Cluster spin glass correlations and dynamics in Zn$_{0.5}$Mn$_{0.5}$Te

TL;DR

This study provides a comprehensive, multi-technique view of Zn$_{0.5}$Mn$_{0.5}$Te, demonstrating that its spin-glass ground state comprises short-range, type-III antiferromagnetic spin clusters with a locally ordered moment of about $3.1\ \mu_B$ and a correlation length near $5.7$ Å. Using magnetometry, $\mu$SR, neutron diffraction, mPDF, and reverse Monte Carlo, the authors show that cluster-like correlations persist well above the freezing temperature $T_f \approx 23$ K, with slow, inhomogeneous dynamics that slow further as temperature decreases. Neutron-derived mPDF, complemented by RMC fits, indicates no evidence for type-I correlations and reveals that intra-cluster correlations remain largely unchanged across $T_f$, while the overall correlation length and LMOP diminish with increasing temperature. A key methodological contribution is a novel Bragg-peak removal algorithm enabling reliable extraction of diffuse magnetic scattering on non-optimized instruments, broadening the applicability of mPDF analyses to spin glasses and related short-range magnetic systems.

Abstract

We present a magnetometry, muon spin relaxation ($μ$SR), and neutron scattering study of the insulating face-centered-cubic spin glass Zn$_{0.5}$Mn$_{0.5}$Te. The magnetometry and $μ$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, 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(1) $μ_{\mathrm{B}}$ 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; 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 Zn$_{0.5}$Mn$_{0.5}$Te and show 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.

Figures (11)

• Figure 1: Structure of $\text{Zn}_{0.5}\text{Mn}_{0.5}\text{Te}$, generated in VESTA momma2011vesta. The lattice exhibits a zincblende structure composed of two interlaced FCC lattices, one containing only Te atoms (gold) and the other with 50% each occupancy of Zn and Mn (violet and silver).
• Figure 2: Rietveld refinement of X-ray diffraction (XRD) data.
• Figure 3: Field cooled (red) and zero-field cooled (blue) magnetization, gathered by superconducting quantum interference device (SQUID) magnetometry. Data were collected in a warming sequence. Inset: Second derivative of magnetization (normalized to maximum value of 1). We note that percent-level magnetic impurity phases obscure the typical temperature dependence expected for a spin glass, but clear signatures of the spin-glass transition nevertheless remain, as explained in the main text.
• Figure 4: X-ray PDF fit and residual at 25 K using a model that assumes a uniform distribution of Zn and Mn atoms, consistent with the average structure. Small features are visible at the interlattice and intralattice nearest and next-nearest neighbor distances, which are determined to not be detrimental to the magnetic structure analysis.
• Figure 5: (a) Zero-field $\mu$SR asymmetry spectra for $\text{Zn}_{0.5}\text{Mn}_{0.5}\text{Te}$ collected between 2 K and 88 K. Colored symbols represent the experimental data, solid curves the fits using Eq. \ref{['eq:muSR']}. Inset: Log-log plot of the fast relaxation rate $\lambda_1$ versus the reduced temperature $(T-T_f)/T_f$ above the freezing temperature. (b) Temperature dependence of the fast-relaxing ($a_1$) and slow-relaxing ($a_2$) asymmetry amplitudes. (c) Temperature dependence of the fast relaxation rate $\lambda_1$ and slow relaxation rate $\lambda_2$, where $\lambda_2$ is multiplied by 50 for convenience.