Magnetic excitations in the geometric frustrated multiferroic CuCrO$_2$

The delafossite CuCrO$_2$, crystallizing in the rhombohedral $R\overline{3}M$ space group, is an interesting case of a multiferroic compound due to its apparent strong coupling of spin and charge. In contrast to other multiferroic compounds CuCrO$_2$ shows a spontaneous electric polarization upon antiferromagnetic ordering at \emph{T}$_{\textrm{N}}\approx$~24~K without an accompanying structural phase transition. Further, CuCrO$_2$ is a rare example where the magnetoelectric properties are tunable by both an electric and a magnetic field. In our contribution we present inelastic neutron scattering experiments on CuCrO$_2$ single crystals. The measured magnetic excitation spectra have been modeled by Monte-Carlo spin wave calculations and allowed the determination of the relevant exchange interaction and anisotropy terms. We will present evidence for a weak ferromagnetic Cr-Cr-interlayer exchange interaction and show that this interaction is relevant for the multiferroic properties of CuCrO$_2$.