Novel Magnetic and Charge Orders in Dimer-Chain Iridate Ba$_{5}$AlIr$_{2}$O$_{11}$

We report a novel magnetic state coexisting with a charge ordering state in a dimer-chain system Ba$_{5}$AlIr$_{2}$O$_{11}$. This newly synthesized single-crystal iridate features both tetravalent Ir$^{4+}$ and pentavalent Ir$^{5+}$ ions in each of dimers that are only linked via AlO$_{4}$-tetrahedra along the b-axis. Despite the evident one-dimensional characteristic, the dimer-chains undergo an unexpected long-rang order at T$_{M} =$ 4.5 K with a large magnetic anisotropy. The magnetic transition is unusually resilient to magnetic field up to 14 T but more susceptible to even modest hydrostatic pressure up to 10 kbar. Furthermore, a subtle structural change discerned at T$_{S}=$200 K marks a charge ordering that accompanies a huge enhancement in the dielectric constant and changes in the electrical resistivity. It is evident that the strong SOC imposes a j$=$1/2 (Ir$^{4+})$ and singlet j$=$0 (Ir$^{5+})$ states in each dimer, which critically hinges on the orbital and lattice degrees of freedom.