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Resistance random access memory, short RRAM, which employs two or more resistive states of a material for data storage, has attracted considerable attention as a highly scalable future non-volatile memory concept.[1, 2] These memory cells that can also be described as so-called memristors are particularly interesting when multilevel resistance values or even analogue values should be stored and processed.[3–5] A large variety of binary and ternary oxides exhibit resistive switching phenomena, however, the details of the complex microscopic mechanisms are rarely understood and depend strongly on the specific material combination. In the search for promising oxide materials for future non-volatile memories, special attention has to be paid to their scaling capabilities. The issue of scaling is strongly linked to the question of, whether the switching current is distributed homogeneously across the device area or localized to one or a few conducting filaments. While in the former case the scaling limit will be connected to the minimum device area, that guarantees sufficient switching currents for a reliable circuit operation, in the latter case, scaling might suffer from too large filament dimensions or their insufficient density and regularity within the material. Complex transition metal oxides, eg manganites,[6–9] titanates and zirconates,[10, 11] usually exhibit different resistance states at opposite polarities of electrical stimulation. It has become widely accepted that this so-called bipolar resistive switching is connected with a voltage-driven oxygen vacancy movement and a resulting redox process.[12] Both, filamentary as well as homogenous …