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A contribution from the next-nearest-neighboring exchange energies is considered as a secondary effect since the infrared active phonons involve no modulation of the oxygen-oxygen bond mediating next-nearest-neighboring Mn ions. A possible contribution from Tb ions is not included since the long-range order of their spin moments occurs below about 7 K (Ref.).
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-
As reported in Refs., the excitation related to the Tb ion is located around 135 cm-1 just above the lowest-lying phonon for E a. While the spectral weight of this mode is comparable to that of the lowest-lying phonon, it shows little change upon the transition to the A-AFM state (Ref.). Therefore, this contribution can be excluded when discussing the spectral weight of the EM which is completely suppressed in the A-AFM state.
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While the spectral-weight changes for ia =3 and 7 (Fig.) exhibit finite differences between the x=0.3 and 0.5 compounds, their possible connection to the ferroelectricity is not clear at the present stage.
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