  With first-principles kinetic simulations, we show that a large-scale
Alfv\'en wave (AW) propagating in an inhomogeneous background decays into
kinetic Alfv\'en waves (KAWs), triggering ion and electron energization. We
demonstrate that the two species can access unequal amounts of the initial AW
energy, experiencing differential heating. During the decay process, the
electric field carried by KAWs produces non-Maxwellian features in the particle
VDFs, in accordance with space observations. The process we present solely
requires the interaction of a large-scale AW with a magnetic shear and may be
relevant for several astrophysical and laboratory plasmas.
