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Spin-orbit effects in heavy 5$d$ transition metal oxides, in particular, iridates, have received enormous current interest due to the prediction as well as the realization of a plethora of exotic and unconventional magnetic properties. While a bulk of these works are based on tetravalent iridates ($d^5$), where the counter-intuitive insulating state of the rather extended 5$d$ orbitals are explained by invoking strong spin-orbit coupling, the recent quest in iridate research has shifted to the other valencies of Ir, of which pentavalent iridates constitute a notable representative. In contrast to the tetravalent iridates, spin-orbit entangled electrons in $d^4$ systems are expected to be confined to the $J = 0$ singlet state without any resultant moment or magnetic response. However, it has been recently predicted that, magnetism in $d^4$ systems may occur via magnetic condensation of excitations across spin-orbit-coupled states. In reality, the magnetism in Ir$^{5+}$ systems are often quite debatable both from theoretical as well as experimental point of view. Here we provide a comprehensive overview of the spin-orbit coupled $d^4$ model systems and its implications in the studied pentavalent iridates. In particular, we review here the current experimental and theoretical understanding of the double perovskite ($A_2B$YIrO$_6$, $A =$ Sr, Ba, $B =$Y, Sc, Gd), 6H-perovskite (Ba$_3M$Ir$_2$O$_9$, $M =$ Zn, Mg, Sr, Ca), post-perovskite (NaIrO$_3$), and Hexagonal (Sr$_3$MIrO$_6$) iridates, along with a number of open questions that require future investigation.
Motivated by RIXS experiments on a wide range of complex heavy oxides, including rhenates, osmates, and iridates, we discuss the theory of RIXS for site-localized $t_{2g}$ orbital systems with strong spin-orbit coupling. For such systems, we present
In the search for topological phases in correlated electron systems, iridium-based pyrochlores A2Ir2O7 -- materials with 5d transition-metal ions -- provide fertile grounds. Several novel topological states have been predicted but the actual realizat
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Spin-orbit coupling in magnetic systems lacking inversion symmetry can give rise to non trivial spin textures. Magnetic thin films and heterostructures are potential candidates for the formation of skyrmions and other non-collinear spin configuration
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