We investigate the low-temperature magnetic properties of the molecule-based chiral spin chain [Cu(pym)(H$_2$O)$_4$]SiF$_6cdot$H$_2$O (pym = pyrimidine). Electron-spin resonance, magnetometry and heat capacity measurements reveal the presence of staggered $g$ tensors, a rich low-temperature excitation spectrum, a staggered susceptibility and a spin gap that opens on the application of a magnetic field. These phenomena are reminiscent of those previously observed in non-chiral staggered chains, which are explicable within the sine-Gordon quantum-field theory. In the present case, however, although the sine-Gordon model accounts well for the form of the temperature-dependence of the heat capacity, the size of the gap and its measured linear field dependence do not fit with the sine-Gordon theory as it stands. We propose that the differences arise due to additional terms in the Hamiltonian resulting from the chiral structure of [Cu(pym)(H$_2$O)$_4$]SiF$_6cdot$H$_2$O, particularly a uniform Dzyaloshinskii-Moriya coupling and a four-fold periodic staggered field.
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