Magnetism of Bi₂Se₃ thin films with Eu-rich flat inclusions

We report the results of experimental and theoretical studies of Eu-doped Bi₂Se₃ thin films with extremely inhomogeneous distribution of magnetic component. The obtained electron microscopy images suggest that Eu atoms are concentrated within platelet-like nanoinclusions. The number of inclusions grows with the increase in Eu content, x. Moreover, at relatively high x values, the stacks of platelets (inclusions located one under another) become rather frequent. A comparative analysis of magnetic properties of the films under study reveals no pronounced changes of their temperature dependence with the increase in x, which, however, leads to the decrease in the average magnetic moment [Formula: see text] per Eu atom. A theoretical analysis of different mechanisms contributing to a possible magnetic ordering in the Eu-doped films demonstrates that at small distances (i.e. within a platelet) a dominant contribution is related to the RKKY interaction via electrons in the bulk, while the ordering at inter-platelet distances is governed by magnetic dipole-dipole interaction. The latter implies the antiferromagnetic ordering within the stacks of platelets explaining a drop of [Formula: see text] per Eu atom. We employ the model of a metallic spin glass to estimate the transition temperature, characterising the interaction within the ensemble of randomly distributed magnetic platelets. This estimate gives satisfactory agreement with the experiment, even if we take into account a finite film thickness, thus, neglecting the interaction anisotropy and including only the antiferromagnetism related to the stacking. While the overall contribution of interface Dirac electrons is damped in the systems under study, we argue that the obtained results can be used for the investigation of ultrathin films with analogous impurity profile, where this contribution should be clearly pronounced.