Single crystal growth and characterization of antiferromagnetically ordering EuIn$_2$

We report the single crystal growth and characterization of EuIn$_2$, a magnetic topological semimetal candidate according to our density functional theory (DFT) calculations. We present results from electrical resistance, magnetization, M\"ossbauer spectroscopy, and X-ray resonant magnetic scattering (XRMS) measurements. We observe three magnetic transitions at $T_{\text{N}1}\sim 14.2~$K, $T_{\text{N}2}\sim12.8~$K and $T_{\text{N}3}\sim 11~$K, signatures of which are consistently seen in anisotropic temperature dependent magnetic susceptibility and electrical resistance data. M\"ossbauer spectroscopy measurements on ground crystals suggest an incommensurate sinusoidally modulated magnetic structure below the transition at $T_{\text{N}1}\sim 14~$K, followed by the appearance of higher harmonics in the modulation on further cooling roughly below $T_{\text{N}2}\sim13~$K, before the moment distribution squaring up below the lowest transition around $T_{\text{N}3}\sim 11~$K. XRMS measurements showed the appearance of magnetic Bragg peaks below $T_{\text{N}1}\sim14~$K, with a propagation vector of $\bm{\tau}$ $=(\tau_h,\bar{\tau}_h,0)$, with $\tau_h$varying with temperature, and showing a jump at $T_{\text{N}3}\sim11$~K. The temperature dependence of $\tau_h$ between $\sim11$~K and $14$~K shows incommensurate values consistent with the M\"{o}ssbauer data. XRMS data indicate that $\tau_h$ remains incommensurate at low temperatures and locks into $\tau_h=0.3443(1)$.