Frustrated spin-12 chains, despite the apparent simplicity, exhibit a remarkably rich phase diagram comprising vector-chiral (VC), spin-density-wave (SDW), and multipolar/spin-nematic phases as a function of the magnetic field. Here we report a study of β-TeVO4, an archetype of such compounds, based on magnetization and neutron diffraction measurements up to 25 T. We find the transition from the helical VC ground state to the SDW state at ∼3 T for the magnetic field along the a and c crystal axes, and at ∼9 T for the field along the b axis. The high-field (HF) state, existing above ∼18 T, i.e., above ∼1/2 of the saturated magnetization, is an incommensurate magnetically ordered state and not the spin-nematic state, as theoretically predicted for the isotropic frustrated spin-1/2 chain. The HF state is likely driven by sizable interchain interactions and symmetric intrachain anisotropies uncovered in previous studies. Consequently, the potential existence of the spin-nematic phase in β-TeVO4 is limited to a narrow field range, i.e., a few tenths of a tesla bellow the saturation of the magnetization, as also found in other frustrated spin-12 chain compounds.
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