Dr Mario Cuoco
CNR-SPIN, Salerno and Dipartimento di Fisica, Università di Salerno, Fisciano 84084, Italy
Transition metal (TM) oxides are fascinating materials characterized by a subtle interplay between charge, spin, and orbital degrees of freedom, which in many cases gives rise to complex types of collective behavior. In this framework, we present how magnetic and orbital patterns in a uniform 4d host are modified by the inclusion of 3d impurities substituting the 4d ions for both insulating and metallic hosts. In particular, for the case of an insulating host, we investigate the changes in spin and orbital patterns induced by magnetic transition-metal ions without an orbital degree of freedom doped in a strongly correlated insulator with spin-orbital order. In this context, we study the 3d ion substitution in 4d transition-metal oxides in the case of 3d3 doping at either 3d2 or 4d4 sites, which realizes orbital dilution in a Mott insulator. Although we concentrate on this doping case as it is known experimentally and more challenging than other oxides due to finite spin-orbit coupling, the conclusions are more general. We derive the effective 3d−4d (or 3d−3d) superexchange in a Mott insulator with different ionic valencies, underlining the emerging structure of the spin-orbital coupling between the impurity and the host sites, and demonstrate that it is qualitatively different from that encountered in the host itself. The impurity either acts as a spin defect accompanied by an orbital vacancy in the spin-orbital structure when the host-impurity coupling is weak or favors doubly occupied active orbitals (orbital polarons) along the 3d−4d bond leading to antiferromagnetic or ferromagnetic spin coupling. 
For the case of a metallic host, we show that doping a t2g system can lead to emergent orbitally directional double-exchange effects. We find that, due to the orbital directionality, the competition between antiferromagnetic (AF) and ferromagnetic (FM) correlations in layered systems makes antiferromagnetically coupled FM zigzag stripes and checkerboard clusters the dominant patterns in the phase diagram over a large range of doping. We demonstrate how the breaking of the orbital directionality as well as the inclusion of the Coulomb interaction can significantly affect the zigzag-checkerboard competition and lead to orbital or charge ordering in the ground state. 
I will finally consider the emergence of topological semimetal and metal phases in such a class of non-symmorphic collinear antiferromagnets  with glide reflection symmetry (zigzag magnetic patterns). We find gapless phases with Dirac points having multiple symmetry-protection as well as electronic structures with triple and quadruple band-crossing points. Glide semimetal is shown to be converted into a unique topological phase with non-trivial topological charges at the Dirac points due to inversion and time-inversion or particle-hole symmetry combination. Besides a new perspective of ordered states in complex materials, such findings indicate the path to get topological gapless phases and edge states in a relevant class of magnetic systems.
[Acknowledgements –EU- MSCA-IF project “UFOX” ]
1. W. Brzezicki, A. M. Oleś, and M. Cuoco, Phys. Rev. X 5, 011037 (2015).
2. W. Brzezicki, C. Noce, A. Romano, and M. Cuoco, Phys. Rev. Lett. 114, 247002 (2015).
3. W. Brzezicki and M. Cuoco, arXiv:1609.06916 .