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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 $\tau_h=0.3443(1)$.

Predicting magnetic ordering in kagome compounds offers the possibility of harnessing topological or flat-band physical properties through tuning of the magnetism. Here, we examine the magnetic interactions and phases of ErMn$_6$Sn$_6$ which belongs to a family of $R$Mn$_6$Sn$_6$, $R=$ Sc, Y, Gd--Lu, compounds with magnetic kagome Mn layers, triangular $R$ layers, and signatures of topological properties. Using results from single-crystal neutron diffraction and mean-field analysis, we find that ErMn$_6$Sn$_6$ sits close to the critical boundary separating the spiral-magnetic and ferrimagnetic ordered states typical for nonmagnetic versus magnetic $R$ layers, respectively. Finding interlayer magnetic interactions and easy-plane Mn magnetic anisotropy consistent with other members of the family, we predict the existence of a number of temperature and field dependent collinear, noncollinear, and noncoplanar magnetic phases. We show that thermal fluctuations of the Er magnetic moment, which act to weaken the Mn-Er interlayer magnetic interaction and quench the Er magnetic anisotropy, dictate magnetic phase stability. Our results provide a starting point and outline a multitude of possibilities for studying the behavior of Dirac fermions in $R$Mn$_6$Sn$_6$ compounds with control of the Mn spin orientation and real-space spin chirality., Comment: Supplementary Information included

We report neutron-diffraction results on single-crystal CaMn$_2$P$_2$ containing corrugated Mn honeycomb layers and determine its ground-state magnetic structure. The diffraction patterns consist of prominent (1/6, 1/6, $L$) reciprocal lattice unit (r.l.u.; $L$ = integer) magnetic Bragg reflections, whose temperature-dependent intensities are consistent with a first-order antiferromagnetic phase transition at the N\'eel temperature $T_{\rm N} = 70(1)$ K. Our analysis of the diffraction patterns reveals an in-plane $6\times6$ magnetic unit cell with ordered spins that in the principal-axis directions rotate by 60-degree steps between nearest neighbors on each sublattice that forms the honeycomb structure, consistent with the $P_Ac$ magnetic space group. We find that a few other magnetic subgroup symmetries ($P_A2/c$, $P_C2/m$, $P_S\bar{1}, P_C2, P_Cm, P_S1$) of the paramagnetic $P\bar{3}m11^\prime$ crystal symmetry are consistent with the observed diffraction pattern. We relate our findings to frustrated $J_1$-$J_2$-$J_3$ Heisenberg honeycomb antiferromagnets with single-ion anisotropy and the emergence of Potts nematicity