  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 cm2 V-1 s-1 at 30 K and 350 cm2 V-1 s-1 at 300 K, implying that
Cr_Te crystals are ferromagnetic elemental semiconductors. When B // c // I,
the maximum negative MR is -27% at T = 20 K and B = 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
field B is parallel to the [100] crystallographic direction and show Landau
quantization dominated Shubnikov-de Haas (SdH) oscillations for B // [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.
