There are more than 1795 magnetic phases recorded in MAGNDATA (http://webbdcrista1.ehu.es/magndata/) (we called them are magnetic phases because one magnetic material may have several magnetic structures). Apart from the incommensurate magnetic structures, there are 1655 magnetic phases with BCS-ID 0.1-0.835, 1.0.1-1.0.52, 1.1-1.663, 2.1-2.86, and 3.1-3.19. Then removing duplicate data, there remains 1432 magnetic phases. We find 496 magnetic phases have SHG effect, 451 magnetic phases have the LMO effect, and 100 magnetic phases have both LMO and SHG effects, as shown in Fig. 4(a). The SHG classification of 496 magnetic phases is shown in Fig. 4(b). We find that each type of SHG has corresponding magnetic phases, and the SHG type with largest number of magnetic phases is PT-wP. The judgements of all magnetic phases are presented in the following. It is worth noting that we only judge the types of SHG and LMO effect here, but their specific numerical values still need to be calculated or experimented further.

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Fig. 4 Statistics on SHG types in MAGNDATA database. (a) Statistics of materials with SHG and LMO effect in the 1432 magnetic phases. (b) Classification the 496 magnetic phases with SHG effect.
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Notation:

[1] Parent SG: the space group of parent phase ,

[2] MSG: magnetic space group,

[3] MSG: magnetic point group,

[4] SHG type: see the definition in xxx,

[5] LMO: linear magneto-optic effect (Faraday effect and Kerr effect), see xxxx,

[6] The “®” in formula menans the magnetic material with same symmetry has already appeared/repeated.

BCS-ID Formula Parent SG MSG MPG SHG type LMO
0.1 LaMnO3_3 PnmaPnma (62) PnmaPn'ma' (62.448) mmmm'm'm ×\times \checkmark
0.2 Cd2_2Os2_2O7_7 Fd3mFd\overline{3}m (227) Fd3mFd\overline{3}m' (227.131) m3mm\overline{3}m' ×\times ×\times
0.3 Ca3_3LiOsO6_6 R3cR\overline{3}c (167) C2/cC2'/c' (15.89) 2/m2'/m' ×\times \checkmark
0.4 NiCr2_2O4_4 I41/amdI4_1/amd (141) FdddFd'd'd (70.530) mmmm'm'm ×\times \checkmark
0.5 Cr2_2S3_3 R3R\overline{3} (148) P1P\overline{1} (2.4) 1\overline{1} ×\times \checkmark
0.6 YMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}cm (185.197) 6mm6mm O-woP ×\times
0.7 ScMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}c'm' (185.201) 6mm6m'm' BW-woP \checkmark
0.8 ScMnO3_3 P63cmP6_3cm (185) P63P6_{3} (173.129) 66 O-woP \checkmark
0.9 GdB4_4 P4/mbmP4/mbm (127) P4/mbmP4/m'b'm' (127.395) 4/mmm4/m'm'm' PT-wP ×\times
0.10 DyFeO3_3 PnmaPnma (62) P212121P2_{1}2_{1}2_{1} (19.25) 222222 O-wP ×\times
