Selective probing of magnetic order on Tb and Ir sites in stuffed Tb$_{2+x}$Ir$_{2-x}$O$_{7-y}$ using resonant X-ray scattering

We study the magnetic structure of the stuffed (Tb-rich) pyrochlore iridate Tb$_{2+x}$Ir$_{2-x}$O$_{7-y}$, using resonant elastic x-ray scattering (REXS). In order to disentangle contributions from Tb and Ir magnetic sublattices, experiments were performed at the Ir $L_3$ and Tb $M_5$ edges, which provide selective sensitivity to Ir $5d$ and Tb $4f$ magnetic moments, respectively. At the Ir $L_3$ edge, we found the onset of long-range ${bf k}={bf 0}$ magnetic order below $T_{N}^text{Ir}sim$ 71 K, consistent with the expected signal of all-in all-out (AIAO) magnetic order. Using a single-ion model to calculate REXS cross-sections, we estimate an ordered magnetic moment of $mu_{5d}^{text{Ir}} approx 0.34(3),mu_B$ at 5 K. At the Tb $M_5$ edge, long-range ${bf k}={bf 0}$ magnetic order appeared below $sim40$ K, also consistent with an AIAO magnetic structure on the Tb site. Additional insight into the magnetism of the Tb sublattice is gleaned from measurements at the $M_5$ edge in applied magnetic fields up to 6 T, which is found to completely suppress the Tb AIAO magnetic order. In zero applied field, the observed gradual onset of the Tb sublattice magnetisation with temperature suggests that it is induced by the magnetic order on the Ir site. The persistence of AIAO magnetic order, despite the greatly reduced ordering temperature and moment size compared to stoichiometric Tb$_{2}$Ir$_{2}$O$_{7}$, for which $T_{N}^{text{Ir}} =130$ K and $mu_{5d}^{text{Ir}}=0.56,mu_B$, indicates that stuffing could be a viable means of tuning the strength of electronic correlations, thereby potentially offering a new strategy to achieve topologically non-trivial band crossings in pyrochlore iridates.