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(a) Comparison of the polarizations of calculated by the average model (open circle), the effective Hamiltonian with interface correction (filled circle), and the first-principles calculations (diamond) with respect to the bulk BTO polarization . We took the reference for the effective Hamiltonian and for the first-principles calculations, respectively. (b) Strain dependence of the polarizations of and superlattices as obtained from the average model and the current model with the interface corrections.
Schematic representation of the TO phonon modes in BTO (down), STO (up), and (center). Large (red) circle corresponds to Ba, medium (blue) circle to Sr, small dark (black) circle to Ti, and small open (white) circle to O. Numbers beside the bold arrows represent the displacements of each TO mode, and numbers beside the dotted arrows indicate the participation of the bulk BTO and STO modes in the mode of .
Best fits to the total energy curves per -formula unit of the local mode distortions at the (a) and (b) points. The lines with square, circle, and diamond symbols represent the total energy curves with respect to the normal modes of superlattice, bulk BTO, and bulk STO, respectively. The line marked by triangles is for the total energy curve obtained by using the BTO and STO bulk-averaged normal modes. The solid line without symbol shows the energy curve obtained from the average of coefficients of BTO and STO.
Harmonic and anharmonic coefficients for the self-energy of local modes in , , the average of BTO and STO, and .
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