To calculate the Curie temperature it is in fact only necessary to know the following parameters：
- J
- D
- Direction
- Patience
My Enlightenment Video. The downside is that the video has no sound and is not detailed enough, but it solves a lot of problems！Thanks lot for it.
I use Monte Carlo Method to calculate and use the Open Source Programs MCSOLVER! I discussed its use with its author（PhD.Liang Liu） and became familiar with its use!Following, I'll explain the usage in detail！
Usually I start by editing all the parameters under Windows, then I exported the input file to run under Linux.
The general interface of the program is as follows：
Now I explain all parameters one by one.
In general, a1(1.0 0.0 0.0), a2(-0.5 0.866 0.0), a3(0.0 0.0 1.0).
It depends on whatever you want to choose, it maybe takes dozens of differences.
ID is beginning at 0 and you need to write out the positions of all unequal atoms in the smallest cell. Spin depends on your system（This parameter is simple to determine but error-prone）and it is also related to J.
For example, Cr's Magnetic moment is 3, but for a single one, you can treat as 3/2. The different Spin will influence the whole simulation(So, be careful with it)!
If you consider D, you need to fill in the parameters for the z-direction. Maybe it has a small effect, but you need to test it. You can use this formula(a example) to estimate:
$D=\frac{E_{\mathrm{FM}}^{\beta}-E_{\mathrm{FM}}^{z}}{4 S^{2}}$
This is the most important and difficult step. It's actually not easy to understand quickly at first.
Generally speaking, we consider that the J-value is calculated by the following formula(a example):
For this system, if you have a very large and positive value of J, this means an antiferromagnetic coupling, which theoretically is prone to resistive frustration and becomes a disordered spin fluid.
Usually J_{xx} and J_{yy} are equal, and as for the difference with J_{zz}, further calculation is needed!
It is also worth noting that J-values usually need to be estimated accurately rather than blindly using the paper's formula, which is often just a J-value and does not include J1, J2, etc.
Next I will elaborate on how to set the correct orientation with the help of a few pictures！
I'll start with CrI3 as an example:
It is obvious that not only the nearest neighbors(J1) but also the next-nearest(J2) and second-nearest neighbors(J3) are considered here,The size of the specific J we will explain later,first figure out the direction is the first and most critical step！
For the central atom, yellow, green, and blue represent J1, J2, and J3, respectively. Obviously, J1 has 3 pairs, J2 has 6 pairs, and J3 still has 3 pairs.
How to describe 3 pairs J1? What exactly does [0 0 0], [-1 0 0], [0 1 0] mean here? If we can solve this, the next directions for J2 and J3 can be written very easily!
It is known that a single cell of CrI3 has two Cr atoms, or it can be described as (CrI3)2. For a single cell,Just as I circled in the picture below:
We write the a1 direction in the diagram as the x-direction and the a2 direction as the y-direction, then for J1,the direction of the superexchange interaction of the central atom with the other three atoms is well understood. The first one [0 0 0] is with an atom in its own cell, so it is noted as [0 0 0]. The second exchange interaction is with an atom in the original cell that is shifted by [-1 0 0]. The third [0 1 0] can be explained in the same way.
You should be patient enough to mark out all the J, D and directions you need, and you will usually get the desired result! Other settings are very simple and easy to understand, if you have questions, you can contact me via e-mail(nickylcq@outlook.com), I am very happy to solve for you!
Last but not least, we cannot forget the developers of this program, who are PhD.Liang Liu If you use this program and publish the results in a paper, don't forget to cite their articles, and of course more tips can be learned from their articles, here is the address:
Liu, L., Ren, X., Xie, J., Cheng, B., Liu, W., An, T., ... & Hu, J. (2019). Magnetic switches via electric field in BN nanoribbons. Applied Surface Science, 480, 300-307.
Liu, L., Chen, S., Lin, Z., & Zhang, X. (2020). A symmetry-breaking phase in two-dimensional FeTe2 with ferromagnetism above room temperature. The Journal of Physical Chemistry Letters, 11(18), 7893-7900.
Thank you for reading, and if you have any questions or inevitable small errors, please contact me, thank you!
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