Spin-orbit effects in pentavalent Iridates: Models and materials

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.