We present a combined magnetometry, muon spin-relaxation $\left(\mu \mathrm{SR}\right)$, and neutron-scattering study of the insulating spin glass ${\mathrm{Zn}}_{0.5}{\mathrm{Mn}}_{0.5}\mathrm{Te}$, for which magnetic ${\mathrm{Mn}}^{2+}$ and nonmagnetic ${\mathrm{Zn}}^{2+}$ ions are randomly distributed on a face-centered cubic lattice. The magnetometry and $\mu \mathrm{SR}$ results confirm a spin freezing transition around $T_f\approx 23$ K, with the spin-fluctuation rate decreasing gradually and somewhat inhomogeneously through the sample volume as the temperature decreases toward $T_f$. Characteristic spin-correlation times well above $T_f$ are on the order of ${10}^{-10}$ s, much slower than typically observed in canonical spin glasses but in line with expectations for a cluster spin glass. Using magnetic pair distribution function (mPDF) analysis and reverse Monte Carlo (RMC) modeling of the magnetic diffuse neutron-scattering data, we show that the spin-glass ground state consists of clusters of spins exhibiting short-range-ordered type-III antiferromagnetic correlations with a locally ordered moment of $3.1\left(1\right){\mu }_{\mathrm{B}}$ between nearest-neighbor spins. The type-III correlations decay exponentially as a function of spin separation distance with a correlation length of approximately 5 Å. The diffuse magnetic scattering and corresponding mPDF show no significant changes across $T_f$, indicating that the dynamically fluctuating short-range spin correlations in the paramagnetic state retain the same basic type-III configuration that characterizes the spin-glass state; the only change apparent from the neutron-scattering data is a gradual reduction of the correlation length and locally ordered moment with increasing temperature. Taken together, these results paint a unique and detailed picture of the local magnetic structure and dynamics in ${\text{Zn}}_{0.5}{\text{Mn}}_{0.5}\text{Te}$ and provide strong evidence that this material is best described as a cluster spin glass. In addition, this work showcases a statistical method for extracting diffuse scattering signals from neutron powder diffraction data, which we developed to facilitate the mPDF and RMC analysis of the neutron data. This method has the potential to be broadly useful for neutron powder diffraction experiments on a variety of materials with short-range atomic or magnetic order.

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• Magnetism
• Spin glasses
• Muon spin relaxation & rotation
• Neutron diffraction
• Neutron pair-distribution function analysis