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Ferroic domain walls are currently investigated by several state-of-the art techniques in order to get a better understanding of their distinct, functional properties. Here, Principal Component Analysis (PCA) of Raman maps is used to study ferroelectric domain walls (DWs) in LiNbO3 and ferroelastic DWs in NdGaO3. It is shown that PCA allows to quickly and reliably identify small Raman peak variations at ferroelectric DWs and that the value of a peak shift can be deduced - accurately and without a-priori - from a first order Taylor expansion of the spectra. The ability of PCA to separate the contribution of ferroelastic domains and DWs to Raman spectra is emphasized. More generally, our results provide a novel route for the statistical analysis of any property mapped across a DW.
Magnetotransport measurements on small single crystals of Cr, the elemental antiferromagnet, reveal the hysteretic thermodynamics of the domain structure. The temperature dependence of the transport coefficients is directly correlated with the real-s
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any b
The domain structure of uniaxial ferroelectric lithium niobate single crystals is investigated using Raman spectroscopy mapping. The influence of doping with magnesium and poling at room temperature is studied by analysing frequency shifts at domain
Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlyin
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fiel