Competing magnetic phases in Cr$_{3+\delta}$Te$_4$ are spatially segregated

Cr$_{1+x}$Te$_2$ is a self-intercalated vdW system that is of current interest for its room-temperature FM phases and tunable topological properties. Early NPD measurements on the monoclinic phase Cr$_3$Te$_4$ ($x=0.5$) presented evidence for competing FM and AFM phases. Here we apply neutron diffraction to a single crystal of Cr$_{3+\delta}$Te$_4$ with $\delta=-0.10$ and discover that it consists of two distinct monoclinic phases, one with FM order below $T_{\rm C} \approx 321$ K and another that develops AFM order below $T_{\rm N} \approx 86$ K. In contrast, we find that a crystal with $\delta=-0.26$ exhibits only FM order. The single-crystal analysis is complemented by results obtained with NPD, XPD, and TEM measurements on the $\delta=-0.10$ composition. From observations of spontaneous magnetostriction of opposite sign at $T_{\rm C}$ and $T_{\rm N}$, along with the TEM evidence for both monoclinic phases in a single thin ($\approx$ 100 nm) grain, we conclude that the two phases must have a fine-grained ($\lesssim$ 100 nm) intergrowth character, as might occur from high-temperature spinodal decomposition during the growth process. Calculations of the relaxed lattice structures for the FM and AFM phases with DFT provide a rationalization of the observed spontaneous magnetostrictions. Correlations between the magnitude and orientation of the magnetic moments with lattice parameter variation demonstrate that the magnetic orders are sensitive to strain, thus explaining why magnetic ordering temperatures and anisotropies can be different between bulk and thin-film samples, when the latter are subject to epitaxial strain. Our results point to the need to investigate the supposed coexistence FM and AFM phases reported elsewhere in the Cr$_{1+x}$Te$_2$ system, such as in the Cr$_5$Te$_8$ phase ($x=0.25$).