  We demonstrate that zero-field $\beta$-detected nuclear quadrupole resonance
and spin relaxation of low energy $^8$Li can be used as a sensitive local probe
of structural phase transitions near a surface. We find that the transition
near the surface of a SrTiO$_3$ single crystal occurs at $T_c \sim 150$ K,
i.e., 45 K higher than $T^{bulk}_c$, and that the tetragonal domains formed
below $T_c$ are randomly oriented.
