  La$_4$Cu$_3$MoO$_{12}$ is a cluster antiferromagnet where copper spin-1/2
form a network of st rongly coupled spin-trimers. The magnetic properties of
this material have bee n examined using magnetic neutron scattering. At low
temperatures, excitations from the ground state are observed at 7.5(3) meV and
132.5(5) meV. An additio nal peak in the neutron scattering spectrum, which
appears at 125.0(5) meV on heating is ascribed to a transition between excited
states. The wave-vector an d temperature-dependence of the inelastic magnetic
scattering cross section is consistent with intra-trimer transitions. Magnetic
neutron diffraction reveal s antiferromagnetic order below T$_N$=2.6 K that
doubles the unit cell along t he {\bf a} direction. The ordered magnetic
structure is described as inter-tri mer order where spin correlations within
trimers are controlled by the strong intra-trimer interactions. Combining the
information derived from elastic and inelastic magnetic neutron scattering with
group theoretical analysis, a consi stent set of intra-trimer interactions and
ordered magnetic structures are der ived. The experiment provides a simple
worked example of magnetism associated with inter-atomic composite degrees of
freedom in the extreme quantum limit.
