We consider a domain wall in the mesoscopic quasi-one-dimensional samp
le (wire or stripe) of weakly anisotropic two-sublattice antiferromagn
et, and estimate the probability of tunneling between two domain wall
states with different chirality, in the Limits of weak and strong rhom
bicity. Topological effects forbid tunneling for the systems with half
-integer spin S of magnetic atoms which consist of an odd number of ch
ains n(perpendicular to). External magnetic field yields an additional
contribution to the Berry phase, resulting in oscillating field depen
dence of the tunneling rate with the period proportional to root JK/n(
perpendicular to), where J and K are exchange and anisotropy constants
, respectively, and in the appearance of two different tunnel splittin
gs in any setup involving a mixture of odd and even n(perpendicular to
). [S0163-1829(98)06242-0].