Far-infrared study of gapped spin excitations in the chains of Sr$_{14}$Cu$_{24}$O$_{41}$

We studied using far-infrared spectroscopy, magnetic field and temperature dependence of the spin gap modes in the chains of Sr$_{14}$Cu$_{24}$O$_{41}$. Two triplet modes T$_{1}$ and T$_{2}$ were found in the center of the Brillouin zone at E$_{1}$=77.8 cm$^{-1 }$(9.65 meV) and E$_{2}$=87.7 cm$^{-1 }$(10.86 meV) in zero magnetic field. Both excitations are electric dipole active modes. T$_{1}$ mode is excited when the light E-vector is along the $b$ crystallographic axis and T$_{2}$ is excited when the light E-vector is along the $a$-axis, both perpendicular to the chain direction. The selection rules of the transitions are compatible with dynamic Dzyaloshinskii-Moria interaction mechanism. Up to the field of 18T the electron g-factors of two modes are similar, g$_{1c}$=2.049 and g$_{2c}$=2.055 with magnetic field applied along the chains. Linewidth of both modes is 1 cm$^{-1}$ (0.12 meV) at 4K and increases with T. The temperature dependence of the mode energies is in agreement with the inelastic neutron scattering (INS) results from other groups. However the T$_{1}$ mode has not been observed by INS. The zone structure model of magnetic excitations in the chains is not complete and must include a triplet mode at 9.65 meV in the center of the magnetic Brillouin zone.