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Magnetic Properties of GeNi$_{2-x}$Mg$_{x}$O$_{4}$ Under High Pressure and Magnetic Dilution

The effects of magnetic dilution and applied pressure on frustrated spinel Ni$_{2-x}$Mg$_{x}$GeO$_{4}$ (0 $\leq x \leq 1.0$) are analyzed using specific heat, AC and DC magnetization and x-ray diffraction. The parent compound has two closely spaced antiferromagnetic transitions $T_{\text{N1}}=12.0$ K (kagomé planes) and $T_{\text{N2}}=11.4$ K (triangular planes). In the dilution range tested, the low temperature magnetic state takes three forms: antiferromagnetic ($0 \leq x \leq 0.05$), ill-defined ($x=0.10$ and 0.15), and spin glass ($0.30 \leq x \leq 1.0$). The AFM region shows an extreme vulnerability to dilution with a percolation threshold of $p_{\text{c1}}=0.74 \pm 0.04$ and $p_{\text{c2}}=0.65 \pm 0.05$ for the kagomé and triangular planes respectively, which are much larger than expected for 3D systems. We suggest that this behavior is possibly due to coupling between the kagomé and triangular spins forming a 'network of networks' (NON). Thermal expansion data on parent NGO indicates a field dependent lattice contraction during ordering events. Furthermore, there is a transition from contraction to expansion in an applied field of 6 T in the kagomé planes. For dilution levels $x \geq 0.30$, the system becomes a spin glass with canonical behavior. Specific heat results suggest that the triangular spins become disordered with increasing Mg$^{2+}$ substitution followed by the onset of glassiness in the kagomé planes. Furthermore, there appears to be a dilution driven shift from 3 dimensional to 2 dimensional behavior as the low temperature magnetic heat capacity scales as $T^{2}$ in the spin glass state.