Spintronics and MRAM in ATK

[sunray55]

In the introduction part of ATK (http://www.quantumwise.com/products/12-products/27-spintronics-with-atk), it says that "calculate (collinear) spin-torque transfer (STT) and intralayer exchange coupling;
investigate the details of the spin transport mechanisms (such as barrier tunneling vs. resonant tunneling), e.g. by analyzing the k-point dependence of the transmission coefficients or scattering eigenchannels. (How?)"

May I know the details how to calculate STT and intralayer exchagne coupling? How to identify barrier or resonate tunneling?
Could you please help to give more detail tutorials or reference papers? Many thanks!

[Anders Blom]

Both of these quantities are, at least in their simplest version, rather trivial to compute once you have the currents and total energies for the parallel and anti-parallel electrode configurations.

Following Phys. Rev. Lett. 97, 237205 (2006), in the collinear approximation you can compute the spin torque parallel to the interface planes as

T||(theta) = hbar/2e*sin(theta)*(I_AP-I_P)/2

where I_AP/I_P is the anti-parallel/parallel SPIN current (i.e. spin up minus spin down current).

The interlayer exchange coupling is the difference in total energy between the two configurations; see http://cnst.nist.gov/epg/Pubs/pdf/epg734.pdf, Eq. (3). Now, ATK actually computes the Gibbs free energy for device configurations, rather than the total energy, and I don't know for sure how that influences the results, esp. given the notes in the references article that it's often difficult - and crucial - to determine the energy difference accurately.

I'm sure the general computed trends wouldn't be much affected, but it is clear one must take care to converge the calculations to a low tolerance, and make sure to have proper k-point sampling etc (as we know this influences at the transmission very much, and hence the current, and the difference between the two configurations).

[sunray55]

Hi Anders Blom,

Thanks for your prompt response.
I found the script in the tutorial of MTJ to calculate the k-point depencence of the transmission coefficients.
Do you have the script (it is better a analysis file which can be dragged and dropped directly into the analyzer window, like I-V curve and PDOS  )  to calculate the spin torque and intralayer exchange coupling from the .nc file?
Many thanks!!!

[Anders Blom]

No, it would be a bit hard to do, since there are no default labels in the NC files that tell us which calculation is for which configuration (AP/P). But really, it's a matter of computing the current (for that there is an Analyzer), and taking the difference, not so complicated

[leslie]

I am wondering how to analyze the barrier tunneling and the resonant tunneling with ATK....

[Anders Blom]

Sorry, I forgot to answer that part. This is not so much a specific analysis, as the conclusions drawn from the shape of the transmission, not least how the k-point dependence looks, or the current as a function of the barrier width, etc. This is discussed at length in various scientific articles on the topic.

[sunray55]

Hi Anders Blom,

You mentioned: "ATK actually computes the Gibbs free energy for device configurations".
Does it mean that we should use a device configuration to calculate the intralayer exchange coupling, not a bulk configuration?
For example, in the Fe/MgO/Fe system, we need calculate the total energy with P and AP configuration of both electrode Fe and surface Fe.
Can we use a Fe/MgO/Fe bulk to calculate the intralayer exchange coupling by setting P and AP configuration of Fe at two sides?

If we don't consider the bias, these two methods look the same.

thanks.

Both of these quantities are, at least in their simplest version, rather trivial to compute once you have the currents and total energies for the parallel and anti-parallel electrode configurations.

Following Phys. Rev. Lett. 97, 237205 (2006), in the collinear approximation you can compute the spin torque parallel to the interface planes as

T||(theta) = hbar/2e*sin(theta)*(I_AP-I_P)/2

where I_AP/I_P is the anti-parallel/parallel SPIN current (i.e. spin up minus spin down current).

The interlayer exchange coupling is the difference in total energy between the two configurations; see http://cnst.nist.gov/epg/Pubs/pdf/epg734.pdf, Eq. (3). Now, ATK actually computes the Gibbs free energy for device configurations, rather than the total energy, and I don't know for sure how that influences the results, esp. given the notes in the references article that it's often difficult - and crucial - to determine the energy difference accurately.

I'm sure the general computed trends wouldn't be much affected, but it is clear one must take care to converge the calculations to a low tolerance, and make sure to have proper k-point sampling etc (as we know this influences at the transmission very much, and hence the current, and the difference between the two configurations).

[Anders Blom]

You can't really compute the AP configuration properly in bulk mode, since the periodic boundary condition along Z doesn't apply.

The standard definition of the IEC is made using the total energy, but that is probably because of an implicit assumption that indeed the total energy is the conserved quantity of relevance. (Partly, I'm sure, because most codes can only compute systems with conserved number of electrons.) But if we are looking at a device system, which is the physical reality of things, in fact the total energy is not conserved, since charge can flow in an out of the central region. Thus, I actually think the Gibbs energy is a better foundation for the IEC for the device junction, although I have not performed any serious analysis to prove this fact But using the Gibbs energy would make the quantity relevant under finite bias too.