Spin parity effects in a monoaxial chiral ferromagnetic chain

While spin parity effects, physics crucially depending on whether the spin quantum number S is half -odd integral or integral, have for decades been a source of new developments for the quantum physics of antiferromagnetic spin chains, the investigation into their possible ferromagnetic counterparts has remained largely unchartered, especially in the fully quantum (as opposed to the semiclassical) regime. Here we present such studies for monoaxial chiral ferromagnetic spin chains. We start by examining magnetization curves for finite-sized systems, where a magnetic field is applied perpendicular to the helical axis. For half-odd integer S, the curves feature discontinuous jumps identified as a series of level crossings, each accompanied by a shift of the crystal momentum k by an amount of pi. The corresponding curves for integer valued S are continuous and exhibit crossover processes. For the latter case, k = 0 throughout. These characteristics are observed numerically when the strength of the Dzyaloshinskii-Moriya interaction (DMI) D is comparable to or larger than that of the ferromagnetic exchange interaction J. Solitons are known to be responsible for stepwise changes seen in magnetization curves in the classical limit. These findings therefore prompt us to revise the notion of a soliton, for arbitrary S, into a quantum mechanical entity. To unravel this phenomenon at the fully quantum level as is appropriate to spin chains with small S, we examine in detail special limiting Hamiltonians amenable to rigorous analysis, consisting of only the DMI and the Zeeman energy. Dubbed the DH model (for S = 12 ) and the projected DH (pDH) model (for general S), they have a set of 2S conserved quantities, each of which is the number of solitons of a specific integer-valued height (as measured in the Sz basis), which ranges from 1 to 2S. We discuss how to determine the exact crystal momentum of the lowest-energy state belonging to a sector with a given set of the 2S soliton numbers. Combined with energetic considerations, this information enables us to reproduce the spin parity effect in the magnetization curves. Finally, we show that the ground states of the special models have substantial numerical overlap with those for generic systems with a finite exchange interaction, suggesting the same physics to be valid there as well.