Magnetically doped topological insulators, possessing an energy gap created at the Dirac point through time-reversal-symmetry breaking, are predicted to exhibit exotic phenomena including the quantized anomalous Hall effect and a dissipationless transport, which facilitate the development of low-power-consumption devices using electron spins. Although several candidates of magnetically doped topological insulators were demonstrated to show long-range magnetic order, the realization of the quantized anomalous Hall effect is so far restricted to the Cr-doped (Sb,Bi)2Te3 system at extremely low temperature; however, the microscopic origin of its ferromagnetism is poorly understood. Here we present an element-resolved study for Cr-doped (Sb,Bi)2Te3 using X-ray magnetic circular dichroism to unambiguously show that the long-range magnetic order is mediated by the p-hole carriers of the host lattice, and the interaction between the Sb(Te) p and Cr d states is crucial. Our results are important for material engineering in realizing the quantized anomalous Hall effect at higher temperatures.

Cuprous oxide films were successfully electrodeposited onto three different substrates through the reduction of copper lactate in alkaline solution at pH = 10. The substrates include indium tin oxide film coated glass, n-Si wafer with (001) orientation and Au film evaporated onto Si substrate. The substrate effects on the structural and optical properties of the electrodeposited films are investigated by in situ voltammetry, current versus time transient measurement, ex situ x-ray diffraction, scanning electron microscopy, UV-vis transmittance and reflectance and photoluminescence techniques. The results indicate that the choice of substrate can strongly affect the film morphology, structure and optical properties.

We classify indecomposable non-projective Gorenstein-projective modules over a monomial algebra via the notion of perfect paths. We apply this classification to a quadratic monomial algebra and describe explicitly the stable category of its Gorenstein-projective modules.