Magnetic Structure and Spin Waves in Co$_{2}$(OD)$_{3}$Cl

We have examined the magnetic structure of Co$_{2}$(OD)$_{3}$Cl with magnetic Co$^{2+}$ (3$d^{7}$; s= 3/2) ions using neutron powder diffraction data. Magnetic structure that yields the best refinement factor is an ``umbrella''-type antiferromagnetic structure with ab-components of magnetic moments in the kagome plane forming a q=0 120$^{\circ}$ structure and the moments are canted out of the plane by $\sim $ 40$^{\circ}$. The magnetic moments in the triangular plane are aligned ferromagnetically along the c-axis. We have performed linear spin wave calculations considering the nearest neighbor interactions J within the kagome plane and J$_{F}$ between the kagome and the triangular plane. The effects of J$_{F}$/J and the canting angle to the spin wave dispersion was studied thoroughly, to find out an effective spin hamiltonian that explains our inelastic neutron scattering data with two prominent excitation modes centered at 3 meV and 19 meV. Single ion-type anisotropy was also included in the spin hamiltonian to study its effect to the spin wave excitation.