# Spin-polarization and SOC

## Non-spin-polarized Calculations
Setting of **"nspin 1"** in INPUT file means calculation with non-polarized spin. 
In this case, electrons with spin up and spin down have same occupations at every energy states, weights of bands per k point would be double. 

## Collinear Spin Polarized Calculations
Setting of **"nspin 2"** in INPUT file means calculation with polarized spin along z-axis. 
In this case, electrons with spin up and spin down will be calculated respectively, number of k points would be doubled.
Potential of electron and charge density will separate to spin-up case and spin-down case.

Magnetic moment Settings in [STRU files](../input_files/stru.md) are not ignored until **"nspin 2"** is set in INPUT file

When **"nspin 2"** is set, the screen output file will contain magnetic moment information. e.g.
```
 ITER   TMAG      AMAG      ETOT(eV)       EDIFF(eV)      DRHO       TIME(s)    
 GE1    4.16e+00  4.36e+00  -6.440173e+03  0.000000e+00   6.516e-02  1.973e+01
```
where "TMAG" refers to total magnetization and "AMAG" refers to average magnetization.
For more detailed orbital magnetic moment information, please use [Mulliken charge analysis](../elec_properties/Mulliken.md).

### Constraint DFT for collinear spin polarized calculations
For some special need, there are two method to constrain electronic spin.

1. **"ocp"** and **"ocp_set"**
If **"ocp=1"** and **"ocp_set"** is set in INPUT file, the occupations of states would be fixed by **"ocp_set"**, this method is often used for excited states calculation. Be careful that: when **"nspin=1"**, spin-up and spin-down electrons will both be set, and when **"nspin=2"**, you should set spin-up and spin-down respectively.

2. **"nupdown"**
If **"nupdown"** is set to non-zero, number of spin-up and spin-down electrons will be fixed, and Fermi energy level will split to E_Fermi_up and E_Fermi_down. By the way, total magnetization will also be fixed, and will be the value of **"nupdown"**.

## Noncollinear Spin Polarized Calculations
The spin non-collinear polarization calculation corresponds to setting **"noncolin 1"**, in which case the coupling between spin up and spin down will be taken into account.
In this case, nspin is automatically set to 4, which is usually not required to be specified manually.
The weight of each band will not change, but the number of occupied states will be double.
If the nbands parameter is set manually, it is generally set to twice what it would be when nspin<4.

In general, non-collinear magnetic moment settings are often used in calculations considering [SOC effects](#soc-effects). When **"lspinorb 1"** in INPUT file, "nspin" is also automatically set to 4.

Note: different settings for "noncolin" and "lspinorb" correspond to different calculations:

| noncolin | lspinorb | nspin | Effect | When to Use |
|----------|----------|-------|--------|-------------|
| 0 | 0 | <4 | No non-collinear magnetism, no SOC | Standard collinear spin-polarized or non-spin-polarized calculations |
| 0 | 0 | 4 | Same as above, but larger calculation | **Not recommended** - wastes computational resources |
| 1 | 0 | 4 | Non-collinear magnetism WITHOUT SOC | Systems with complex magnetic structures (e.g., spin spirals, frustrated magnets) where SOC is negligible |
| 0 | 1 | 4 | SOC WITH z-axis magnetism only | Non-magnetic materials with SOC (e.g., semiconductors with band splitting), or magnetic materials where magnetism is along z-axis |
| 1 | 1 | 4 | Both SOC AND non-collinear magnetism | Heavy-element magnetic materials where both SOC and non-collinear magnetism are important (e.g., magnetic anisotropy, Dzyaloshinskii-Moriya interaction) |

**Special case**: `noncolin=0, lspinorb=1` is commonly used for non-magnetic materials with SOC effects (e.g., topological insulators, semiconductors with spin-orbit splitting). In this case, the magnetization is NOT automatically set, implying no magnetic moments in the system.

