Weak trimerization in the frustrated two-dimensional triangular Heisenberg antiferromagnet LuyY1−yMnO3

To understand the 2D triangular Heisenberg antiferromagnetic system, we investigated the magnetic structures and the dynamics of ${\mathrm{Lu}}_{y}{\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{MnO}}_{3}$ in detail. The substitutions are adjusted to the Mn atomic position close to ${x}_{\text{Mn}}=\frac{1}{3}$. The neutron powder diffraction data claims that the magnetic structure of ${\mathrm{Lu}}_{y}{\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{MnO}}_{3}$ is described as a mixture of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ ($P{6}_{3}^{\ensuremath{'}}c{m}^{\ensuremath{'}}$) and ${\mathrm{\ensuremath{\Gamma}}}_{4}$ ($P{6}_{3}^{\ensuremath{'}}{c}^{\ensuremath{'}}m$) at the ${x}_{\text{Mn}}$ position for $y=0.15$, 0.30, and 0.45. The ratio of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ and ${\mathrm{\ensuremath{\Gamma}}}_{4}$ depends on temperature and composition and the fraction of ${\mathrm{\ensuremath{\Gamma}}}_{3}$ increases upon cooling, while no clear trimerization was observed at the ${x}_{\text{Mn}}$ position. We estimated exchange parameters from the analysis of the low-energy part of the spin waves. The results showed a weak trimerization effect on cooling because the nearest-neighbor exchange interaction is slightly enhanced. The temperature dependence of the spin-wave dispersion around the $\mathrm{\ensuremath{\Gamma}}$ point shows that the spin gap closes with increasing temperature because the exchange interactions in the nearest Mn-Mn neighbor become smaller. Gapless diffusive magnetic excitation from a Mn triangular lattice has been observed in a wide range in $Q$ and $E$ space of ${\mathrm{Lu}}_{y}{\mathrm{Y}}_{1\ensuremath{-}y}{\mathrm{MnO}}_{3}$. We found that ${\mathrm{Lu}}_{0.3}{\mathrm{Y}}_{0.7}{\mathrm{MnO}}_{3}$ could be an ideal case to investigate the trimerization, frustrated magnetism, and magnetoelastic coupling often observed in two-dimensional triangular lattice Heisenberg antiferromagnet systems.