points in the Brillouin zone integration to 5 by modifying Number of k-points both for the A and B directions.

The scripter window looks now like this

When you have specified all the parameters in the scripter, create your NanoLanguage script by left-clicking Save/Save As. A script named twoprobe_configuration_script.py is created in your working folder. Rename it to Fe-MgO_2Layers-Fe.py. Now, we have created the NanoLanguage script for the parallel spin configuration and are ready to submit the script. However, before we do that we go back to the Method tab to generate a script to calculate the anti-parallel spin system.

Generating the anti-parallel case and modifying the script

Return to the Method tab and navigate to the electron-density dialog window. Change the initial scaled spin for the right electrode from 1 to -1; leave the other parameters the way they are. Generate a new script by left-clicking Save/Save As, and rename the script.

Open the generated NanoLanguage script with your favorite editor, and locate the section where the density parameters are defined for the central region, it should be lines 81-84 if you have followed this tutorial, which looks like this:

electron_density_parameters = electronDensityParameters(
    mesh_cutoff = 150.0*Rydberg,
    initial_scaled_spin = [ 1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1.,  1. ]
)

Modify the elements in the list to look like this:

electron_density_parameters = electronDensityParameters(
    mesh_cutoff = 150.0*Rydberg,
    initial_scaled_spin = [ 1.,  1.,  0.,  0.,  0.,  0.,  0.,  0., -1., -1. ]
)

This sets the initial spin-polarization of each surface atom to the maximum spin-up value for the left electrode and the maximum spin-down value for the right electrode. This is also what we want for the anti-parallel spin configuration. The insulating MgO layer is spin unpolarized and should therefore have the values 0; since MgO is a closed shell system, however, it does not make any difference if you leave these at the value 1.

Now, create the scripts for the remaining configurations, i.e. Fe-MgO_3Layers-Fe.py, Fe-MgO_4Layers-Fe.py, and Fe-MgO_5Layers-Fe.py.

To create a simple batch queue for execution on a local system, the Job Manager tool can be used. From your file browser, simply drag-and-drop all the script files created in the previous section one by one onto the icon of the Job Manager tool (the tool is located in the Virtual NanoLab Toolbar.

The calculations will be executed in the order that they were submitted. Note that these calculations are relatively time consuming and it will take a powerful CPU and some patience to get the corresponding results. Depending on your CPU and memory, you might need to leave a single computer running for a couple of days.

An alternative method, that would eventually allow you to save time, is to execute the computations externally and in parallel if possible, using ATK. Note that several licenses for the Atomistix ToolKit are needed in this case.

We expect that the conductance of the magnetic tunnel junction device drops exponentially with the thickness of the central insulating layer (in this case the MgO layer). This is caused by the fact that the insulating layer acts as a tunneling barrier for the incident electrons, which is well-known property of 1D systems. Note that this is approximately a 1D case since the important variations of the system are only along the Z axis.

The other expectation — and this is why these devices have a high technological interest — is that the electrical conductance is strongly dependent on the magnetic polarization of the electrodes. When both electrodes have the same magnetic polarization (parallel polarization case) the conductance should be higher than in the case when both electrodes have opposite magnetization. In fact, for some devices, the difference in conductance between the parallel case and the anti-parallel can be of several orders of magnitude.

The results of this tutorial already show both of the above mentioned effects. In the following figure, we have plotted the conductance of the iron-magnesium oxide-iron junctions as a function of the number of MgO layers, both for the parallel and anti-parallel cases.