Sharp Magnetoabsorption Resonances in the Vortex State of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$

We report the observation of narrow resonances in the absorption of mm wavelength radiation (30 to 50 GHz) in the vortex state of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. When the applied field $\mathbf{B}\left(\parallel \mathbf{c}\right)$ is swept at fixed frequency $\omega$, the absorption displays two distinct Lorentzian peaks at the resonance fields $B_0$ and $B_1$. The resonance frequency decreases with increasing field, consistent with anticyclotronic behavior. At fixed $\omega$, $B_0$ and $B_1$ also vary strongly with temperature $T$. $B_0$ and $B_1$ increase to a sharp maximum when $T$ crosses the vortex solid-to-liquid transition line inferred from resistivity results. The coupling of cyclotron resonance with collective modes giving rise to an anticyclotronic mode is discussed.