Spin-parity effects in the resonant quantum coherence of the Néel vector in antiferromagnets withm-fold rotational symmetries

Abstract

Based on the two-sublattice model, the quantum interference effects induced by the topological phase term in the Euclidean action are studied in resonant quantum coherence of the N\'eel vector between energetically degenerate easy directions in single-domain antiferromagnetic nanoparticles with m-fold rotational symmetries around the z axis and reflection symmetry in the $x\ensuremath{-}y$ plane at zero magnetic field, where $m=3,$ $4$, and $6$, which corresponds to the trigonal, tetragonal, and hexagonal crystal symmetries, respectively. By applying the standard instanton technique in the spin-coherent-state path-integral representation, we evaluate both the Wentzel-Kramers-Brillouin exponent and the preexponential factors in the instanton's contribution to the tunneling level splitting. The Euclidean transition amplitudes between energetically degenerate easy directions are obtained by making use of the dilute instanton-gas approximation. The effective Hamiltonian approach is applied to give the final results of the ground-state tunneling level splittings for each kind of crystal symmetry. The low-lying tunneling level spectrum and the thermodynamic properties of magnetic tunneling states are found to depend significantly on the parity of the excess spin of single-domain antiferromagnet. The topological quenching of the ground-state tunneling level splitting for the half-integer excess spins obtained previously for the biaxial crystal symmetry (i.e., double-well system at zero magnetic field) can be recovered by a simple diagonalization of the effective Hamiltonian. It is shown that the effective Hamiltonian approach is equivalent to the dilute instanton-gas approximation. Possible relevance to experiments is also discussed.