  Comparisons of the alignment of exoplanets with a common host star can be
used to distinguish among concurrent evolution scenarios. However, multi-planet
systems usually host mini-Neptunes and super-Earths, whose size make orbital
architecture measurements challenging. We introduce the Rossiter-McLaughlin
effect Revolutions technique, which can access spin-orbit angles of small
planets by exploiting the full information contained in spectral transit time
series. We validated the technique on published HARPS-N data of the
mini-Neptune HD3167c, refining its high sky-projected spin-orbit angle
(-108.9+5.4-5.5 deg), and we applied it to new ESPRESSO observations of the
super-Earth HD3167b, revealing an aligned orbit (-6.6+6.6-7.9 deg).
Surprisingly different variations in the contrast of the stellar lines occulted
by the planets can be reconciled with a latitudinal dependence of the stellar
line shape. In this scenario, a joint fit to both datasets constrains the
inclination of the star (111.6+3.1-3.3 deg) and the 3D spin-orbit angles of
HD3167b (29.5+7.2-9.4 deg) and HD3167c (107.7+5.1-4.9 deg). The projected
spin-orbit angles do not depend on the model for the line contrast variations,
and so, with a mutual inclination of 102.3+7.4-8.0 deg, we conclude that the
two planets are on perpendicular orbits. This could be explained by HD3167b
being strongly coupled to the star and retaining its primordial alignment,
whereas HD3167c would have been brought to a nearly polar orbit via secular
gravitational interactions with an outer companion. Follow-up observations and
dynamical evolution simulations are required to search for this companion and
explore this scenario. HD3167b is the smallest exoplanet with a confirmed
spectroscopic Rossiter-McLaughlin signal. Our new technique opens the way to
determining the orbital architectures of the super-Earth and Earth-sized planet
populations.
