Spin-glass-like behavior of Ge:Mn

We present a detailed study of the magnetic properties of low-temperature molecular-beam-epitaxy-grown Ge:Mn dilute magnetic semiconductor films. We find strong indications for a frozen state of ${\mathrm{Ge}}_{1-x}{\mathrm{Mn}}_x$, with freezing temperatures of $T_f=12\mathrm{K}$ and $T_f=15\mathrm{K}$ for samples with $x=0.04$ and $x=0.2$, respectively, determined from the difference between field-cooled and zero-field-cooled magnetization. For ${\mathrm{Ge}}_{0.96}{\mathrm{Mn}}_{0.04}$, ac susceptibility measurements show a peak around $T_f$, with the peak position $T_f^{\prime }$ shifting as a function of the driving frequency $f$ by $\Delta T_f^{\prime }∕\left[T_f^{\prime }\Delta \log f\right]\approx 0.06$, whereas for sample ${\mathrm{Ge}}_{0.8}{\mathrm{Mn}}_{0.2}$ a more complicated behavior is observed. Furthermore, both samples exhibit relaxation effects of the magnetization after switching the magnitude of the external magnetic field below $T_f$ which are in qualitative agreement with the field- and zero-field-cooled magnetization measurements. These findings consistently show that Ge:Mn exhibits a frozen magnetic state at low temperatures and that it is not a conventional ferromagnet.

Figure 1

(a) Temperature dependence of the magnetization of the ${\mathrm{Ge}}_{0.96}{\mathrm{Mn}}_{0.04}$ sample. The measurements were performed at ${\mu }_0{H}_m=1\mathrm{mT}$ (solid symbols) and ${\mu }_0{H}_m=100\mathrm{mT}$ (open symbols). The sample was cooled down in the maximum external magnetic field (MFC, ${\mu }_0{H}_C=7\mathrm{T}$), in zero magnetic field (ZFC), and in a field identical to the measuring field (FC). The open stars denote the difference between FC and ZFC magnetization. (b) Logarithmic plot of FC-ZFC difference. (c) Magnification of the low-temperature regime of the measurements with ${\mu }_0{H}_m=100\mathrm{mT}$ in (a).

Figure 2

(Color online) (a) Illustration of the two different kinds of clusters present in our samples. (b) Schematic FC and ZFC magnetization curves for both kinds of clusters (black dotted curves for the contribution of the ${\mathrm{Mn}}_5{\mathrm{Ge}}_3$ clusters, red dashed curves for the Mn-rich nanoparticles) and the sum of both (solid blue curves).

Figure 3

(a) Real part ${\chi }^{\prime }\left(T\right)$ of the ac susceptibility of the ${\mathrm{Ge}}_{0.96}{\mathrm{Mn}}_{0.04}$ sample. The measurement was performed with ${\mu }_0{H}_{\mathit{dc}}=0\mathrm{T}$ and ${\mu }_0{H}_{\mathit{ac}}=0.5\mathrm{mT}$ at different driving frequencies $f=0.01\mathrm{Hz}$ (open squares), $f=0.2\mathrm{Hz}$ (solid circles), and $f=10\mathrm{Hz}$ (open circles). (b) Imaginary part ${\chi }^{″}\left(T\right)$ of the ac susceptibility.

Figure 4

(Color online) Real part ${\chi }^{\prime }\left(T\right)$ of the ac susceptiblity of the ${\mathrm{Ge}}_{0.96}{\mathrm{Mn}}_{0.04}$ sample in the vicinity of the peak positions. The notation is the same as in Fig. 3. The peak positions $T_f^{\prime }$ are indicated by arrows; the smooth solid lines are guides to the eye. The inset shows the dependence of the peak position temperatures $T_f^{\prime }$ (solid squares) on the measuring frequency $f$ fitted with the Vogel-Fulcher law (straight line).

Figure 5

Switching procedures of the external magnetic field (upper panels) for the time-dependent magnetization measurements shown schematically in the lower panels for (a) ZFC and (b) MFC.

Figure 6

Increase of magnetization $M_1\left(t\right)$ (a) and decay of magnetization $M_2\left(t\right)$ (c) and $M_3\left(t\right)$ (d) measured as a function of time at different constant measurement temperatures. The solid lines are fitted curves. (b) Magnetization $M_1\left(t\right)$ normalized to the magnetization $M_1\left(t_1\right)$.

Figure 7

Temperature dependence of fit parameters (a) $M_i^0$ and (b) $M_i^r$ of sample ${\mathrm{Ge}}_{0.96}{\mathrm{Mn}}_{0.04}$. The solid squares display $M_1^0$ and $M_1^r$, the open squares $M_2^0$ and $M_2^r$, and the open circles $M_3^0$ and $M_3^r$. The thick solid lines in (a) are the ZFC, FC, and MFC $M\left(T\right)$ measurements performed at ${\mu }_0{H}_m=100\mathrm{mT}$ (open symbols in Fig. 1).

Figure 8

(a) Temperature dependence of magnetization of sample ${\mathrm{Ge}}_{0.8}{\mathrm{Mn}}_{0.2}$. The notation is the same as in Fig. 1. (b) Logarithmic plot of FC-ZFC difference. (c) and (d) show the temperature dependence of the fit parameters $M^0$ and $M^r$, respectively. The solid squares display $M_1^0$ and $M_1^r$, the open squares $M_2^0$ and $M_2^r$, and the open circles denote $M_3^0$ and $M_3^r$. The thick solid lines in (c) are the ZFC, FC, and MFC $M\left(T\right)$ measurements performed at ${\mu }_0{H}_m=100\mathrm{mT}$, shown by open symbols in (a).

Figure 9

Real part ${\chi }^{\prime }\left(T\right)$ (a) and imaginary part ${\chi }^{″}\left(T\right)$ (b) of the ac susceptibility of ${\mathrm{Ge}}_{0.8}{\mathrm{Mn}}_{0.2}$ measured with ${\mu }_0{H}_{\mathit{dc}}=0\mathrm{T}$ and ${\mu }_0{H}_{\mathit{ac}}=0.5\mathrm{mT}$ at $f=0.2\mathrm{Hz}$ (solid circles), $f=10\mathrm{Hz}$ (open circles), and $f=1000\mathrm{Hz}$ (solid triangles).