  Strong spin-orbital coupling (SOC) was found previously to lead to dramatic
effects in quantum materials, such as those found in topological insulators. It
was shown theoretically that local noncentrosymmetricity resulting from the
rotation of RuO$_6$ octahedral in Sr$_3$Ru$_2$O$_7$ will also give rise to an
effective SOC\cite{SocSr327,MicroscopicnematicSr327}. In the presence of a
magnetic field applied along a specific in-plane direction, the Fermi surface
was predicted to undergo a reconstruction. Here we report results of our
in-plane magnetoresistivity and magnetothermopower measurements on single
crystals of Sr$_3$Ru$_2$O$_7$ with an electrical or a thermal current applied
along specific crystalline directions and a magnetic field rotating in the $ab$
plane (Fig. 1a), showing a minimal value for field directions predicted by the
local noncentrosymmetricity theory. Furthermore, the thermopower, and
therefore, the electron entropy, were found to be suppressed as the field was
applied perpendicular to the thermal current, which suggests that the spin and
the momentum in Sr$_3$Ru$_2$O$_7$ are locked over substantial parts of the
Fermi surface, likely originating from local noncentrosymmetricity as well.
