Spin-orbit coupling (SOC) plays a crucial role in magnetic and electronic properties of $5d$ iridates. In this paper we have experimentally investigated the structural and physical properties of a series of Ir-based double perovskite compounds ${\mathrm{Pr}}_{2-x}{\mathrm{Sr}}_x{\mathrm{MgIrO}}_6(x$ = 0, 0.5, 1; hereafter abbreviated as PMIO, PSMIO1505, and PSMIO). Interestingly, these compounds have recently been proposed to undergo a transition from the spin-orbit-coupled Mott insulating phase at $x=0$ to the elusive half-metallic antiferromagnetic (HMAFM) state with Sr doping at $x=1$. However, our detailed magnetic and electrical measurements refute any kind of HMAFM possibility in either of the doped samples. In addition, we establish that within these ${\mathrm{Pr}}_{2-x}{\mathrm{Sr}}_x{\mathrm{MgIrO}}_6$ double perovskites, changes in Ir-oxidation states ($4+$ for PMIO to $5+$ for PSMIO via mixed $4+/5+$ for PSMIO1505) lead to markedly different magnetic behaviors. While SOC on Ir is at the root of the observed insulating behaviors for all three samples, the correlated magnetic properties of these three compounds develop entirely due to the contribution from local Ir moments. Additionally, the magnetic ${\mathrm{Pr}}^{3+}$ ($4f^2$) ions, instead of showing any kind of ordering, only contribute to the total paramagnetic moment. It is seen that the ${\mathrm{PrSrMgIrO}}_6$ sample does not order down to 2 K despite antiferromagnetic interactions. But, the $d^5$ iridate ${\mathrm{Pr}}_2{\mathrm{MgIrO}}_6$ shows a sharp antiferromagnetic (AFM) transition at around 14 K, and in the mixed valent ${\mathrm{Pr}}_{1.5}{\mathrm{Sr}}_{0.5}{\mathrm{MgIrO}}_6$ sample the AFM transition is shifted to a much lower temperature ($\sim 6$ K) due to weakening of the AFM exchange.

Perovskite iridates of $6H$ hexagonal structure present a plethora of possibilities in terms of the variety of ground states resulting from a competition between spin-orbit coupling (SOC), hopping, noncubic crystal field (${\mathrm{\Delta }}_{\text{CFE}}^{\text{NC}}$), and superexchange energy scales within the ${\mathrm{Ir}}_2{\mathrm{O}}_9$ dimers. Here we investigate one such compound, ${\mathrm{Ba}}_3{\mathrm{CdIr}}_2{\mathrm{O}}_9$, by x-ray diffraction, dc magnetic susceptibility ($\chi$), heat capacity ($C_p$), and also ${}^{113}\mathrm{Cd}$ nuclear magnetic resonance (NMR) spectroscopy. We have established that the magnetic ground state has a small but finite magnetic moment on $\mathrm{Ir}^{5+}$ in this system, which likely arises from intradimer Ir-Ir hopping and local crystal distortions. Our heat capacity, NMR, and dc magnetic susceptibility measurements further rule out any kind of magnetic long- or short-range ordering among the Ir moments down to at least 2 K. In addition, the magnetic heat capacity data show linear temperature dependence at low temperatures under applied high fields ($>30$ kOe), suggesting a gapless spin density of states in the compound.

We address the concomitant metal-insulator transition (MIT) and antiferromagnetic ordering in the novel pyrochlore iridate ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ by combining x-ray absorption spectroscopy, x-ray and neutron diffractions, and density functional theory (DFT)-based calculations. The temperature dependent powder x-ray diffraction clearly rules out any change in the lattice symmetry below the MIT, nevertheless a clear anomaly in the Ir-O-Ir bond angle and Ir-O bond length is evident at the onset of MIT. From the x-ray absorption near edge structure (XANES) spectroscopic study of Ir-$L_3$ and $L_2$ edges, the effective spin-orbit coupling is found to be intermediate, at least quite far from the strong atomic spin-orbit coupling limit. Powder neutron diffraction measurement is in line with an all-in-all-out magnetic structure of the Ir-tetrahedra in this compound, which is quite common among rare-earth pyrochlore iridates. The sharp change in the Ir-O-Ir bond angle around the MIT possibly arises from the exchange striction mechanism, which favors an enhanced electron correlation via weakening of Ir-Ir orbital overlap and an insulating phase below $T_{MI}$. The theoretical calculations indicate an insulating state for shorter bond angle validating the experimental observation. Our DFT calculations show a possibility of intriguing topological phase below a critical value of the Ir-O distance, which is shorter than the experimentally observed bond length. Therefore, a topological state may be realized in bulk ${\mathrm{Eu}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ sample if the Ir-O bond length can be reduced by the application of sufficient external pressure.

