Spin-phase interference, coherent superposition, and quantum tunneling at excited levels in nano-antiferromagnets

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.