Tetrahedrally ferromagnetic correlations and a glassy-freezing anomaly in the breathing pyrochlore magnet $\mathrm{AgInCr_4S_8}$ with partial $A$-site disorder
We investigate the chromium breathing pyrochlore sulfide $\mathrm{AgInCr_4S_8}$, a chromium-based thiospinel, by synchrotron x-ray and neutron powder diffraction, dc magnetization, and heat capacity. Diffraction confirms the $F\bar{4}3m$ breathing structure with alternating large and small $\mathrm{Cr_4}$ tetrahedra, a large breathing ratio ($d^\prime/d = 1.106$ at 300 K), and substantial Ag/In intermixing on the $A$ sublattice ($\sim 16\%$). No structural transition or magnetic Bragg peaks are detected down to 1.5 K. An enlarged low-angle difference plot between the 1.5 and 20 K neutron diffraction patterns shows a weak broad diffuse-like enhancement, consistent with short-range or frozen correlated moments within the sensitivity of the present data. Susceptibility yields a positive Weiss temperature $\theta_{\mathrm{W}} = +92$ K and a moment enhancement in 30--60 K, while the magnetic entropy released by $\sim 30$ K approaches a scale of order $R\ln 13$, together consistent with the development of short-range tetrahedral ferromagnetic correlations and an effective $S = 6$ cluster-moment picture. A broad susceptibility cusp with ZFC--FC bifurcation and a low-temperature specific heat anomaly near 9 K indicate a phenomenological glassy-freezing anomaly without long-range order. $\mathrm{AgInCr_4S_8}$ provides a benchmark for the interplay of strong breathing distortion and quenched $A$-site disorder in chromium breathing pyrochlores.