Classification of SHG
Classification of SHG according to MPGs and parent space group is shown in below table and figure.
| MSGs ↓ / Parent SG→ | With inversion symmetry (wP) | Without inversion symmetry (woP) |
|---|---|---|
| 1. Original MPGs (O) (Type-I MSGs) | O-wP Even/odd: from magnetism | O-woP Even: from magnetism+ crystal Odd: from magnetism |
| 2. Gray MPGs (G) (Type-IV MSGs) | G-wP Even: from magnetism | G-woP Even: from magnetism + crystal |
| 3. BW MPGs with PT symmetry (PT) (Type-III MSGs) | PT-wP Odd: from magnetism | Not possible |
| 4. BW MPGs without PT nor P symmetry (BW) (Type-III MSGs) | BW-wP Even/odd: from magnetism | BW-woP Even: from magnetism + crystal Odd: from magnetism |
Notation: the symmetry of SHG refer the page of original and gray SHG table and black-white SHG table.
Flow chart to determine the SHG type of magnetic materials. M means the MSP, and the G means the SG of parent phase.