## For the continuation job
- Continuation job for "nspin 1" need file "SPIN1_CHG.cube" which is generated by setting "out_chg=1" in task before. By setting "init_chg file" in new job's INPUT file, charge density will start from file but not atomic. 
- Continuation job for "nspin 2" need files "SPIN1_CHG.cube" and "SPIN2_CHG.cube" which are generated by "out_chg 1" with "nspin 2", and refer to spin-up and spin-down charge densities respectively. It should be note that reading "SPIN1_CHG.cube" only for the continuation target magnetic moment job is not supported now.
- Continuation job for "nspin 4" need files "SPIN%s_CHG.cube", where %s in {1,2,3,4}, which are generated by "out_chg 1" with any variable setting leading to 'nspin'=4, and refer to charge densities in Pauli spin matrixes. It should be note that reading charge density files printing by 'nspin'=2 case is supported, which means only $\sigma_{tot}$ and $\sigma_{z}$ are read.

# SOC Effects
## SOC
`lspinorb` is used for control whether or not SOC(spin-orbit coupling) effects should be considered.

Both `basis_type=pw` and `basis_type=lcao` support `scf` and `nscf` calculation with SOC effects.

Atomic forces and cell stresses can be calculated with SOC effects (supported since ABACUS v3.9.0). 

## Pseudopotentials and Numerical Atomic Orbitals
For Norm-Conserving pseudopotentials, there are differences between SOC version and non-SOC version.

Please check your pseudopotential files before calculating.
In `PP_HEADER` part, keyword `has_so=1` and `relativistic="full"` refer to SOC effects have been considered, 
which would lead to different `PP_NONLOCAL` and `PP_PSWFC` parts.
Please be careful that `relativistic="full"` version can be used for SOC or non-SOC calculation, but `relativistic="scalar"` version only can be used for non-SOC calculation.
When full-relativistic pseudopotential is used for non-SOC calculation, ABACUS will automatically transform it to scalar-relativistic version.

Numerical atomic orbitals in ABACUS are unrelated with spin, and same orbital file can be used for SOC and non-SOC calculation.

## Partial-relativistic SOC Effect
Sometimes, for some real materials, both scalar-relativistic and full-relativistic can not describe the exact spin-orbit coupling.
Artificial modulation can help for these cases.

`soc_lambda`, which has value range [0.0, 1.0] , is used for modulate SOC effect.
In particular, `soc_lambda 0.0` refers to scalar-relativistic case and `soc_lambda 1.0` refers to full-relativistic case.

## Pseudopotential Requirements for SOC

When performing SOC calculations (`lspinorb=1`), specific pseudopotential requirements must be met:

### Checking Pseudopotential Files

In the UPF (Unified Pseudopotential Format) file header (`PP_HEADER` section), look for:
- `has_so="T"` or `has_so="1"`: Indicates SOC information is included
- `relativistic="full"`: Indicates full-relativistic pseudopotential

Example from a full-relativistic UPF file:
```
<PP_HEADER
   ...
   relativistic="full"
   has_so="T"
   ...
/>
```

### Pseudopotential Usage Rules

1. **For SOC calculations** (`lspinorb=1`):
   - **MUST** use full-relativistic pseudopotentials with `has_so=true`
   - Code will terminate with error: "no soc upf used for lspinorb calculation" if scalar-relativistic PP is used

2. **For non-SOC calculations** (`lspinorb=0`):
   - Can use either scalar-relativistic or full-relativistic pseudopotentials
   - If full-relativistic PP is used, ABACUS automatically transforms it to scalar-relativistic version

3. **For ultrasoft pseudopotentials (USPP)**:
   - Full-relativistic USPP **requires** `lspinorb=true`
   - Code will show warning: "FR-USPP please use lspinorb=.true." if this requirement is not met

### Where to Find SOC Pseudopotentials

- **SG15_ONCV**: Full-relativistic versions available at [quantum-simulation.org](http://quantum-simulation.org/potentials/sg15_oncv/upf/)
- **PseudoDOJO**: Provides both scalar and full-relativistic versions
- **ABACUS official**: [abacus.ustc.edu.cn](http://abacus.ustc.edu.cn/pseudo/list.htm)

