LS separation of J=1/2 Mott insulator observed by magnetic X-ray diffraction

Spin-orbit coupling is a key concept to realize spin Hall effect in insulating materials. A perovskite iridate Sr$_2$IrO$_4$ is known to show insulating transport properties in spite of large spatial extent of 5d electrons. The origin of this unconventional behavior is argued to be a strong LS coupling which results in $J_{\mathrm{eff}}=1/2$ Mott insulator. We performed off-resonant magnetic X-ray scattering in the antiferromagnetically ordered state of this material and found that considerable contribution from orbital moment for the ordered moment. The estimated ratio, $\langle \psi | L_z | \psi | \rangle / \langle \psi | S_z | \rangle$ is 5. This is consistent with $J_{\mathrm{eff}}=1/2$ which expects the ratio as 4. This justifies unconventional $J_{\mathrm{eff}}=1/2$ Mott insulator for this transition metal oxides.