Structural symmetry changes in SmB ₆ - 2D correlation spectroscopy and principal component analysis

2D correlation analysis (2DCOS) and principal component analysis (PCA) have been performed on temperature-dependent Raman spectra from 12 K to 300 K of SmB ₆ single crystals grown from Boron with a purity of 99.9% (3N) or 99.9999% (6N). Significant differences in the Raman spectra of SmB ₆ (3N) and SmB ₆ (6N) are observed. The Raman active T _2g , E _g , and A _1g modes of SmB ₆ (3N) are broader and shift to higher wavenumbers compared with those of SmB ₆ (6N). The results of 2DCOS and PCA on temperature-dependent Raman spectra of SmB ₆ (3N) and SmB ₆ (6N) give us further information. We find that all the T _2g , E _g , and A _1g modes of SmB ₆ (6N) are single bands, while those of SmB ₆ (3N) show all doublet features. The appearance of multiple bands in Raman vibrational modes of SmB ₆ (3N) sample implies that the structure of boron octahedra of the SmB ₆ (3N) has lower symmetry than that of SmB ₆ (6N). Our findings in 2DCOS and PCA of the Raman spectra strongly support the differences in the behavior of SmB ₆ (3N) and SmB ₆ (6N).