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We report the synthesis of transition-metal-doped ferromagnetic elementalsingle-crystal semiconductors with quantum oscillations using the physicalvapor transport method. The 7.7 atom% Cr-doped Te crystals (Cr_Te) showferromagnetism, butterfly-like negative magnetoresistance in the lowtemperature (< 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 thatCr_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 temperaturesemiconducting region, Cr_Te crystals show strong discrete scale invariancedominated logarithmic quantum oscillations when the direction of the magneticfield B is parallel to the [100] crystallographic direction and show Landauquantization dominated Shubnikov-de Haas (SdH) oscillations for B // [210]direction, which suggests the broken rotation symmetry of the Fermi pockets inthe Cr_Te crystals. The findings of coexistence of multiple quantumoscillations and ferromagnetism in such an elemental quantum material mayinspire more study of narrow bandgap semiconductors with ferromagnetism andquantum phenomena.

Coexistence of Logarithmic and SdH Quantum Oscillations in Ferromagnetic Cr-doped Tellurium Single Crystals