Spin-orbit coupling and coupled charge-spin-orbital state in iridates Xuedong Ou, Hua Wu* Laboratory for Computational Physical Sciences (MOE), State Key Laboratory of Surface Physics ,and Department of Physics, Fudan University Iridates are of current great interest for their entangled spin-orbital state and possibly exotic properties. Through DFT calculations including spin-orbit coupling (SOC) and electron correlation, our results show that：(1). In the hexagonal spin-chain materials Sr3MIrO6 (M=Ni, Co), the significant SOC alters the orbital state, the exchange pathway, and thus the magnetic structure. (2). In the Fe- or Co- doped Sr2IrO4, a Fe3+ (Co3+)-Ir5+ mixed charge state appears on the Ir4+ matrix, with Fe3+ (Co3+) in a high-spin state, and Ir5+ in a singlet. Assisted by the strong SOC and electron correlation, the coupled charge-spin-orbital state accounts for their insulating behavior and varying magnetic moments. I. Impact of SOC on the magnetism of Sr3MIrO6 (M = Ni, Co) [1] II. Coupled charge-spin-orbital state in Fe- or Co-doped Sr2IrO4[2] D=240nm D=340nm (a) (b) (c) (d) Fig. 2.1 | (a) Crystal structure of M=Fe or Co half doped Sr2IrO4 (b)Orbital resolved DOS of Fe half-doped Sr2IrO4 calculated by LSDA+UFe,Ir, showing Fe3+ and Ir5+ charge state (a) (b) IrO6 MO6 Fig.1.1 | Crystal structure of Sr3MIrO6 (a) projected to the ab plane and (b) in a perspective view. Octahedral IrO6 and trigonal prisms MO6 are alternating in the spin chains. Intra-chain magnetism is so far unclear. Fig. 1.2 Fig.1.3 (e) Fig. 2.2 | (a) The j =3/2 and j =1/2 decomposed DOS of the Ir5+ 5d state, and (b) Band structure of Co half-doped Sr2IrO4 calculatedted by LSDA+UCo Ir.+SOCCo,Ir Conclusion: I. For the Sr3MIrO6(M = Ni, Co) materials a).The strong SOC of the Ir4+ ion plays an essential role in determining the intra-chain antiferromagnetism of Sr3MIrO6. b). In absence of the SOC, the single t2g hole would occupy the a1g singlet, which mediates an unreal FM. c).This work well accounts for the most recent experiments[3] and magnifies again the significance of the SOC in iridates. II. For the Fe or Co doped Sr2IrO4 system a). Fe3+ (Co3+)-Ir5+ mixed charge state appears on the Ir4+ matrix. b). Due to a strong SOC, the Ir5+ (5d4, t 42g) ion could form a closed jeff = 3/2 subshell and hence behave like a singlet. The Fe3+ and Co3+ ions are both in a HS state. c). Assisted by the SOC and electron correlation, the coupled charge-spin-orbital state accounts for their insulating behavior and varying magnetic moments[4]. Fig.1.2 | Partial DOS of Sr3NiIrO6 calculated by LDA, showing the crystal field levels. Fig.1.3 | The partial DOS of the Ir-5d a1g and eg’ orbitals in Sr3NiIrO6 (a) The FM calculated by LSDA+U and (b) AF state by LSDA+U+SOC. Fig.1.4 Fig. 1.4 | Schematic level diagrams of the Ir4+ 5d and Ni2+ 3d orbitals, and exchange pathways. (a) and (b): FM, (b) and (c): AF [1] X. D. Ou, H. Wu, Sci. Rep. 4, 4609 (2014). [2] X. D. Ou, H. Wu, Phys. Rev. B 89,035138 (2014) [3] D. Mikhailova, et al, Phys. Rev. B 86, 13409 (2012). [4] A. J. Gatimu, et al, J. Solid State. Chem. 190, 257 (2012)