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We present a comprehensive study of the short-ranged nuclear and magneticorder in the two-dimensional spin glass, Mn$_{0.5}$Fe$_{0.5}$PS$_3$. Nuclearneutron scattering data reveal a random distribution of Mn$^{2+}$ and Fe$^{2+}$ions within the honeycomb layers, which gives rise to a spin glass statethrough inducing competition between neighbouring exchange interactions,indicated in magnetic susceptibility data by a cusp at the glass transition,$T_g = 35$ K. Analysis of magnetic diffuse neutron scattering data collectedfor both single crystal and polycrystalline samples gives further insight intothe origin of the spin glass phase, with spin correlations revealing a mixtureof satisfied and unsatisfied correlations between magnetic moments within thehoneycomb planes, which can be explained by considering the magnetic structuresof the parent compounds, MnPS$_3$ and FePS$_3$. We found that, on approaching$T_g$ from above, an ensemble-averaged correlation length of $\xi = 5.5(6)$\r{A} developed between satisfied correlations, and below $T_g$, the glassybehaviour gave rise to a distance-independent correlation between unsatisfiedmoments. Correlations between the planes were found to be very weak, whichmirrored our observations of rod-like structures parallel to the c* axis in oursingle crystal diffraction measurements, confirming the two-dimensional natureof Mn$_{0.5}$Fe$_{0.5}$PS$_3$.

Local nuclear and magnetic order in the two-dimensional spin glass, Mn$_{0.5}$Fe$_{0.5}$PS$_3$