Antiferromagnetic molecular nanomagnets with odd-numbered coupled spins

Abstract: 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.