Abstract
In this paper detailed neutron scattering measurements of the
magnetic excitation spectrum of \CCO\ in the ordered state below
$T_{\rm{N1}}=24.2$~K are presented.
The spectra are analyzed using a model Hamiltonian which includes
intralayer-exchange up to the next-next-nearest neighbor and
interlayer-exchange.
We obtain a definite parameter set and show that exchange interaction
terms beyond the next-nearest neighbor are important to describe
the inelastic excitation spectrum.
The magnetic ground state structure generated with our parameter set is in agreement with the structure proposed for \CCO\ from the results
of single crystal diffraction experiments previously published.
We argue that the role of the interlayer exchange is crucial to
understand the incommensurability of the magnetic structure as
well as the spin-charge coupling mechanism.
