Possible candidate for the realization of the floating phase in the S=52 frustrated spin-chain model: K3Fe(MoO4)2(Mo2O7)

The frustrated spin-chain (FSC) systems exhibit exotic ground states and distinct quantum phase transitions. The $S=\frac{1}{2}$ FSC is known to exhibit the Kosterlitz-Thouless transition from a commensurate gapless phase to a fully dimerized gapped phase upon the ratio of next-nearest-neighbor to nearest-neighbor coupling $(\ensuremath{\alpha}=\frac{{J}₂}{{J}₁})$ being tuned. On the other hand, the $S=\frac{5}{2}$ FSC system is known to show transitions from a commensurate gapless phase to partially dimerized and incommensurate floating phases [Chepiga, Affleck, and Mila, Phys. Rev. B 105, 174402 (2022)]. While a large region of the floating phase has been theoretically predicted for the $S=\frac{5}{2}$ FSC model when $\ensuremath{\alpha}>0.43$, it is yet to be explored experimentally. Here, we have investigated a compound ${\mathrm{K}}₃\mathrm{Fe}{({\mathrm{MoO}}₄)}₂({\mathrm{Mo}}₂{\mathrm{O}}₇)$, having well-separated $S=\frac{5}{2}$ FSCs. The electronic structure calculations show that the $\ensuremath{\alpha}=\frac{{J}₂}{{J}₁}$ is close to 0.9, being similar to another FSC compound ${\mathrm{Bi}}₃{\mathrm{FeMo}}₂{\mathrm{O}}₁₂$ $(\ensuremath{\alpha}\ensuremath{\approx}1.1)$. No magnetic long-range order is found down to 0.09 K, despite the relatively sizable Curie-Weiss temperature ${\ensuremath{\theta}}_CW=\ensuremath{-}18\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The magnetic heat capacity shows the power-law behavior, indicating that the compound exhibits gapless excitations. Based on the experimental results and the theoretical calculations employed by density functional theory, we argue that the titled system is a possible candidate for exhibiting the floating phase.