We use single-crystal neutron diffraction to determine the crystal structure symmetry and the magnetic evolution in the rhodium-doped iridates Sr2Ir1-xRhxO4 (0 <= x <= 0.16). Throughout this doping range, the crystal structure retains a tetragonal symmetry (space group I4(1)/a) with two distinct magnetic Ir sites in the unit cell forming staggered IrO6 rotation. Upon Rh doping, the magnetic order is suppressed and the magnetic moment of Ir4+ is reduced from 0.21 mu(B)/Ir for x = 0 to 0.18 mu(B)/Ir for x = 0.12. The magnetic structure at x = 0.12 is different from that of the parent compound, while the moments remain in the basal plane.
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