  We report magnetization and neutron diffraction studies on crystal and
magnetic structures of Ir- and Rh-substituted honeycomb lattice
$\alpha$-RuCl$_3$. The iridium or rhodium atoms are distributed at the Ru site
with little structural modification. Both systems undergo a room-temperature
monoclinic $C2/m$ to low-temperature trigonal $R\bar{3}$ phase transformation
with a large recoverable hysteresis. At low temperature, a zigzag spin order is
observed with the same characteristic wavevector $(0,0.5,1)$ as in the parent
$\alpha$-RuCl$_3$. Detailed magnetic structure refinement reveals an ordered
moment of $\rm 0.32(5) \mu_B/Ru$ and a upper boundary of canting angle of
$15(4)^\circ$ away from the basal plane at 5~K for the 10\% Ir-substituted
$\alpha$-RuCl$_3$, which is different from the 0.45-0.73~$\rm \mu_B/Ru$ and
$32^\circ$-$48^\circ$ canting angle reported in the parent compound
$\alpha$-RuCl$_3$. The observation of unchanged RuCl$_6$ local octahedral
environment, reduced magnetic moment size and canting angle highlights the
potential to study quantum spin liquid behavior through non-magnetic ion
doping.
