grid overlaid on the imaged area. This corresponds to a
pixel size of 10 × 10 nm2. Figure 8a,b illustrates a typical
ambient c-AFM result including topography and a conductivity
map collected at 100 mV shown in Figure 8b.
Notice that the current is maximized at the edges of the
pillars extending into the BFO matrix. Furthermore, some
of the pillars feature a central spot of low conductivity,
while others are fully conductive. The inset of Figure 8d
illustrates details of the FORC-IV experiment, specifically
the applied triangular bias waveform, shown in blue, and
average current response for the entire 50 × 50 pixel
spectroscopy area as a function of time, shown in green.
Figure 8d shows the average current loop for the whole
bias waveform as a function of voltage; note that these
curves are essentially featureless with little to no hysteresis
and are highly smooth in both forward and reverse voltage
sweep directions.
The multidimensional nature of these data, combined
with the lack of analytical or numerical physical models,
naturally calls for multivariate statistical analysis in order
to extract the most comprehensive view of the physical
behavior of the CFO-BFO system. While PCA and ICA
are powerful methods that allow one to take a closer
look into the structure of the data, a preferable method
would preserve physical information in the data and
allow fully quantitative analysis. Such a method will
separate the data into a combination of well-defined
components with clear spectroscopic behavior that has
an intensity weight component, providing insight into
the spatial distribution of the behavior. Ideally, these