  Spin-orbit torques in noncentrosymmetric polycrystalline magnetic
heterostructures are usually described in terms of field-like and damping-like
torques. However, materials with a lower symmetry point group can exhibit
torques whose behavior substantially deviates from the conventional ones. In
particular, based on symmetry arguments it was recently proposed that systems
belonging to the C_{3v} point group display spin-orbit torques that can promote
field-free switching [Liu et al. Nature Nanotechnology 16, 277 (2021)]. In the
present work, we analyze the general form of the torques expected in C3v
crystals using the Invariant Theory. We uncover several new components that
arise from the coexistence of the three-fold rotation and mirror symmetries.
Using both tight binding model and first principles simulations, we show that
these unconventional torque components arise from the onset of trigonal warping
of the Fermi surface and can be as large as the damping-like torque. In other
words, the Fermi surface warping is a key indicator to the onset of field-free
switching in low symmetry crystals.
