Non-collinear 2k antiferromagnetism in the Zintl semiconductor Eu\(_5\)In\(_2\)Sb\(_6\)

Eu\(_5\)In\(_2\)Sb\(_6\) is an orthorhombic non-symmorphic small band gap semiconductor with three distinct Eu\(^{2+}\) sites and two low-temperature magnetic phase transitions. The material displays one of the greatest (negative) magnetoresistances of known stoichiometric antiferromagnets and belongs to a family of Zintl materials that may host an axion insulator. Using single crystal neutron diffraction, we show that the \(T_{\mathrm{N1}}=14\mathrm{~K}\) second-order phase transition is associated with long-range antiferromagnetic order within the chemical unit cell \(\left( k_1 = (000) \right)\). Upon cooling below \(T_{\mathrm{N1}}\), the relative sublattice magnetizations of this structure vary until a second-order phase transition at \(T_{\mathrm{N2}}=7\mathrm{~K}\) that doubles the unit cell along the \(\hat{c}\) axis \(\left( k_2 = \left(00\frac{1}{2}\right) \right)\). We show the anisotropic susceptibility and our magnetic neutron diffraction data are consistent with magnetic structures described by the \(\Gamma_3\) irreducible representation with the staggered magnetization of the \(k_1\) and \(k_2\) components polarized along the \(\hat{b}\) and \(\hat{a}\) axis, respectively. As the \(k_2\) component develops, the amplitude of the \(k_1\) component is reduced, which indicates a 2k non-collinear magnetic structure. Density functional theory is used to calculate the energies of these magnetic structures and to show the \(k_1\) phase is a metal so \(T_{\mathrm{N1}}\) is a rare example of a unit-cell-preserving second-order phase transition from a paramagnetic semiconductor to an antiferromagnetic metal. DFT indicates the transition at \(T_{\mathrm{N2}}\) to a doubled unit cell reduces the carrier density of the metal, which is consistent with resistivity data.