Magnetic correlations in the magnetic topological insulator (Cr,Sb)2Te3

Chromium-doped ${\mathrm{Sb}}_{2}{\mathrm{Te}}_{3}$ is a magnetic topological insulator (MTI), which belongs to the $(\mathrm{Sb},{\mathrm{Bi})}_{2}(\mathrm{Se},{\mathrm{Te})}_{3}$ family. When doped with the transition metals V, Cr, and Mn this family displays long-range ferromagnetic order above liquid nitrogen temperature and is currently intensely explored for quantum device applications. Despite the large magnetic ordering temperature, the experimental observation of dissipationless electrical transport channels, i.e., the quantum anomalous Hall effect, is limited in these materials to temperatures below $\ensuremath{\approx}2$ K. Inhomogeneities in the MTI have been identified as a major concern, affecting the coupling between the Dirac states and the magnetic dopants. Nevertheless, details on the local magnetic order in these materials are not well understood. Here, we report the study of the magnetic correlations in thin films using a combination of muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$, and magnetic soft x-ray spectroscopy and imaging. $\ensuremath{\mu}\mathrm{SR}$ provides two key quantities for understanding the microscopic magnetic behavior: The magnetic volume fraction, i.e., the percentage of the material that is ferromagnetically ordered, and the relaxation rate, which is sensitive to the magnetic static $(\ensuremath{\approx}\ensuremath{\mu}\mathrm{s})$ and dynamic disorder. By choosing different implantation depths for the muons, one can further discriminate between near-surface and bulk properties. No evidence for a surface enhancement of the magnetic ordering is observed, but, instead, we find evidence of small magnetically ordered clusters in a paramagnetic background, which are coupled. The significant magnetic field shift that is present in all samples indicates a percolation transition that proceeds through the formation and growth of magnetically ordered spin clusters. We further find that fluctuations are present even at low temperatures, and that there appears to be a transition between superparamagnetism and superferromagnetism.