Coexistence of logarithmic and SdH quantum oscillations in ferromagnetic Cr-doped tellurium single crystals

We report the synthesis of transition-metal-doped ferromagnetic elemental single-crystal semiconductors with quantum oscillations using the physical vapor transport method. The 7.7 atom% Cr-doped Te crystals (Cr:Te) show ferromagnetism, butterfly-like negative magnetoresistance in the low temperature (<3.8 K) and low field (<0.15 T) region, and high Hall mobility, e.g. 1320 cm²V^-1s^-1at 30 K and 350 cm²V^-1s^-1at 300 K, implying that Cr:Te crystals are ferromagnetic elemental semiconductors. WhenB// [001] // I, the maximum negative MR is ∼-27% atT= 20 K andB= 8 T. In the low temperature semiconducting region, Cr:Te crystals show strong discrete scale invariance dominated logarithmic quantum oscillations when the direction of the magnetic fieldBis parallel to the [100] crystallographic direction (B// [100]) and show Landau quantization dominated Shubnikov-de Haas oscillations forB// [210] direction, which suggests the broken rotation symmetry of the Fermi pockets in the Cr:Te crystals. The findings of coexistence of multiple quantum oscillations and ferromagnetism in such an elemental quantum material may inspire more study of narrow bandgap semiconductors with ferromagnetism and quantum phenomena.