0.11 DyFeO3_3 PnmaPnma (62) Pna21Pn'a'2_{1} (33.148) mm2m'm'2 BW-wP \checkmark
0.12 U3_3Ru4_4Al12_{12} P63/mmcP6_3/mmc (194) CmcmCmcm' (63.461) mmmm'mm PT-wP ×\times
0.13 Ca3_3Co2x_{2-x}Mnx_{x}O6_6 R3cR\overline{3}c (167) R3cR3c (161.69) 3m3m O-wP ×\times
0.14 Gd5_5Ge4_4 PnmaPnma (62) PnmaPnm'a (62.444) mmmm'mm PT-wP ×\times
0.15 MnF2_2 P42/mnmP4_2/mnm (136) P42/mnmP4_{2}'/mnm' (136.499) 4/mmm4'/mm'm ×\times ×\times
0.16 EuTiO3_3 I4/mcmI4/mcm (140) FmmmFm'mm (69.523) mmmm'mm PT-wP ×\times
0.17 FePO4_4 PnmaPnma (62) P212121P2_{1}2_{1}2_{1} (19.25) 222222 O-wP ×\times
0.18 BaMn2_2As2_2 I4/mmmI4/mmm (139) I4/mmmI4'/m'm'm (139.536) 4/mmm4'/m'm'm PT-wP ×\times
0.19 MnTiO3_3 R3R\overline{3} (148) R3R\overline{3}' (148.19) 3\overline{3}' PT-wP ×\times
0.20 MnTe2_2 Pa3Pa\overline{3} (205) Pa3Pa\overline{3} (205.33) m3m\overline{3} ×\times ×\times
0.21 PbNiO3_3 R3cR3c (161) R3cR3c (161.69) 3m3m O-woP ×\times
0.22 DyB4_4 P4/mbmP4/mbm (127) PbamPb'am (55.355) mmmm'mm PT-wP ×\times
0.23 Ca3_3Mn2_2O7_7 Cmc21Cmc2_1 (36) Cmc21Cm'c2_{1}' (36.174) mm2m'm2' BW-woP \checkmark
0.24 LiMnPO4_4 PnmaPnma (62) PnmaPn'm'a' (62.449) mmmm'm'm' PT-wP ×\times
0.25 NaOsO3_3 PnmaPnma (62) PnmaPn'ma' (62.448) mmmm'm'm ×\times \checkmark
0.26 TmAgGe P62mP\overline{6}2m (189) Amm2Am'm'2 (38.191) mm2m'm'2 BW-woP \checkmark
0.27 YFe4_4Ge2_2 PnnmPnnm (58) PnnmPn'n'm' (58.399) mmmm'm'm' PT-wP ×\times
0.28 LiFeSi2_2O6_6 P21/cP2_1/c (14) P21/cP2_{1}/c' (14.78) 2/m2/m' PT-wP ×\times
0.29 Er2_2Ti2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}'/am'd (141.554) 4/mmm4'/mm'm ×\times ×\times
0.30 YbMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}'c'm (185.199) 6mm6'mm' BW-woP ×\times
0.31 HoMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}c'm' (185.201) 6mm6m'm' BW-woP \checkmark
0.32 HoMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}cm (185.197) 6mm6mm O-woP ×\times
0.33 HoMnO3_3® P63cmP6_3cm (185) P63cmP6_{3}cm (185.197) 6mm6mm O-woP ×\times
0.34 La0.5_{0.5}Sr0.5_{0.5}FeO2.5_{2.5}F0.5_{0.5} PnmaPnma (062) PnmaPn'ma' (62.448) mmmm'm'm ×\times \checkmark
0.35 Cu2_2OSeO3_3 P213P2_13 (198) R3R3 (146.10) 33 O-woP \checkmark
0.36 NiF2_2 P42/mnmP4_2/mnm (136) PnnmPnn'm' (58.398) mmmm'm'm ×\times \checkmark
0.37 U3_3Al2_2Si3_3 I4I4 (79) C2C2' (5.15) 22' BW-woP \checkmark
0.38 GaFeO3_3 Pna21Pna2_1 (33) Pna21Pna'2_{1}' (33.147) mm2m'm2' BW-woP \checkmark
0.39 Nd2_2NaRuO6_6 P21/nP2_1/n (14) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.40 Mn2_2O3_3-alpha PbcaPbca (61) PbcaPbca (61.433) mmmmmm ×\times ×\times
