  We have successfully synthesized three quasi-2D geometrically frustrated
magnetic compounds (\alpha-MCr_2O_4, M=Ca, Sr, Ba) using the
spark-plasma-sintering technique. All these members of the \alpha-MCr_2O_4
family consist of the stacking planar triangular lattices of Cr$^{3+}$ spins
(${\rm S}=3/2$), separated by non-magnetic alkaline earth ions. Their
corresponding magnetic susceptibility, specific heat, dielectric permittivity
and ferroelectric polarization are systematically investigated. A long-range
magnetic ordering arises below the N\'{e}el temperature (around 40K) in each
member of the \alpha-MCr_2O_4 family, which changes to the quasi-120\degree
proper-screw-type helical spin structure at low temperature. A very small but
confirmed spontaneous electric polarization emerges concomitantly with this
magnetic ordering. The direction of electric polarization is found within the
basal triangular plane. The multiferroicity in \alpha-MCr_2O_4 can not be
explained within the frameworks of the magnetic exchange striction or the
inverse Dzyaloshinskii-Moriya interaction. The observed results are more
compatible with the newly proposed Arima mechanism that is associated the d-p
hybridization between the ligand and transition metal ions, modified by the
spin-orbit coupling. The evolution of multiferroic properties with the
increasing inter-planar spacing (as M changes from Ca to Ba) reveals the
importance of interlayer interaction in this new family of frustrated magnetic
systems.
