Anomalous Hall effect in polycrystalline Mn$_{x}$Si$_{1-x}$ ($x\approx0.5$) films with the self-organized distribution of crystallites over their shapes and sizes

The structural, transport, and magnetic characteristics of polycrystalline Mn$_{x}$Si$_{1-x}$ ($x\approx0.51$–$0.52$) films grown by pulsed laser deposition onto Al$_2$O$_3$($0001$) substrates when the low-energy components are deposited owing to collisions with the atoms of the buffer gas have been studied in the “shadow” geometry. The magnetization of these films is determined by two ferromagnetic phases — the high-temperature phase with the Curie temperature $T_{\mathrm{C}}\approx 370$ K and the low-temperature one with $T_{\mathrm{C}}\approx 46$ K. The anomalous Hall effect changes sign from positive to negative with a decrease in temperature. The sign change occurs in the temperature range of $30$–$50$ K; the specific value of this temperature depends on the thickness of the Mn$_{x}$Si$_{1-x}$ film. The results can be interpreted in terms of the structural self-organization related to the formation of two layers in the course of film growth. These layers have nearly the same chemical composition but significantly differ in the shapes and sizes of crystallites. This leads to a drastic difference in the values of $T_{\mathrm{C}}$ and in the value and the sign of the anomalous Hall effect for such layers.