Abstract
Elementary excitations in valence bond magnets have a finite spin gap $\ensuremath{\Delta}=g{\ensuremath{\mu}}_{B}{H}_{c}$ to well-defined triplet states. The degeneracy of the triplet states is lifted in the presence of an external field, according to the Zeeman interaction term. The energy and intensity of the excitation spectra in $S=1/2$ valence bond ${\mathrm{KCuCl}}_{3}$ and ${\mathrm{TlCuCl}}_{3}$ are investigated by inelastic neutron scattering at finite external fields. Experimental observations along representative directions of reciprocal space are addressed up to ${H/H}_{c}\ensuremath{\sim}0.6$ and ${H/H}_{c}\ensuremath{\sim}0.9,$ respectively. A comprehensive analysis of the split Zeeman modes is reported, which shows excellent agreement with first principles. The obtained results extend former characterizations at $H=0$ and are of importance in the context of the field-driven quantum criticality realized in the sister compounds ${\mathrm{KCuCl}}_{3}$ and ${\mathrm{TlCuCl}}_{3}.$
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