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Magnetic and dielectric properties of the hexagonal triangular latticeantiferromagnet 2H-AgFeO2 have been studied by neutron diffraction, magneticsusceptibility, specific heat, pyroelectric current, and dielectric constantmeasurements. The ferroelectric polarization, P ~ 5 {\mu}C/m2, has been foundto appear below 11 K due to a polar nature of the magnetic ground state of thesystem. In the temperature range of 11 K < T < 18 K, an incommensurate spindensity wave (ICM1) with the nonpolar magnetic point group mmm1' and the k1 =(0,q1_b,0; q1_b = 0.390-0.405)propagation vector takes place. Below 14 K, aproper screw ordering (ICM2) and k2 = (0,q2_b,0; q2_b = 0.385-0.396) appears asa minor phase which coexists with ICM1 and the ground state down to thelowestmeasured temperature 5.5 K. No ferroelectric polarization associated withthe ICM2 phase was observed in agreement with its nonpolar point group 2221'.Finally, a spiral order with cycloid and proper screw components (ICM3), and k3= (q3_a,q3_b,0; q3_a = 0.0467, q3_b = 0.349) emerges below 11 K as the groundstate of the system. Based on the deduced magnetic point group 21', we concludethat the ferroelectric polarization in ICM3 is parallel to the c axis and iscaused by the inverse Dzyloshinskii-Moriya effect with p1 ~ rij x (Si x Sj ).Unlike the rhombohedral 3R-AgFeO2 polytype, the additional contribution to themacroscopic polarization p2 ~ Si x Sj is not allowed in the present case due tothe symmetry constraints imposed by the hexagonal lattice of 2H-AgFeO2.

Magnetic ordering and ferroelectricity in multiferroic 2H-AgFeO2: Comparison between hexagonal and rhombohedral polytypes