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The $T^{\prime}$ infinite layered nickelates have recently garneredsignificant attention owing to the discovery of superconductivity in hole-dopedRNiO$_2$ (R $=$ La, Pr, or Nd), which is the $n = \infty$ member of the seriesR$_{n+1}$Ni$_n$O$_{2n+2}$. Here, we investigate the $n = 3$ member, namelyR$_4$Ni$_3$O$_8$ (R $=$ La, Pr, or Nd) of this family. The compoundLa$_4$Ni$_3$O$_8$ exhibits simultaneous charge/spin-stripe ordering atT$_N^\ast$ $=$ 105 K, which is also concomitant with the onset ofmetal-to-insulator (MIT) transition upon lowering the temperature belowT$_N^\ast$. We investigate the conspicuous absence of this transition in the Prand Nd analogues of La$_4$Ni$_3$O$_8$. To achieve this purpose, we synthesizedsolid-solutions of the form (La, Pr)$_4$Ni$_3$O$_8$ and (La, Nd)$_4$Ni$_3$O$_8$and examined the behavior of T$_N^\ast$ as a function of the average R-siteionic radius ($r_{\overline{R}}$). We show that after an initial quasilineardecrease with decreasing $r_{\overline{R}}$, T$_N^\ast$ suddenly vanishes inthe narrow range 1.134 $\AA$ $\leq$ $r_{\overline{R}}$ $\leq$ 1.143 $\AA$. Inthe same range, we observed the emergence of a new transition below T$^\ast$,whose onset temperature increases as $r_{\overline{R}}$ further decreases. We,therefore, argue that the sudden vanishing of charge/spin-stripe/MIT orderingupon decreasing $r_{\overline{R}}$ is due to the appearance of a new competingphase. The point $r_{\overline{R}}$ $\approx$ $r_c$, where T$_N^\ast$ vanishesand T$^\ast$ appears -- a quantum critical point -- should be investigatedfurther. In this regard, Pr$_4$Ni$_3$O$_8$ and Pr-rich samples should be usefuldue to the weak magnetization response associated with the Pr-sublattice, asshown here.

Investigating the cause of crossover from charge/spin stripe insulator to correlated metallic phase in layered T' nickelates -- R$_4$Ni$_3$O$_8$