We report here the observation of the inverse exchange bias phenomenon in the ferrimagnetic double-perovskite ${\mathrm{Gd}}_2{\mathrm{CoRuO}}_6$. The compound crystallizes in a monoclinic structure (space group $P{2}_1/n$), and it undergoes long-range magnetic ordering below $T_C=60$ K. The ferrimagnetic state of the sample is manifested through magnetization reversal at low temperature. In order to corroborate the role of local structure on the magnetic properties of ${\mathrm{Gd}}_2{\mathrm{CoRuO}}_6$, we have performed a combined magnetization and x-ray absorption spectroscopy study on two different samples prepared through different cooling protocols (slow cooling and furnace cooling). Extended x-ray absorption fine-structure analysis indicates the presence of strong antisite disorder between Co and Ru in both samples. However, the slow-cooled sample shows completely random antisite disorder, whereas, small Co- and Ru-rich patches appear in the furnace-cooled sample. In both samples, a significant amount of mixed valency in Co and Ru ions is evident from our x-ray absorption near-edge structure. The antiparallel ordering along with different temperature dependence of the three magnetic sublattices, Gd, Co, and Ru, can be responsible for negative magnetization, whereas the inverse exchange bias effect can be attributed to the mixed interfacial coupling between adjacent magnetic nanoclusters. The difference in local structure can nicely be accounted for by the observed variations of the magnetic properties between two samples of ${\mathrm{Gd}}_2{\mathrm{CoRuO}}_6$.

We have investigated the structural and physical properties of double perovskite (DP) $\mathrm{La}A{\mathrm{VMoO}}_6$ ($A={\mathrm{Ca}}^{2+}$, ${\mathrm{Ba}}^{2+}$; abbreviated as LCVMO and LBVMO from now on) compounds, proposed to be possible half-metallic antiferromagnets (HMAFMs). Here we show that within $\mathrm{La}A{\mathrm{VMoO}}_6$ double perovskite structure, La-O covalency competes against $B$-site as well $A$-site cationic order and this competition critically influences their physical properties. Evidently, the presence of ${\mathrm{Ca}}^{2+}$ or ${\mathrm{Ba}}^{2+}$ at the $A$ site along with ${\mathrm{La}}^{3+}$ would offer a tool to modify the $A$-site ordering and consequently influence the La-O covalency as well. Our experimental results reveal that LCVMO lies at the extreme end of this family and accommodates large scale phase separation in terms of La, V, and Ca, Mo-rich phases as a result of dominant La-O covalency. On the other hand, LBVMO is more correctly described as a layered $A$-site ordered and nearly complete $B$-site disordered double perovskite where cationic order dominates the La-O covalency. The general trend of our experimental findings is in agreement with the ab initio electronic structure calculations, carried out on realistic structures based on local coordination obtained from extended x-ray-absorption fine-structure study.

In the presence of strong atomic spin-orbit coupling (SOC), tending to the $j\text{−}j$ coupling limit, $5d^4$ iridates are speculated to possess a nonmagnetic $J_{\mathrm{eff}}=0$ singlet ground state from atomic consideration, which invariably gets masked due to different solid-state effects (e.g., hopping). Here, we try to probe the trueness of the atomic SOC-based proposal in an apparently one-dimensional system, ${\mathrm{Sr}}_3{\mathrm{NaIrO}}_6$, with well-separated ${\mathrm{Ir}}^{5+}$ $\left(5d^4\right)$ ions. But all the detailed experimental as well as theoretical characterizations reveal that the ground state of ${\mathrm{Sr}}_3{\mathrm{NaIrO}}_6$ is not nonmagnetic. However, our combined dc susceptibility $\chi$, ${}^{23}\mathrm{Na}$ nuclear magnetic resonance (NMR), muon spin relaxation/rotation $\left(\mu \mathrm{SR}\right)$, and heat capacity $C_p$ measurements clearly refute any sign of spin freezing or ordered magnetism among the ${\mathrm{Ir}}^{5+}$ moments due to geometrical exchange frustration, while in-depth zero-field and longitudinal field $\mu \mathrm{SR}$ investigations strongly point towards an inhomogeneous quantum spin liquid (QSL)-like ground state. In addition, the linear temperature dependence of both the NMR spin-lattice relaxation rate and the magnetic heat capacity at low temperatures suggest low-lying gapless spin excitations in the QSL phase of this material. Finally, we conclude that the effective SOC realized in $d^4$ iridates is unlikely to offer a ground state which will be consistent with a purely atomic $j\text{−}j$ coupling description.