  A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a
nonvanishing parallel spinor field; here the connection is assumed to be
Levi-Civita. We generalise this definition to metric compatible spacetimes with
torsion and describe basic properties of such spacetimes. We use our
generalised pp-waves for constructing new explicit vacuum solutions of
quadratic metric-affine gravity.
