Mn$_{1.4}$PtSn Structure: A3B2C2_tI28_122_ad_c_d-001
| Prototype | Mn$_{1.4}$PtSn |
| AFLOW prototype label | A3B2C2_tI28_122_ad_c_d-001 |
| ICSD | 11061 |
| Pearson symbol | tI28 |
| Space group number | 122 |
| Space group symbol | $I\overline{4}2d$ |
| AFLOW prototype command |
aflow --proto=A3B2C2_tI28_122_ad_c_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak x_{4}$ |
- (Vir, 2019) found that the Mn (4a) site (in the layer with the platinum (8c) atoms) has 20% vacancies, giving the noted departure from the nominal Mn$_{3}$Pt$_{2}$Sn$_{2}$ stoichiometry.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Mn I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4a) | Mn I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (8c) | Pt I |
| $\mathbf{B_{4}}$ | = | $- z_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (8c) | Pt I |
| $\mathbf{B_{5}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(z_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Pt I |
| $\mathbf{B_{6}}$ | = | $\left(z_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8c) | Pt I |
| $\mathbf{B_{7}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{8}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{10}}$ | = | $\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Mn II |
| $\mathbf{B_{11}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\left(x_{4} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(x_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Sn I |
| $\mathbf{B_{12}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}- \left(x_{4} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(x_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (8d) | Sn I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{4} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}- \left(x_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Sn I |
| $\mathbf{B_{14}}$ | = | $\left(x_{4} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\left(x_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (8d) | Sn I |
References
- P. Vir, N. Kumar, H. Borrmann, B. Jamijansuren, G. Kreiner, C. Shekhar, and C. Felser, Tetragonal Superstructure of the Antiskyrmion Hosting Heusler Compound Mn$_{1.4}$PtSn, Chem. Mater. 31, 5876–5880 (2019), doi:10.1021/acs.chemmater.9b02013.
Prototype Generator
aflow --proto=A3B2C2_tI28_122_ad_c_d --params=$a,c/a,z_{2},x_{3},x_{4}$