0.41 Mn2_2O3_3-alpha® PbcaPbca (61) PbcaPbca (61.433) mmmmmm ×\times ×\times
0.42 HoMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}'c'm (185.199) 6mm6'mm' BW-woP ×\times
0.43 HoMnO3_3 P63cmP6_3cm (185) P63cmP6_{3}'cm' (185.2) 6mm6'mm' BW-woP ×\times
0.44 YMnO3_3 P63cmP6_3cm (185) P63P6_{3}' (173.131) 66' BW-woP ×\times
0.45 La2_2NiO4_4 P42/ncmP4_2/ncm (138) PccnPc'c'n (56.369) mmmm'm'm ×\times \checkmark
0.46 CaBaCo4_4O7_7 Pbn21Pbn2_1 (33) Pna21Pna'2_{1}' (33.147) mm2m'm2' BW-woP \checkmark
0.47 Gd2_2Sn2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}'/amd' (141.555) 4/mmm4'/mm'm ×\times ×\times
0.48 Tb2_2Sn2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.49 Ho2_2Ru2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.50 MnTiO3_3 R3cR3c (161) CcCc' (9.39) mm' BW-woP \checkmark
0.51 Ho2_2Ru2_2O7_7® Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.52 Ky_{y}Fe2x_{2-x}Se2_2 I4/mI4/m (87) C2/mC2'/m' (12.62) 2/m2'/m' ×\times \checkmark
0.53 Rby_{y}Fe2x_{2-x}Se2_2 I4/mI4/m (87) C2/mC2'/m' (12.62) 2/m2'/m' ×\times \checkmark
0.54 Rby_{y}Fe2x_{2-x}Se2_2 I4/mI4/m (87) I4/mI4/m' (87.78) 4/m4/m' PT-wP ×\times
0.55 Ky_{y}Fe2_2-xSe2_2 I4/mI4/m (87) I4/mI4/m' (87.78) 4/m4/m' PT-wP ×\times
0.56 Ba2_2CoGe2_2O7_7 P421mP\overline{4}2_1m (113) Cmm2Cm'm2' (35.167) mm2m'm2' BW-woP \checkmark
0.57 ScFeO3_3 R3cR3c (161) CcCc' (9.39) mm' BW-woP \checkmark
0.58 CoAl2_2O4_4 Fd3mFd\overline{3}m (227) I41/amdI4_{1}'/a'm'd (141.556) 4/mmm4'/m'm'm PT-wP ×\times
0.59 Cr2_2O3_3 R3cR\overline{3}c (167) R3cR\overline{3}'c' (167.106) 3m\overline{3}'m' PT-wP ×\times
0.60 [NH2_2(CH3_3)2_2]n_{n}[FeIII^{III}FeII^{II}(HCOO)6_6]n_n R3cR\overline{3}c (167) R3cR\overline{3}c' (167.107) 3m\overline{3}m' ×\times \checkmark
0.61 Li2_2FeP2_2O7_7 P21/cP2_1/c (14) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.62 SrMn2_2V2_2O8_8 I41cdI4_1cd (110) Iba2Ib'a2' (45.237) mm2m'm2' BW-woP \checkmark
0.63 Ho2_2CrSbO7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.64 MnV2_2O4_4 I41/aI4_1/a (88) I41/aI4_{1}/a (88.81) 4/m4/m ×\times \checkmark
0.65 Fe2_2O3_3-alpha R3cR\overline{3}c (167) C2/cC2'/c' (15.89) 2/m2'/m' ×\times \checkmark
0.66 Fe2_2O3_3-alpha R3cR\overline{3}c (167) P1P\overline{1} (2.4) 1\overline{1} ×\times \checkmark
0.67 BiFe0.5_{0.5}Sc0.5_{0.5}O3_3 Ima2Ima2 (46) Ima2Im'a2' (46.243) mm2m'm2' BW-woP \checkmark
0.68 BiFe0.5_{0.5}Sc0.5_{0.5}O3_3 PnmaPnma (62) PnmaPn'm'a (62.446) mmmm'm'm ×\times \checkmark
0.69 Co4_4(OH)2_2(C10_{10}H16_{16}O4_4)3_3 P21/cP2_1/c (14) P21/cP2_{1}'/c' (14.79) 2/m2'/m' ×\times \checkmark
