Origin of the large positive magnetoresistance of $\mathrm{G}{\mathrm{e}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ granular thin films

$\mathrm{G}{\mathrm{e}}_{1-x}\mathrm{M}{\mathrm{n}}_x$ (GeMn) granular thin films are a unique and promising material for spintronic applications owing to their large positive magnetoresistance (MR). Previous studies of GeMn have suggested that the large MR is related to the nanospinodal decomposition of GeMn into Mn-rich ferromagnetic nanoparticles and a Mn-poor paramagnetic matrix. However, the microscopic origin of the MR has not yet been clarified. Here, we develop a method to separately investigate the magnetic properties of the nanoparticles and the matrix, utilizing the extremely high sensitivity of x-ray magnetic circular dichroism (XMCD) to the local magnetic state of each atom. We find that the MR ratio is proportional to the product of the magnetizations originating from the nanoparticles and the matrix. This result indicates that the spin-polarized holes in the nanoparticles penetrate into the matrix and that these holes undergo first order magnetic scattering by the paramagnetic Mn atoms in the matrix, which induces the large MR.

Figure 1

Transmission electron microscope lattice image of the $\mathrm{G}{\mathrm{e}}_{0.86}\mathrm{M}{\mathrm{n}}_{0.14}$ layer projected along the $\mathrm{Ge}\langle 110\rangle$ axis. The nanoparticles are indicated by white dashed circles. By the spatially resolved energy dispersive x-ray spectroscopy, the local Mn concentrations at *1 (matrix) and *2 (nanoparticle) are estimated to be ∼6 and ∼60%, respectively.

Figure 2

(a) $\mathrm{Mn}-L_{2,3}$ edge XAS $[({\mu }^{+}+{\mu }^{-})/2]$ spectrum for the $\mathrm{G}{\mathrm{e}}_{0.86}\mathrm{M}{\mathrm{n}}_{0.14}$ film at 6 K with a magnetic field ${\mu }_{0}H=7\mathrm{T}$ applied perpendicular to the film surface. The inset shows a magnified plot of the spectrum at the $\mathrm{Mn}-L_3$ edge. (b) $\mathrm{Mn}-L_{2,3}$ edge XMCD ($={\mu }^{+}-{\mu }^{-}$) spectra for the $\mathrm{G}{\mathrm{e}}_{0.86}\mathrm{M}{\mathrm{n}}_{0.14}$ film at 6 K with various magnetic fields H applied perpendicular to the film surface. The inset shows a magnified plot of the spectra at the $\mathrm{Mn}-L_3$ edge. Here, the XMCD data have been normalized at $c$.

Figure 3

(a)–(c) Experimentally obtained XMCD-H curves (a) and derived FM (b) and PM (c) components of the XMCD-H curves for the $\mathrm{G}{\mathrm{e}}_{0.86}\mathrm{M}{\mathrm{n}}_{0.14}$ film at various temperatures.

Figure 4

(a) and (b) Experimentally obtained XMCD spectra (red curve), derived FM (green triangles), and PM (blue circles) components of the XMCD spectra at 6 K with ${\mu }_{0}H=7\mathrm{T}$ applied perpendicular to the film surface for the $\mathrm{G}{\mathrm{e}}_{0.86}\mathrm{M}{\mathrm{n}}_{0.14}$ film (a) and $\mathrm{G}{\mathrm{e}}_{0.91}\mathrm{M}{\mathrm{n}}_{0.09}$ film (b).

Figure 5

(a) and (b) MR ratio (blue, black, and gray curves) as a function of ${\mu }_{0}H$ applied perpendicular to the film surface for the $\mathrm{G}{\mathrm{e}}_{0.86}\mathrm{M}{\mathrm{n}}_{0.14}$ film (a) and the $\mathrm{G}{\mathrm{e}}_{0.91}\mathrm{M}{\mathrm{n}}_{0.09}$ film (b). The magnetic field dependence of the product of the FM and PM components of the XMCD intensity is also plotted (red points and curves). (c) and (d) Schematic illustration of the spatial distribution of the spin-polarized holes (pink regions) originating from the Mn-rich nanoparticles (black dashed circles) when the temperature $T\le T_{\mathrm{p}}$ (c) and $T_{\mathrm{p}}<T\le 100\mathrm{K}$ (d). The red and blue arrows correspond to the magnetic moments of the Mn atoms in the FM nanoparticles and PM matrix, respectively.