  The spin-phase interference effects are studied analytically in resonant
quantum tunneling of the N\'{e}el vector between degenerate excited levels in
nanometer-scale single-domain antiferromagnets in the absence of an external
magnetic field. We consider a model for mesoscopic antiferromagnets with
uncompensated excess spins for the more general structure of magnetic
anisotropy, such as biaxial, trigonal, tetragonal and hexagonal crystal
symmetry. This study provides a nontrivial generalization of the Kramers
degeneracy for double-well system to coherently spin tunneling at ground states
as well as low-lying excited states in AFM system with $m$-fold rotational
symmetry around the $\hat{z}$ axis. The energy level spectrum and the
thermodynamic properties of magnetic tunneling states are found to depend
significantly on the parity of the excess spins at sufficiently low
temperatures. Possible relevance to experiments is also discussed.
