  We report the structural, magnetic and thermodynamic properties of the double
perovskite compound La2CuIrO6 from X-ray, neutron diffraction, neutron
depolarization, dc magnetization, ac susceptibility, specific heat,
muon-spin-relaxation (uSR), electron-spin-resonance (ESR) and nuclear magnetic
resonance (NMR) measurements. Below ~113 K, short-range spin-spin correlations
occur within the Cu2+ sublattice. With decreasing temperature, the Ir4+
sublattice progressively involves in the correlation process. Below T = 74 K,
the magnetic sublattices of Cu (spin s = 1/2) and Ir (pseudospin j = 1/2) in
La2CuIrO6 are strongly coupled and exhibit an antiferromagnetic phase
transition into a non-collinear magnetic structure accompanied by a small
uncompensated transverse moment. A weak anomaly in ac-susceptibility as well as
in the NMR and {\mu}SR spin lattice relaxation rates at 54 K is interpreted as
a cooperative ordering of the transverse moments which is influenced by the
strong spin-orbit coupled 5d ion Ir4+. We argue that the rich magnetic
behaviour observed in La2CuIrO6 is related to complex magnetic interactions
between the strongly correlated spin-only 3d ions with the strongly spin-orbit
coupled 5d transition ions where a combination of the spin-orbit coupling and
the low-symmetry of the crystal lattice plays a special role for the spin
structure in the magnetically ordered state.
