  Low-frequency 1/f voltage noise has been employed to probe stochastic charge
dynamics in AlO$_{x}$-based non-volatile resistive memory devices exhibiting
both resistive switching (RS) and magneto-resistive (MR) effects. A
1/f$^{\gamma}$ noise power spectral density is observed in a wide range of
applied voltage biases. By analyzing the experimental data within the framework
of Hooge's empirical relation, we found that the Hooge's parameter $\alpha$ and
the exponent $\gamma$ exhibit a distinct variation upon the resistance
transition from the low resistance state (LRS) to the high resistance state
(HRS), providing strong evidence that the electron trapping/de-trapping
process, along with the electric field-driven oxygen vacancy migration in the
AlO$_x$ barrier, plays an essential role in the charge transport dynamics of
AlO$_x$-based RS memory devices.
