(Color online) (a) TEM plane view along  of an 80 nm-thick Ge0.9Mn0.1 thin film grown on Ge(001) at 100 °C using molecular beam epitaxy. The columns’ diameter and density are 3 nm and 35 000 μm−2, respectively. (b) Discretization of the physical regions (Ge matrix and Mn-rich nanocolumns) using the finite element generation of the gmsh package (Ref. 37). The calculation box contains 15 nanocolumns randomly distributed in the Ge matrix and almost corresponds to a 25 nm × 25 nm square of the TEM image. The mesh has been made finer in the vicinity of the columns. Neumann boundary conditions were applied with a uniform normal current on the bottom edge (incoming) and top edge (outcoming) and a vanishing normal current on the lateral edges.
(Color online) (a) Simulated temperature dependence of the saturation magnetization of nanocolumns using a simple Bloch law. The columns are superparamagnetic with a blocking temperature TB = 0.1 × TC , in agreement with experimental data. (b) Magnetization curves for different temperatures; nanocolumns are assumed to be identical noninteracting single magnetic domains. Above TB , they are superparamagnetic, and their magnetization curves are simulated using Langevin functions.
(Color online) Results of numerical simulations. (a),(c) Magnetoresistance and (b),(d) Hall angle as a function of the b value. a and t are set to 100 and 0.5, respectively. (e) The magnetoresistance and (f) the Hall angle as a function of temperature t for a = 100 and b = 1000. In (a), the inset shows the high field MR for b = 20 and b = −20.
(Color online) The (a) MR and (b) Hall angle for broad ranges of a and b values. The temperature was set to t = 0.1, and the field to 5 T.
(Color online) (a) The magnetization, (b) the magnetoresistance and Hall angle, and (c)–(f) maps of current density vectors and equipotential lines for four different applied fields: 0 T, 0.05 T, 0.2 T, and 2 T. The following parameters were used: a = 100, b = 1000, and t = 0.5. The color scale is related to the current intensity and is kept the same for all four magnetic fields.
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