  The observation of spinon excitations in the $S=\frac{1}{2}$ triangular
antiferromagnet Ca$_3$ReO$_5$Cl$_2$ reveals a quasi-one-dimensional (1D) nature
of magnetic correlations, in spite of the nominally 2D magnetic structure. This
phenomenon is known as frustration-induced dimensional reduction. Here, we
present high-field electron spin resonance spectroscopy and magnetization
studies of Ca$_3$ReO$_5$Cl$_2$, allowing us not only to refine spin-Hamiltonian
parameters, but also to investigate peculiarities of its low-energy spin
dynamics. We argue that the presence of the uniform Dzyaloshinskii-Moriya
interaction (DMI) shifts the spinon continuum in momentum space and, as a
result, opens a zero-field gap at the $\Gamma$ point. We observed this gap
directly. The shift is found to be consistent with the structural modulation in
the ordered state, suggesting this material as a perfect model
triangular-lattice system, where a pure DMI-spiral ground state can be
realized.
