Spin Dynamics in the Floating Phase of a Frustrated Spin-5/2 Chain Magnet

The J₁–J₂ Heisenberg chain is a paradigmatic model for exploring how frustration tunes quantum phases in one-dimensional magnets. For spin-1/2, increasing J₂ drives a transition from a commensurate critical Tomonaga–Luttinger liquid at small frustration to a dimerized gapped phase. For larger spins (S ≥ 3/2), a critical incommensurate phase, known as the floating phase, emerges in the intermediate regime, characterized by gapless excitations, algebraically decaying correlations, and a continuously varying wavevector. Inelastic neutron scattering (INS) is employed to investigate Bi₃FeMo₂O₁₂, a frustrated spin-5/2 chain compound and compelling candidate for realizing floating-phase physics. The exchange couplings J₁ and J₂, determined from the ordering wavevector and saturation field, place the material firmly within the floating-phase regime. Driven by weak interchain coupling, this floating-phase state evolves into three-dimensional incommensurate magnetic order at low temperature. INS measurements reveal a highly structured excitation continuum that cannot be accounted for by conventional spin-wave theory based on the long-range ordered ground state. Instead, full quantum density matrix renormalization group (DMRG) simulations of the minimal J₁–J₂ model capture the key features of the experimental spectra, providing direct evidence that the observed excitations originate from the underlying floating phase.