0.70 Na3_3Co(CO3_3)2_2Cl Fd3Fd\overline{3} (203) Fd3Fd\overline{3} (203.26) m3m\overline{3} ×\times ×\times
0.71 Li2_2Ni(SO4_4)2_2 PbcaPbca (61) PbcaPb'c'a' (61.437) mmmm'm'm' PT-wP ×\times
0.72 CaMnBi2_2 P4/nmmP4/nmm (129) P4/nmmP4'/n'm'm (129.416) 4/mmm4'/m'm'm PT-wP ×\times
0.73 SrMnBi2_2 I4/mmmI4/mmm (139) I4/mmmI4'/m'm'm (139.536) 4/mmm4'/m'm'm PT-wP ×\times
0.74 Mn3_3Cu0.5_{0.5}Ge0.5_{0.5}N Pm3mPm\overline{3}m (221) R3mR\overline{3}m (166.97) 3m\overline{3}m ×\times ×\times
0.75 Cr2_2WO6_6 P42/mnmP4_2/mnm (136) PnnmPn'nm (58.395) mmmm'mm PT-wP ×\times
0.76 Cr2_2TeO6_6 P42/mnmP4_2/mnm (136) PnnmPn'nm (58.395) mmmm'mm PT-wP ×\times
0.77 Tb2_2Ti2_2O7_7 Fd3mFd\overline{3}m (227) R3mR\overline{3}m' (166.101) 3m\overline{3}m' ×\times \checkmark
0.78 NiN2_2O6_6 R3R\overline{3} (148) R3R\overline{3} (148.17) 3\overline{3} ×\times \checkmark
0.79 CaIrO3_3 CmcmCmcm (63) CmcmCm'cm' (63.464) mmmm'm'm ×\times \checkmark
0.80 U2_2Pd2_2In P4/mbmP4/mbm (127) P4/mbmP4'/m'bm' (127.394) 4/mmm4'/m'm'm PT-wP ×\times
0.81 U2_2Pd2_2Sn® P4/mbmP4/mbm (127) P4/mbmP4'/m'bm' (127.394) 4/mmm4'/m'm'm PT-wP ×\times
0.82 Gd2_2CuO4_4 AeamAeam (64) CmcaCm'ca' (64.476) mmmm'm'm ×\times \checkmark
0.83 LiFeP2_2O7_7 P21P2_1 (4) P21P2_{1} (4.7) 22 O-woP \checkmark
0.84 Mn2_2FeMoO6_6 R3R3 (146) R3R3 (146.10) 33 O-woP \checkmark
0.85 KCo4_4(PO4_4)3_3 PnnmPnnm (58) PnnmPnn'm' (58.398) mmmm'm'm ×\times \checkmark
0.86 KMn4_4(PO4_4)3_3 PnamPnam (62) PnmaPnma' (62.445) mmmm'mm PT-wP ×\times
0.87 NaFePO4_4 PnmaPnma (62) PnmaPnma' (62.445) mmmm'mm PT-wP ×\times
0.88 LiNiPO4_4 PnmaPnma (62) PnmaPnm'a (62.444) mmmm'mm PT-wP ×\times
0.89 BaMn2_2Bi2_2 I4/mmmI4/mmm (139) I4/mmmI4'/m'm'm (139.536) 4/mmm4'/m'm'm PT-wP ×\times
0.90 Rb2_2Fe2_2O(AsO4_4)2_2 PnmaPnma (62) PnmaPnma (62.441) mmmmmm ×\times ×\times
0.91 Rb2_2Fe2_2O(AsO4_4)2_2 PnmaPnma (62) PnmaPn'ma' (62.448) mmmm'm'm ×\times \checkmark
0.92 CaMn2_2Sb2_2 P3m1P\overline{3}m1 (164) C2/mC2'/m (12.60) 2/m2'/m PT-wP ×\times
0.93 Ca2_2Fe2_2O5_5 PcmnPcmn (62) PcmnPcm'n' (62.446) mmmm'm'm ×\times \checkmark
0.94 TeNiO3_3 PnmaPnma (62) PnmaPn'm'a (62.446) mmmm'm'm ×\times \checkmark
0.95 LiFePO4_4 PnmaPnma (62) PnmaPnma' (62.445) mmmm'mm PT-wP ×\times
0.96 CoSO4_4 PnmaPnma (62) PnmaPnma (62.441) mmmmmm ×\times ×\times
0.97 FeSb2_2O4_4 P42/mbcP4_2/mbc (135) Pmc21Pmc2_{1} (26.66) mm2mm2 O-wP ×\times
0.98 YBaMn2_2O5.5_{5.5} IcamIcam (72) IbamIb'a'm (72.543) mmmm'm'm ×\times \checkmark
0.99 YBaMn2_2O5.5_{5.5} IcamIcam (72) C2/mC2/m (12.58) 2/m2/m ×\times \checkmark
0.100 YCr0.5_{0.5}Mn0.5_{0.5}O3_3 PnmaPnma (62) PnmaPn'ma' (62.448) mmmm'm'm ×\times \checkmark
