Spin reorientation and interplanar interactions of the two-dimensional triangular-lattice Heisenberg antiferromagnets h − ( Lu , Y ) MnO 3 and h − ( Lu , Sc ) FeO 3

This study explored the magnetic properties and dynamics of two, two-dimensional (2D) triangular-lattice Heisenberg antiferromagnets (2D-TLHAF), $h\text{\ensuremath{-}}(\mathrm{Lu},\mathrm{Y}){\mathrm{MnO}}₃$ and $h\text{\ensuremath{-}}(\mathrm{Lu},\mathrm{Sc}){\mathrm{FeO}}₃$, through neutron powder diffraction, single-crystal neutron scattering, and polarized neutron-scattering experiments. We identified that the magnetic structures of both materials are described by two irreducible representations ${\mathrm{\ensuremath{\Gamma}}}₁$ $(P{6}₃cm)$ and ${\mathrm{\ensuremath{\Gamma}}}₂$ $(P{6}₃{c}^{\ensuremath{'}}{m}^{\ensuremath{'}})$ for $h\text{\ensuremath{-}}{\mathrm{Lu}}_0.47{\mathrm{Sc}}_0.53{\mathrm{FeO}}₃$, ${\mathrm{\ensuremath{\Gamma}}}₃$ $(P{6}₃^{\ensuremath{'}}c{m}^{\ensuremath{'}})$, and ${\mathrm{\ensuremath{\Gamma}}}₄$ $(P{6}₃^{\ensuremath{'}}{c}^{\ensuremath{'}}m)$ for $h\text{\ensuremath{-}}{\mathrm{Lu}}_0.3{\mathrm{Y}}_0.7{\mathrm{MnO}}₃$. Polarized neutron scattering has shown that accurately describing the magnetic structures of a 2D triangular-lattice Heisenberg antiferromagnet (2D-TLHAF) requires the use of two irreducible representations, rather than relying on the assumption that the system undergoes spin reorientation when using only one irreducible representation. We then investigated the spin-wave dispersion of both materials on the basis of these magnetic structures. The branch in the lowest energy of the spin wave of $h\text{\ensuremath{-}}{\mathrm{Lu}}_0.47{\mathrm{Sc}}_0.53{\mathrm{FeO}}₃$ showed a flat dispersion along the $c$ axis, while ${\mathrm{Lu}}_0.3{\mathrm{Y}}_0.7{\mathrm{MnO}}₃$ displayed a distinct dispersion along the $c$ axis, suggesting the presence of interplanar interactions in the latter. We discuss the potential causes of spin reorientation and multiferroicity in the triangular antiferromagnetic on the basis of the parameters determined.