Crystal and magnetic structures of $R_2$Ni$_2$In compounds ($R$ = Tb and Ho)

Crystal and magnetic structures of $R_2$Ni$_2$In ($R$ = Tb and Ho) have been studied by powder neutron diffraction at low temperatures. The compounds crystallize in an orthorhombic crystal structure of the Mn$_2$AlB$_2$-type. At low temperatures, the magnetic moments localized solely on the rare earth atoms form antiferromagnetic structures. The Tb magnetic moments, equal to 8.65(6) $\mu_B$ and parallel to the $c$-axis, form a collinear magnetic structure described by the propagation vector $\boldsymbol{k} = [\frac{1}{2}, \frac{1}{2}, \frac{1}{2}]$. This magnetic structure is stable up to the N\'eel temperature equal to 40 K. For Ho$_2$Ni$_2$In a complex, temperature-dependent magnetic structure is detected. In the temperature range 3.5-8.6 K, an incommensurate magnetic structure, described by the propagation vector $\boldsymbol{k}_1 = [0.76, 0, 0.52]$ is observed, while in the temperature interval 2.2-3.1 K the magnetic order is described by two propagation vectors, namely, $\boldsymbol{k}_2 = [\frac{5}{6}, 0.16, \frac{1}{2}]$ and its third harmonics $3\boldsymbol{k}_2 = [\frac{5}{2}, 0.48, \frac{3}{2}]$. Below 2 K, a coexistence of all magnetic structures detected at higher temperatures is observed. For all magnetic phases, the Ho magnetic moments are parallel to the $c$-axis. The low temperature heat capacity data confirm a first order transition near 3 K