Quaternary Heusler alloys Co2Cr1−xFexAl with varying Cr to Fe ratio x were investigated experimentally and theoretically. The electronic structure and spectroscopic properties were calculated using the full relativistic Korringa–Kohn–Rostocker method with coherent potential approximation to account for the random distribution of Cr and Fe atoms as well as random disorder. Magnetic effects are included using spin dependent potentials in the local spin density approximation.Magnetic circular dichroism in x-ray absorption was measured at the L2,3 edges of Co, Fe and Cr of the pure compounds and the x = 0.4 alloy in order to determine element specific magnetic moments. Calculations and measurements show an increase of the magnetic moments with increasing iron content. Resonant (560–800 eV) soft x-ray as well as high resolution–high energy (⩾3.5 keV) hard x-ray photo emission was used to probe the density of the occupied states in Co2Cr0.6Fe0.4Al.

Ga,Mn)As is a paradigm of a diluted magnetic semiconductor which shows ferromagnetism induced by doped hole carriers. With a few controversial models emerging from numerous experimental and theoretical studies, the mechanism of the ferromagnetism in (Ga,Mn)As still remains a puzzling enigma. In this article, we use soft x-ray angle-resolved photoemission spectroscopy to positively identify the ferromagnetic Mn 3d-derived impurity band (IB) in (Ga,Mn)As. The band appears dispersionless and hybridized with the light-hole band of the host GaAs. These findings conclude the picture of the valence-band structure of (Ga,Mn)As disputed for more than a decade. The nondispersive character of the IB and its location in vicinity of the valence-band maximum indicate that the Mn 3d-derived IB is formed as a split-off Mn-impurity state predicted by the Anderson impurity model. Responsible for the ferromagnetism is predominantly the transport of hole carriers in the IB.

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.