Fundamental questions arise when dealing with TM substitutions that modify the atomic spin and orbital character in an electron correlated environment. The impact of dopants on spin-orbital correlations can be extraordinary large by either transforming the pattern of the long-range order or by breaking the ordering into a quantum liquid and vice versa. On a general ground, although the large variety of TM configurations sets a highly complex scenario, UFOX succeeded in identifying two fundamental paths for designing magnetic and orbital correlations in a uniform TMO host through a transition metal substitution. First, when considering a TM element with a given configuration of n electrons in the d-shell [d(n)], we demonstrate that d(3) high-spin state plays a unique role because it has only active spin degree of freedom while the orbital one is basically frozen. Hence, d(3) substitution can realize an orbital dilution. Orbital doping is a novel and general concept that clearly indicates fundamental paths to design and control the entanglement of spin-orbital degrees in an electron correlated environment by removing the orbital component while keeping active the spin-degree of freedom. Second, the replacement of d(2) with d(4) TM elements (or vice versa) allows to distinctively design a spin-orbital correlated environment with an orbital degree of freedom having non-equivalent charge character. Indeed, for d(2) and d(4) valence configurations, the empty orbital (i.e. holon) and the doubly occupied state (i.e. doublon) set the orbital degree of freedom, respectively. We unveil how orbital doping, e.g. of the type 3d(3) in a 4d(4) host, can reorganize the spin-orbital ordering around the defect by acting as a spin defect accompanied by an orbital vacancy in the spin-orbital structure when the host-impurity coupling is weak or favoring an orbital polaronic behaviour with antiferromagnetic or ferromagnetic spin coupling.
Such results allowed to revisit the concept of band and Mott insulators as well as superconductors and conventional metals in view of their topological behaviour. The search for topological phases of matter and, more specifically, the occurrence of non-Abelian states set remarkable challenges both for fundamental physics and the development of innovative solutions in quantum engineering. The investigation of TM substitution guided the general idea that, though harmful for some types of topological protections, inhomogeneous perturbations can open a completely different perspective in the area of topological matter because they represent a rich intrinsic source of topological phases or topological transitions. Taking the d(2)-d(4) exchange and motivated by this innovative outlook, we face a new route to get Majorana end modes in low-dimensional spin-orbital systems with spatially inhomogeneous anisotropic exchange. Apart from the impact on the targeted materials, such study provides a general correspondence between inhomogeneous spin-orbital exchange and itinerant systems with a distribution of pairing centers. The investigation of the phase diagram indicates how different types of orbital exchange interfere to yield topological transitions and domains in the parameter space that are robust to local variations of the dopant configuration. This result is novel, general, and can have significant impact both on the generation and on the manipulation of topological modes in the presence of disorder by suitably modifying the host or the dopant configuration.
Concerning the d(3)-d(4) hybrids, on a general ground the competition of ferromagnetic and antiferromagnetic exchanges for orbital directional correlated systems leads to distinct antiferromagnetic order which is robust to doping and relevant for addressing the observed physical phase diagram in Mn-doped bilayered ruthenates. Taking the paradigmatic example of zig-zag antiferromagnetic patterns arising in doped multi-orbital electron systems, we successfully demonstrate the occurrence of magnetic Dirac semimetal phases in systems with strong spin-orbital-charge entanglement and dictated by new symmetry conditions.
Indeed, we identify novel topological semimetal and metal phases in a large variety of non-symmorphic collinear antiferromagnets with glide reflection symmetry, a combination of mirror and half-lattice translation. Taking into account the intrinsic glide symmetry of the zig-zag antiferromagnetic order we find metal-insulator transitions and semimetal phases made of Dirac points having multiple symmetry-protection as well as with triple and quadruple band-crossing points. Such phases occur when driving the transition between different types of insulator due to magnetic exchange and spin-orbit coupling. The study can have a high impact in various class of materials as zig-zag antiferromagnets represent a common and ubiquitous realization of magnetic order in a large variety of TMOs as experimentally demonstrated in ruthenates, manganites, dichalcogenides, iridates, and nickelates. Thus, besides providing a new perspective of ordered states in complex materials, these findings indicate that topological gapless phases may occur in a wide area of interacting magnetic systems.
