  In recent years, studies on cyclic molecular nanomagnets have captivated the
attention of researchers. These magnets are finite in size and contain very
large spins. They are interesting because they possess macroscopic quantum
tunneling of N\'eel vectors. For antiferromagnetic molecular nanomagnets with
finite number of even-numbered coupled spins, tunneling involves two classical
localized N\'eel ground states separated by a magnetic energy barrier. The
question is: can such phenomena be observed in nano magnets with odd number of
magnetic ions? The answer is not directly obvious because cyclic chains with
odd-numbered coupled spins are frustrated as one cannot obtain a perfect N\'eel
order. These frustrated spins can indeed be observed experimentally, so they
are of interest. In this Letter, we theoretically investigate macroscopic
quantum tunneling in these odd spin systems with arbitrary spins $s$, in the
presence of a magnetic field applied along the plane of the magnet. In contrast
to systems with an even-numbered coupled spins, the ground state of the cyclic
odd-spin system contains a topological soliton due to spin frustration. Thus
the classical ground state is $2N$-fold degenerate as the soliton can be placed
anywhere along the ring with total $S_z=\pm s$. Small quantum fluctuations
delocalize the soliton with a formation of an energy band. We obtain this
energy band using degenerate perturbation theory at order $2s$. We show that
the soliton ground state is chiral for half-odd integer spins and non-chiral
for integer spins. From the structure of the energy band we infer that as the
value of the spin increases the inelastic polarized neutron-scattering
intensity may increase or decrease depending on the strengths of the parameters
of the Hamiltonian.
