Magnetic and electronic transport percolation in epitaxial ${\mathrm{Ge}}_{1–x}{\mathrm{Mn}}_x$ films

Electronic transport and magnetic properties of ${\mathrm{Ge}}_{1–x}{\mathrm{Mn}}_x∕\mathrm{Ge}\left(100\right)$ films are investigated as a function of Mn dilution. Depending on $x$, characteristic temperatures separate different regimes in both properties. Resistivity exhibits an insulatorlike behavior in the whole temperature range and, below about $80\mathrm{K}$, two distinct activation energies are observed. At a higher temperature value, $T_R$, resistivity experiences a sudden reduction. The Hall coefficient shows a strong contribution from the anomalous Hall effect and, at $T_R$, a sign inversion, from positive to negative, is recorded. The magnetic properties, inferred from magneto-optical Kerr effect, evidence a progressive decrease of the ferromagnetic long range order as the temperature is raised, with a Curie temperature $T_C$ not far from $T_R$. The transport and magnetic results are qualitatively consistent with a percolation mechanism due to bound magnetic polarons in a GeMn diluted magnetic semiconductor, with localized holes [A. Kaminski and S. Das Sarma, Phys. Rev. B 68, 235210 (2003)].

Figure 1

Absolute Hall coefficient values measured at $850\mathrm{Oe}$ as a function of the temperature for the investigated set of GeMn alloy films. Squares: ${\mathrm{Ge}}_{0.99}{\mathrm{Mn}}_{0.01}$; triangles: ${\mathrm{Ge}}_{0.949}{\mathrm{Mn}}_{0.051}$. Open and closed symbols indicate positive and negative values, respectively.

Figure 2

Resistivity as a function of temperature. Squares: ${\mathrm{Ge}}_{0.99}{\mathrm{Mn}}_{0.01}$; open triangles: ${\mathrm{Ge}}_{0.949}{\mathrm{Mn}}_{0.051}$. In the inset, the resistance as a function of temperature is shown, including also the data relative to the sample constituted only by the Ge buffer on the Ge(100) wafer (diamonds).

Figure 3

Arrhenius plot of the resistivity vs the reciprocal of the thermal energy. Squares: ${\mathrm{Ge}}_{0.99}{\mathrm{Mn}}_{0.01}$; crosses: ${\mathrm{Ge}}_{0.974}{\mathrm{Mn}}_{0.026}$; circles: ${\mathrm{Ge}}_{0.967}{\mathrm{Mn}}_{0.033}$; open triangles: ${\mathrm{Ge}}_{0.949}{\mathrm{Mn}}_{0.051}$. The curves change their slope at a characteristic temperature, $T_S$. The arrow indicates $T_S$ for the ${\mathrm{Ge}}_{0.967}{\mathrm{Mn}}_{0.033}$ film.

Figure 4

(a) Longitudinal (●) and polar (◻) MOKE hysteresis loops for the ${\mathrm{Ge}}_{0.949}{\mathrm{Mn}}_{0.051}$ film at $12\mathrm{K}$. The vertical scale has been renormalized to allow a comparison. The saturation MOKE rotation is 0.0018° and 0.0423° for longitudinal and polar geometry, respectively. The difference between these values causes the evident smaller signal-to-noise ratio for the longitudinal hysteresis. (b) MOKE hysteresis loops for the ${\mathrm{Ge}}_{0.967}{\mathrm{Mn}}_{0.033}$ film at several temperatures. Note the irregular shape of the loops at intermediate temperature $\left(189\mathrm{K}\right)$ suggesting an inhomogeneous magnetic structure.

Figure 5

Temperature dependence of the magnetic parameters measured by MOKE for the ${\mathrm{Ge}}_{1–x}{\mathrm{Mn}}_x$ films: (a) saturation; (b) remanence; (c) coercive field. The symbols refer to the different values of $x$, as explained in the legend of (b). The lines in (a) are a guide to the eye; in (b) and (c) the lines are the fitting curves following a relation of the form ${(1-T∕T_C)}^{\beta }$ with $\beta =1∕2$ and $\beta =1$ for (b) and (c), respectively. The insets in (b) and (c) show in detail the data close to $T_C$; the axis labels are the same as for the main figures and the lines are guides to the eye. Note that the inset (b) reveals a concavity of opposite sign with respect to the lower temperature trend for remanence.

Figure 6

Dependence of $T_{\mathit{\text{cover}}}$ (triangles) and $T_S$ (circles, see the inset of Fig. 2) on Mn content, $x$. The values of $T_{\mathit{\text{cover}}}$ have been computed using Eq. (3) and the data quoted in Table , with $a_0=2\times {10}^{-9}\mathrm{m}$. The two lines are linear regressions of the data points.