Evidence of a large quantum shift of the antiferromagnetic resonance in three quasi-one-dimensional antiferromagnets

Antiferromagnetic resonance experiments in three one-dimensional manganese compounds [CsMn${\mathrm{Cl}}_3$′2${\mathrm{H}}_2$O (CMC), (${\mathrm{C}{\mathrm{H}}_3)}_2$ N${\mathrm{H}}_2$ Mn${\mathrm{Cl}}_3$ (DMMC), and (${\mathrm{C}{\mathrm{H}}_3)}_4$ NMn${\mathrm{Cl}}_3$ (TMMC)] show disagreement with the classical antiferromagnetic resonance theory. In the three compounds we observe a positive shift in magnetic field of the resonance lines corresponding to the low-frequency mode. We show that this shift is larger for the compounds with smaller ratio $\left|\frac{J^{\prime }}{J}\right|$ and try to explain this effect in terms of the quantum spin reduction of the magnon energy.