  We report the revised crystal structure, static and dynamic magnetic
properties of quasi-two dimensional honeycomb-lattice silver delafossite
Ag3Co2SbO6. The magnetic susceptibility and specific heat data are consistent
with the onset of antiferromagnetic long range order at low temperatures with
N\'eel temperature TN ~ 21.2 K. In addition, the magnetization curves revealed
a field-induced (spin-flop type) transition below TN in moderate magnetic
fields. The GGA+U calculations show the importance of the orbital degrees of
freedom, which maintain a hierarchy of exchange interaction in the system. The
strongest antiferromagnetic exchange coupling was found in the shortest Co-Co
pairs and is due to direct and superexchange interactions between the
half-filled xz+yz orbitals pointing directly to each other. The other four out
of six nearest neighbor exchanges within the cobalt hexagon are suppressed,
since for these bonds active half-filled orbitals turned out to be parallel and
do not overlap. The electron spin resonance (ESR) spectra reveal a Gaussian
shape line attributed to Co2+ ion in octahedral coordination with average
effective g-factor g=2.3+/-0.1 at room temperature and shows strong divergence
of ESR parameters below 120 K, which imply an extended region of short-range
correlations. Based on the results of magnetic and thermodynamic studies in
applied fields, we propose the magnetic phase diagram for the new
honeycomb-lattice delafossite.
