Spin-orbit coupling

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:

\[ \begin{equation} \hat{H}_\text{soc}=\sum_i \lambda_i \boldsymbol L_i \cdot \boldsymbol S_i \end{equation} \]

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.

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:

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.

non soc band

2. train the soc model#

in the inputs folder:

For training: turn on soc in the model_options of input_soc_fz.json

    "model_options": {
        "nnsk": {
            ...
            "soc":{"method":"uniform"},
            "freeze": ["onsite", "hopping"]
            ...
        }
    }

or the input_soc.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:

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:

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.

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.

soc band
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