Refined values of the mode-amplitudes (in Å) taking part in the symmetry breaking from Fm \overline{3} m to P 2_{1} / n (RT) for \mathrm{La}_{2} \mathrm{CoMnO}_{6} in the present work [PW] with all modes freed and [PW*] with only the mode-amplitude (see the text): \mathrm{GM}_{4}{ }^{+}, \mathrm{X}_{3}{ }^{+}and \mathrm{X}_{5}{ }^{+}. The results are compared to mode-amplitudes calculated for the materials in the \mathrm{Ln}_{2} \mathrm{MMnO} family, which also show the same space group P 2_{1} / n at RT: \mathrm{La}_{2} \mathrm{CoMnO}_{6}{ }^{2,6} \mathrm{Lu}_{2} \mathrm{CoMnO}_{6},{ }^{41} \mathrm{Nd}_{2} \mathrm{CoMnO}_{6},{ }^{42,43} \mathrm{La}_{2} \mathrm{NiMnO}_{6},{ }^{2} \mathrm{Sm}_{2} \mathrm{NiMnO}_{6},{ }^{5} \mathrm{ Tb}_{2} \mathrm{NiMnO}_{6},{ }^{5} \mathrm{Ho}_{2} \mathrm{NiMnO}_{6},{ }^{46} \mathrm{Y}_{2} \mathrm{NiMnO}_{6}{ }^{47} and Bi \mathrm{NiMnO}_{6}{ }^{48}
| Amplitude | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Irrep | Isotropy subgroup | \mathrm{La}_{2} \mathrm{CoMnO}_{6} | \mathrm{Lu}_{2} \mathrm{CoMnO}_{6} | \mathrm{Nd}_{2} \mathrm{CoMnO}_{6} | \mathrm{Ln}_{2} \mathrm{NiMnO}_{6} | \mathrm{Y}_{2} \mathrm{NiMnO}_{6} | \mathrm{Bi}_{2} \mathrm{NiMnO}_{6} | |||||||
| [PW] | [PW*] | 2 | 6 | 41 | 42 | 43 | \mathrm{Ni}^{2} | \mathrm{Sm}^{5} | \mathrm{Ho}^{46} | \mathrm{Tb}^{5} | 47 | 48 | ||
| F m \overline{3} m \rightarrow P 21 / n | ||||||||||||||
| \mathrm{GM}_{1}{ }^{+} | Fm \overline{3} m(225) | 0.004(11) | 0.000 | 0.14(3) | 0.17(2) | 0.09(3) | 0.11(2) | 0.15(1) | 0.05(4) | 0.18(4) | 0.09(2) | 0.16(3) | 0.15(3) | 0.06(5) |
| \mathrm{GM}_{3}{ }^{+} | I4/mmm (139) | 0.01(3) | 0.000 | 0.03(3) | 0.02(2) | 0.05(3) | 0.07(3) | 0.19(7) | 0.04(6) | 0.25(4) | 0.01(3) | 0.02(3) | 0.07(3) | 0.02(5) |
| \mathrm{GM}_{4}{ }^{+} | C 2 / m(12) | 1.087(6) | 1.080(3) | 1.12(3) | 1.10(2) | 1.84(4) | 1.32(3) | 1.29(8) | 0.73(5) | 1.46(5) | 1.70(3) | 1.51(3) | 1.65(3) | 1.35(7) |
| \mathrm{GM}_{5}{ }^{+} | C 2 / m(12) | 0.14(4) | 0.000 | 0.15(2) | 0.10(2) | 0.26(1) | 0.12(2) | 0.42(7) | 0.61(2) | 0.25(5) | 0.21(1) | 0.22(8) | 0.21(1) | 0.15(7) |
| \mathrm{X}_{2}{ }^{+} | P 4_{2} / m n m(136) | 0.042(15) | 0.000 | 0.07(3) | 0.01(2) | 0.09(3) | 0.01(2) | 0.04(7) | 0.09(2) | 0.02(5) | 0.04(2) | 0.12(3) | 0.03(2) | 0.01(6) |
| \mathrm{X}_{3}{ }^{+} | P4/mnc (128) | 0.523(6) | 0.532(5) | 0.53(3) | 0.58(2) | 1.31(3) | 1.02(2) | 0.96(7) | 0.40(2) | 0.83(5) | 1.27(2) | 1.06(3) | 1.27(2) | 0.68(6) |
| \mathrm{X}_{5}{ }^{+} | Pnnm (58) | 0.336(4) | 0.334(3) | 0.27(6) | 0.27(5) | 0.99(1) | 0.60(6) | 0.56(2) | 0.71(2) | 0.74(3) | 0.88(1) | 0.82(1) | 0.90(1) | 0.67(5) |
| Tolerance factor ( t_{\mathrm{obs}} ) | 0.9477 | 0.9477 | 0.9437 | 0.9436 | 0.8546 | 0.8926 | 0.8976 | 0.9795 | 0.8893 | 0.8578 | 0.8586 | 0.9020 | 0.8596 | |
| K-vector: \mathrm{GM}_{1}{ }^{+}(0,0,0), \mathrm{GM}_{3}{ }^{+}(0,0,0), \mathrm{GM}_{4}{ }^{+}(0,0,0), \mathrm{GM}_{5}{ }^{+}(0,0,0), \mathrm{X}_{2}{ }^{+}(0,1,0), \mathrm{X}_{3}{ }^{+}(0,1,0), \mathrm{X}_{5}{ }^{+}(0,1,0) Direction: \mathrm{GM}_{1}{ }^{+}(a), \mathrm{GM}_{3}{ }^{+}(a, 0), \mathrm{GM}_{4}{ }^{+}(a, a, 0), \mathrm{GM}_{5}{ }^{+}(-b, a,-a), \mathrm{X}_{2}{ }^{+}(0, a, 0), \mathrm{X}_{3}{ }^{+}(0, a, 0), \mathrm{X}_{5}{ }^{+}(a, a, 0,0, a,-a) |