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We report the analysis of magnetic susceptibility $\chi$($T$) of Sr$_2$IrO$_4$ single crystal in the paramagnetic phase. We formulate the theoretical susceptibility based on isotropic Heisenberg antiferromagnetism incorporating the Dzyaloshinsky-Moriya interaction exactly, and include the interlayer couplings in a mean-field approximation. $\chi$($T$) above $T_{\rm N}$ was found to be well described by the model, indicating the predominant Heisenberg exchange consistent with the microscopic theory. The analysis points to a competition of nearest and next-nearest neighbor interlayer couplings, which results in the up-up-down-down configuration of the in-plane canting moments identified by the diffraction experiments.

Binary ruthenium pnictides, RuP and RuAs, with an orthorhombic MnP structure, were found to show a metal to a nonmagnetic insulator transition at ${T}_{\mathrm{MI}}$ $=$ 270 and 200 K, respectively. In the metallic region above ${T}_{\mathrm{MI}}$, a structural phase transition, accompanied with a weak anomaly in the resistivity and the magnetic susceptibility, indicative of a pseudogap formation, was identified at ${T}_{s}$ $=$ 330 and 280 K, respectively. These two transitions were suppressed by substituting Ru with Rh. We found superconductivity with a maximum ${T}_{\mathrm{c}}$ $=$ 3.7 and 1.8 K in a narrow composition range around the critical point for the pseudogap phase, Rh content ${x}_{\mathrm{c}}$ $=$ 0.45 and 0.25 for Ru${}_{1\ensuremath{-}x}$Rh${}_{x}$P and Ru${}_{1\ensuremath{-}x}$Rh${}_{x}$As, respectively, which may provide us with a nonmagnetic route to superconductivity at a quantum critical point.