0.101 Mn2_2GeO4_4 PnmaPnma (62) PnmaPn'm'a (62.446) mmmm'm'm ×\times \checkmark
0.102 Mn2_2GeO4_4 PnmaPnma (62) PnmaPnma (62.441) mmmmmm ×\times ×\times
0.103 Mn2_2GeO4_4 PnmaPnma (62) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.104 ErVO3_3 PbnmPbnm (62) P21/mP2_{1}'/m' (11.54) 2/m2'/m' ×\times \checkmark
0.105 ErVO3_3 PbnmPbnm (62) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.106 DyVO3_3 PbnmPbnm (62) P21/mP2_{1}'/m' (11.54) 2/m2'/m' ×\times \checkmark
0.107 Ho2_2Ge2_2O7_7 P41212P4_12_12 (92) P41212P4_{1}2_{1}2 (92.111) 422422 O-woP ×\times
0.108 Mn3_3Ir Pm3mPm\overline{3}m (221) R3mR\overline{3}m' (166.101) 3m\overline{3}m' ×\times \checkmark
0.109 Mn3_3Pt Pm3mPm\overline{3}m (221) R3mR\overline{3}m' (166.101) 3m\overline{3}m' ×\times \checkmark
0.110 Cr2_2O3_3 R3cR\overline{3}c (167) C2/cC2'/c (15.87) 2/m2'/m PT-wP ×\times
0.111 Co4_4Nb2_2O9_9 P3c1P\overline{3}c1 (165) P3c1P\overline{3}'c'1 (165.94) 3m\overline{3}'m' PT-wP ×\times
0.112 FeBO3_3 R3cR\overline{3}c (167) C2/cC2'/c' (15.89) 2/m2'/m' ×\times \checkmark
0.113 NiCO3_3 R3cR\overline{3}c (167) C2/cC2/c (15.85) 2/m2/m ×\times \checkmark
0.114 CoCO3_3 R3cR\overline{3}c (167) C2/cC2/c (15.85) 2/m2/m ×\times \checkmark
0.115 MnCO3_3 R3cR\overline{3}c (167) C2/cC2/c (15.85) 2/m2/m ×\times \checkmark
0.116 FeCO3_3 R3cR\overline{3}c (167) R3cR\overline{3}c (167.103) 3m\overline{3}m ×\times ×\times
0.117 LuFeO3_3 P63cmP6_3cm (185) P63cmP6_{3}c'm' (185.201) 6mm6m'm' BW-woP \checkmark
0.118 Ba5_5Co5_5ClO13_{13} P63/mmcP6_3/mmc (194) P63/mmcP6_{3}'/m'm'c (194.268) 6/mmm6'/m'mm' ×\times ×\times
0.119 CoSe2_2O5_5 PbcnPbcn (60) PbcnPb'cn (60.419) mmmm'mm PT-wP ×\times
0.120 LiFe(SO4_4)2_2 P21/cP2_1/c (14) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.121 Li2_2Co(SO4_4)2_2 P21/cP2_1/c (14) P21/cP2_{1}'/c' (14.79) 2/m2'/m' ×\times \checkmark
0.122 Li2_2Mn(SO4_4)2_2 P21/cP2_1/c (14) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.123 Mn3_3NiN Pm3mPm\overline{3}m (221) R3R\overline{3} (148.17) 3\overline{3} ×\times \checkmark
0.124 Mn3_3NiN® Pm3mPm\overline{3}m (221) R3R\overline{3} (148.17) 3\overline{3} ×\times \checkmark
0.125 MnGeO3_3 R3R\overline{3} (148) R3R\overline{3}' (148.19) 3\overline{3}' PT-wP ×\times
0.126 NpCo2_2 Fd3mFd\overline{3}m (227) I41/amdI4_{1}'/a'm'd (141.556) 4/mmm4'/m'm'm PT-wP ×\times
0.127 Dy3_3Al5_5O12_{12} Ia3dIa\overline{3}d (230) Ia3dIa\overline{3}d' (230.148) m3mm\overline{3}m' ×\times ×\times
0.128 FeSO4_4F C2/cC2/c (15) C2/cC2'/c' (15.89) 2/m2'/m' ×\times \checkmark
