Hole doping in frustrated spinels, ZnCr$_{2}$O$_{4}$ and MgCr$_{2}$O$_{4}$, and their two dimensional analogue SCGO, SrCr$_{8}$Ga$_{4}$O$_{19}$

Recent experiments on the complex geometrically frustrated magnet, $\beta $-CaCr$_{2}$O$_{4}$, clearly illustrate the divergent effect of hole and static doping on the magnetic properties [1]. Given the complex parent state of $\beta $-CaCr$_{2}$O$_{4}$ this is not an ideal system for studying perturbations to the magnetic interactions. However, the onset of ferromagnetic fluctuations and ferrimagnetic ordering in $\beta $-Ca$_{1-y}$Cr$_{2}$O$_{4}$ suggests that other hole doped Cr$^{3+/4+}$ systems may be of interest. The extreme sensitivity in the balance of competing magnetic interactions in geometrically frustrated magnets is illustrated clearly in Cr$^{3+}$ spinels, ACr$_{2}$O$_{4}$. Antiferromagnetic (AFM) ordering in ACr$_{2}$O$_{4}$ occurs at a spin-Peierls transition. Both the low temperature magnetic and structural regimes are found to be highly sensitive to the A cation. In the case of ZnCr$_{2}$O$_{4}$ we find that very fine control of the reaction conditions is necessary to make stoichiometric ZnCr$_{2}$O$_{4}$, rather than hole doped Zn$_{1+x}$Cr$_{2-x}$O$_{4}$ (x $\le $ 0.04). From analysis of magnetic measurements, specific heat and neutron diffraction we have probed the nature of the transitions at $T_{N}$ [2]. How hole doping effects the low temperature properties and the role of the $d^{2}$ Cr$^{4+}$ cations on the isotropic $d^{3}$ Cr$^{3+}$ magnetic lattice will be discussed. Our results on the more robust MgCr$_{2}$O$_{4}$ spinel will also be presented. A 2D analogue of the 3D pyrochlore magnetic lattice in the ACr$_{2}$O$_{4}$ spinels is found in SCGO, SrCr$_{8}$Ga$_{4}$O$_{19}$. In hole doped SCGO, SrCr$_{8}$M$_{x}$Ga$_{4-x}$O$_{19}$ (M = Zn, Mg, Cu), a larger fraction of the Cr$^{3+}$ can be oxidized. Hole doping is found to have a significant effect on the magnetic fluctuations, how this depends on the nature of the dopant cation will be addressed [3]. \\[4pt] [1] S. E. Dutton, C. L. Broholm, and R. J. Cava, Journal of Solid State Chemistry \textbf{183}, 1798 (2010). \\[0pt] [2] S. E. Dutton\textit{ et al.}, Physical Review B \textbf{83}, 064407 (2011). \\[0pt] [3] S. E. Dutton\textit{ et al.}, Journal of Physics-Condensed Matter \textbf{23}, 386001 (2011).