# Spin-orbit coupling
## Method Introduction:
for the systems with non-negligible SOC effect (usually the case of heavy atoms), this effect must be considered, which can be formulated as [Ref:1](https://doi.org/10.1016/j.commatsci.2023.112090):
$$
\begin{equation}
\hat{H}_\text{soc}=\sum_i \lambda_i \boldsymbol L_i \cdot \boldsymbol S_i
\end{equation}
$$
Here, $\boldsymbol L_i$ and $\boldsymbol S_i$ are the orbital and spin momentum operators with interaction strength $\lambda_i$.
The full Hamiltonian $\mathcal{H}$ with SOC effect can be constructed as $\mathcal{H}= \mathcal{I}_2 \otimes H + H_{\text{soc}}$, where $\mathcal{I}_2$ is the $2\times 2$ identity matrix and $\otimes$ is the Kronecker product.
In the following, we will use Sn as an example include SOC interaction in DeePTB.
## Example: SOC effect in alpha-Sn
This example can be seen in the `example/Sn_soc` folder.
### Training data
The training data is generated by the ABACUS code. The training data is stored in the `/data` folder. The `data` folder contains the following files:
- `non_soc`: folder contains the band structure and training data for the non-soc case.
- `soc`: folder contains the band structure and training data for the soc case.
Inside of the `non_soc` and `soc` folder, the following files are included:
- `BANDS_1.dat`: the band structure data generated by the ABACUS code.
- `Sn.vasp`: the structure file of the alpha-Sn material.
- `ref_eig_band.npy`: the reference band structure data, read from `BANDS_1.dat` by removing the core electronic bands.
- `set.0`: the training data with dense k points.
- `set_sparseK.0`: the training data with sparse k points. usually, the sparse k points are used for the training data.
```shell
data
├── non_soc
│ ├── Sn.vasp
│ └── set.0
│ ├── eigenvalues.npy
│ ├── info.json
│ ├── kpoints.npy
│ └── xdat.traj
└── soc
├── Sn.vasp
└── set.0
├── eigenvalues.npy
├── info.json
├── kpoints.npy
└── xdat.traj
```
### Training
#### 1. train the non-soc model
This is already explained in other examples, here we just give a model checkpoint. one can just to visualize the band structure and compare with the reference band structure. in the `reference` folder:
```shell
cd examples/Sn_soc
# run the command manually
dptb run ./reference/non_soc/band.json -i ./reference/non_soc/v2ckpt/checkpoint/nnsk.ep100.pth -o ./band
```
This will generate the non-soc band structure in the `band`.
#### 2. train the soc model
in the `inputs` folder:
For training: turn on soc in the `model_options` of `input_soc_fz.json`
```json
"model_options": {
"nnsk": {
...
"soc":{"method":"uniform"},
"freeze": ["onsite", "hopping"]
...
}
}
```
or the `input_soc.json`
```json
"model_options": {
"nnsk": {
...
"soc":{"method":"uniform"},
"freeze": false
...
}
}
```
Here, the tag `freeze` is to freeze parameters. In the `input_soc_fz.json` the `onsite` and `hopping` parameters are frozen and only `soc` parameters are optimized during the training.
then run the command:
```shell
dptb train ./inputs/input_soc_fz.json -i ./reference/non_soc/v2ckpt/checkpoint/nnsk.ep100.pth -o ./soc_model
```
after or during the training you can monitor the training process by plotting the band structure typing the command:
```shell
dptb run ./reference/soc/band.json -i ./soc_model/checkpoint/nnsk.best.pth -o ./band
```
This will plot the band structure and save the results in the `band` folder.
Or you can use the jupyter notebook to plot the band structure.
In the reference, we have already trained a soc model, you can just use it to plot the band structure.
```shell
dptb run ./reference/soc/band.json -i ./reference/soc/v2ckpt/checkpoint/nnsk.ep100.pth -o ./band
```
This will generate the soc band structure in the `band`.
