Susceptibility and dilution effects of the kagomé bilayer geometrically frustrated network: A Ga NMR study of ${\mathrm{SrCr}}_{9p}{\mathrm{Ga}}_{12-9p}{\mathrm{O}}_{19}$

The archetype of geometrically frustrated compounds ${\mathrm{SrCr}}_{9p}{\mathrm{Ga}}_{12-9p}{\mathrm{O}}_{19}$ is a kagomé bilayer of Heisenberg ${\mathrm{Cr}}^{3+}$ ions $\mathrm{}(S=3/2\mathrm{})\mathrm{}$ with antiferromagnetic interactions. We present an extensive gallium nuclear magnetic resonance (NMR) study over a broad Cr-concentration range $(0.72\mathrm{}<~p<~0.95).$ This allows us to probe locally the susceptibility of the kagomé bilayer and separate the intrinsic properties due to geometric frustration from those related to site dilution. Compared to the partial study on one sample, $p=0.90,$ presented in Phys. Rev. Lett. $85,$ 3496 (2000), we perform here a refined study of the evolution of all the magnetic properties with dilution, with a great emphasis on the lowest diluted $p=0.95\mathrm{}$ sample synthesized for this study. Our major findings are the following (1) The intrinsic kagomé bilayer susceptibility reaches a maximum at a temperature of $\approx 40-50\hspace{0.5em}\mathrm{K},$ which we show here to be robust up to a dilution as high as $\approx 20\%;$ this maximum is the signature of the development of short-range antiferromagnetic correlations in the kagomé bilayer. (2) At low T, a highly dynamical state induces a strong wipeout of the NMR intensity, regardless of dilution. (3) The low-$T$ upturn of the macroscopic susceptibility is associated with paramagnetic defects, which stem from the dilution of the kagomé bilayer. The low-$T$ analysis of the $p=0.95\mathrm{}$ NMR line shape, coupled with a more accurate determination of the nuclear Hamiltonian at high T, allows us to discuss in detail the nature of the defect. Our analysis suggests that the defect can be associated with a staggered spin response to the vacancies of the kagomé bilayer. This, altogether with the maximum in the kagomé bilayer susceptibility, is very similar to what is observed in most low-dimensional antiferromagnetic correlated systems, even those with a short spin-spin correlation length. (4) The spin-glass-like freezing observed at $T_g$ $\approx 2–4\hspace{0.5em}\mathrm{K}$ is not driven by the dilution-induced defects.