0.129 Cu3_3Mo2_2O9_9 PnmaPnma (62) P212121P2_{1}'2_{1}'2_{1} (19.27) 2222'2'2 BW-wP \checkmark
0.130 Cu3_3Mo2_2O9_9 PnmaPnma (62) Pmc21Pm'c2_{1}' (26.68) mm2m'm2' BW-wP \checkmark
0.131 Mn(N(CN2_2))2_2 PnnmPnnm (58) PnnmPnn'm' (58.398) mmmm'm'm ×\times \checkmark
0.132 Fe(N(CN2_2))2_2 PnnmPnnm (58) PnnmPnn'm' (58.398) mmmm'm'm ×\times \checkmark
0.133 Ni3_3B7_7O13_{13}Cl Pca21Pca2_1 (29) Pca21Pc'a2_{1}' (29.101) mm2m'm2' BW-woP \checkmark
0.134 Mn3_3B7_7O13_{13}I Pca21Pca2_1 (29) Pca21Pc'a2_{1}' (29.101) mm2m'm2' BW-woP \checkmark
0.135 Ni3_3B7_7O13_{13}Br Pca21Pca2_1 (29) Pca21Pc'a2_{1}' (29.101) mm2m'm2' BW-woP \checkmark
0.136 Co3_3B7_7O13_{13}Br Pca21Pca2_1 (29) Pca21Pc'a2_{1}' (29.101) mm2m'm2' BW-woP \checkmark
0.137 Cu2_2V2_2O7_7 Fdd2Fdd2 (43) Fdd2Fd'd'2 (43.227) mm2m'm'2 BW-woP \checkmark
0.138 BiCrO3_3 C2/cC2/c (15) C2/cC2/c (15.85) 2/m2/m ×\times \checkmark
0.139 BiCrO3_3 C2/cC2/c (15) P1P\overline{1} (2.4) 1\overline{1} ×\times \checkmark
0.140 LuFe4_4Ge2_2 P42/mnmP4_2/mnm (136) PnnmPn'n'm' (58.399) mmmm'm'm' PT-wP ×\times
0.141 Tb5_5Ge4_4 PnmaPnma (62) PnmaPnm'a (62.444) mmmm'mm PT-wP ×\times
0.142 Fe2_2TeO6_6 P42/mnmP4_2/mnm (136) P42/mnmP4_{2}/m'n'm' (136.503) 4/mmm4/m'm'm' PT-wP ×\times
0.143 Cr2_2TeO6_6® P42/mnmP4_2/mnm (136) PnnmPn'nm (58.395) mmmm'mm PT-wP ×\times
0.144 Cr2_2WO6_6® P42/mnmP4_2/mnm (136) PnnmPn'nm (58.395) mmmm'mm PT-wP ×\times
0.145 Co3_3TeO6_6 C2/cC2/c (15) C2/cC2'/c (15.87) 2/m2'/m PT-wP ×\times
0.146 EuZrO3_3 PnmaPnma (62) PnmaPnm'a (62.444) mmmm'mm PT-wP ×\times
0.147 EuZrO3_3 PnmaPnma (62) PnmaPn'm'a' (62.449) mmmm'm'm' PT-wP ×\times
0.148 La2_2LiRuO6_6 P21/nP2_1/n (14) P21/cP2_{1}/c (14.75) 2/m2/m ×\times \checkmark
0.149 Nd3_3Ru4_4Al12_{12} P63/mmcP6_3/mmc (194) CmcmCm'c'm (63.462) mmmm'm'm ×\times \checkmark
0.15 NiS2_2 Pa3Pa\overline{3} (205) Pa3Pa\overline{3} (205.33) m3m\overline{3} ×\times ×\times
0.151 Tm2_2Mn2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.152 LiFePO4_4 PnmaPnma (62) P21/cP2_{1}/c' (14.78) 2/m2/m' PT-wP ×\times
0.153 Bi2_2RuMnO7_7 Fd3mFd\overline{3}m (227) FdddFd'd'd (70.530) mmmm'm'm ×\times \checkmark
0.154 Er2_2Ru2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}'/am'd (141.554) 4/mmm4'/mm'm ×\times ×\times
0.155 CaMnGe2_2O6_6 C2/cC2/c (15) P1P\overline{1}' (2.6) 1\overline{1}' PT-wP ×\times
0.156 CaMnGe2_2O6_6 C2/cC2/c (15) C2/cC2'/c (15.87) 2/m2'/m PT-wP ×\times
0.157 Yb2_2Sn2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.158 Yb2_2Ti2_2O7_7 Fd3mFd\overline{3}m (227) I41/amdI4_{1}/am'd' (141.557) 4/mmm4/mm'm' ×\times \checkmark
0.159 DyCoO3_3 PbnmPbnm (62) PnmaPn'm'a' (62.449) mmmm'm'm'