## Automatic Parameter Settings

When using SOC or non-collinear calculations, ABACUS automatically adjusts several parameters:

### When `lspinorb=true`:
1. **nspin**: Automatically set to 4 (noncollinear spin representation)
2. **Symmetry**: Automatically disabled (`symm_flag=-1`) because SOC breaks inversion symmetry
3. **Magnetization**: NOT automatically set when `noncolin=0` (implies non-magnetic material with SOC)

### When `noncolin=true`:
1. **nspin**: Automatically set to 4
2. **npol**: Set to 2 (wave function has two spinor components)
3. **Magnetization**: Automatically set if user provides zero values (unless `lspinorb=1` and `noncolin=0`)

### Important Notes:
- You do NOT need to manually set `nspin=4` when using `lspinorb=1` or `noncolin=1`
- Symmetry operations are incompatible with SOC, so they are automatically turned off
- For `lspinorb=1, noncolin=0`: This is a special case for non-magnetic materials with SOC, where magnetization is not initialized

## Common Errors and Solutions

### Error: "no soc upf used for lspinorb calculation"
**Cause**: Using scalar-relativistic pseudopotentials with `lspinorb=1`

**Solution**: Download and use full-relativistic pseudopotentials with `has_so=true`. Check the UPF file header to verify `relativistic="full"` and `has_so="T"`.

### Error: "nspin=4(soc or noncollinear-spin) does not support gamma only calculation"
**Cause**: Trying to use `gamma_only=true` with `lspinorb=1` or `noncolin=1`

**Solution**: Set `gamma_only=false` or `gamma_only=0` in your INPUT file. SOC and non-collinear calculations require k-point sampling beyond the gamma point.

### Warning: "FR-USPP please use lspinorb=.true."
**Cause**: Using full-relativistic ultrasoft pseudopotentials without enabling SOC

**Solution**: Set `lspinorb=true` in your INPUT file, or switch to scalar-relativistic USPP if SOC is not needed.

### Issue: Forces or stresses not calculated
**Note**: This issue has been resolved. Atomic forces and cell stresses can now be calculated with SOC effects (supported since ABACUS v3.9.0).

If you are using an older version of ABACUS (before v3.9.0), force and stress calculations with SOC were not supported. Please upgrade to the latest version to use this feature.

## INPUT File Examples

### Example 1: SOC without Non-collinear Magnetism
For non-magnetic materials with SOC (e.g., GaAs, topological insulators):

```
INPUT_PARAMETERS
calculation         scf
basis_type          pw
ecutwfc             50
lspinorb            1        # Enable SOC
noncolin            0        # No non-collinear magnetism
# nspin will be automatically set to 4
# symmetry will be automatically disabled
```

### Example 2: Non-collinear Magnetism without SOC
For systems with complex magnetic structures but negligible SOC:

```
INPUT_PARAMETERS
calculation         scf
basis_type          lcao
lspinorb            0        # No SOC
noncolin            1        # Enable non-collinear magnetism
# nspin will be automatically set to 4
# Magnetization directions should be specified in STRU file
```

### Example 3: Both SOC and Non-collinear Magnetism
For heavy-element magnetic materials (e.g., Fe with SOC, materials with DMI):

```
INPUT_PARAMETERS
calculation         scf
basis_type          pw
ecutwfc             60
lspinorb            1        # Enable SOC
noncolin            1        # Enable non-collinear magnetism
# nspin will be automatically set to 4
# symmetry will be automatically disabled
# Magnetization directions should be specified in STRU file
```

### Example 4: Partial-relativistic SOC
For fine-tuning SOC strength:

```
INPUT_PARAMETERS
calculation         scf
basis_type          pw
ecutwfc             50
lspinorb            1        # Enable SOC
soc_lambda          0.5      # 50% SOC strength
# Useful when full SOC overestimates or underestimates experimental results
```