Random telegraph noise from magnetic nanoclusters in the ferromagnetic semiconductor $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$

Measurements of the low-frequency electrical noise in the ferromagnetic semiconductor $(\mathrm{Ga},\mathrm{Mn})\mathrm{As}$ reveal an enhanced integrated noise at low temperature. For moderate localization, we find a $1∕f$ normalized power spectrum density over the entire range of temperatures studied $(4.2\mathrm{K}<T<70\mathrm{K})$. However, for stronger localization and a high density of Mn interstitials, we observe Lorentzian noise spectra accompanied by random telegraph noise. Magnetic field dependence and annealing studies suggest that interstitial Mn defects couple with substitutional Mn atoms to form nanoscale magnetic clusters characterized by a net moment of $\sim 20{\mu }_{\mathrm{B}}$ whose fluctuations modulate hole transport.

Figure 1

(Color online) (a) Normalized PSD of sample $A$ at two temperatures showing $1∕f$ dependence (dashed line). (b) Temperature dependence of the integrated normalized PSD (left) and ${\rho }_{xx}$ (right) for sample $A$. Inset shows the ${\rho }_{xx}\left(T\right)$ over an expanded temperature range. (c) Normalized PSD of sample $B$ at different temperatures. Dashed line shows $1∕f$ and $1∕f^2$ relations. Strong deviations of PSD from $1∕f$ are clear over range $6\mathrm{K}\lesssim T\lesssim 29\mathrm{K}$. (d) Temperature dependence of the integrated normalized PSD (left) and ${\rho }_{xx}$ (right) for sample $B$. Inset shows the ${\rho }_{xx}\left(T\right)$ over an expanded temperature range.

Figure 2

(Color online) (a) Time-dependent voltage fluctuations in sample $B$, showing RTN. (b) $f{S}_V\left(f\right)∕V^2$ at different temperatures in sample $B$. Solid lines are fits to Lorentzian spectra with a superposition of a $1∕f$ background [Eq. (2)]. (c) Relative strengths of the Lorentzian term $\left(A\right)$ and the $1∕f$ term $\left(B\right)$ obtained by fits to Eq. (2). Inset shows the corner frequency $f_c$ vs $T$.

Figure 3

(Color online) (a) Magnetic field dependence of the relative rms fluctuation (solid squares) at $T=9\mathrm{K}$. For comparison, we also plot the GPHE with red (blue) circles for up (down) field sweeps. (b) Time traces of RTN at different fields, also at $T=9\mathrm{K}$.

Figure 4

(Color online) (a) Magnetic field dependence of energy difference $\mathrm{\Delta }E$ between the two states of the TLF in sample $B$ at $T=6\mathrm{K}$. (b) Comparison between RTN at $T=6\mathrm{K}$ in as-grown and annealed pieces of sample $B$.