  Some short gamma-ray bursts (SGRBs) exhibit a short duration and spectral
hard emission (referred to as a "hard spike") followed by a slightly longer
soft emission (known as a "soft tail"). We identified nine SGRBs with known
redshift in the \textit{Swift}/BAT gamma-ray burst catalog by specifically
searching for the soft tail. We found that spectra of these SGRBs can be
described as a cutoff power-law model for both hard spike and soft tail, and
both show time variation keeping the $E_{\rm peak}$--$L_{\rm iso}$ correlation.
This suggests that the emission mechanism of both phenomena is identical.
Furthermore, we found a trend of luminosity evolution as a function of
redshift. This phenomenon suggests that these bursts originate from sources
that have intrinsically bright and/or energy density concentrated within a
narrower jet at higher redshift. We demonstrate that the average jet opening
angle, derived from the jet break, can be explained by considering a model
based on a strongly redshift-dependent jet opening angle.
