  The magnetic properties of the high temperature alpha form of the CaCr2O4
compound have been investigated for the first time by magnetic susceptibility,
specific heat and powder neutron diffraction. The system undergoes a unique
magnetic phase transition at 43K to a long range order incommensurate helical
phase with magnetic propagation vector k=(0,0.3317(2),0). The magnetic model
proposed from neutron diffraction data shows that the plane of rotation of the
spins is perpendicular to the wave-vector, and that the magnetic modulation is
consistent with two modes belonging to distinct irreducible representations of
the group. The magnetic point group 2221' is not compatible with
ferroelectricity unlike the CuCrO2 delafossite [Kimura et al., Phys. Rev. B, 78
140401 (2008)] but predicts the existence of quadratic magnetoelectric effects,
discussed based on a Landau analysis.
