We report a study of the spin dynamics of the frustrated ferromagnetic J1-J2 chain compound linarite, PbCuSO4(OH)2, in applied magnetic fields up to field polarization. By means of an extremeenvironment inelastic neutron scattering experiment, we have measured the low-energy spin excitations of linarite in fields up to 8.8 T for H b axis and temperatures as low as 500 mK. We have recorded the spin wave excitation spectra along h, k and l for the field-induced magnetic phases IV, V and the field polarized state close to saturation. By employing first-principles calculations, we estimate the leading magnetic exchanges out of the bc plane and model the dispersion relations using linear spin wave theory. In this way, we find evidence for a (very weak) residual magnetic exchange coupling out of the bc plane. Together with the previously established dominant in-chain couplings J1 and J2 and the interchain coupling J3, we derive an effective set of exchange couplings for a microscopic description of linarite. Further, we find that the peculiar character of the spin-density wave phase V manifests itself in the measured spin dynamics. Having gained new insights from our applied-field spin wave analysis, we discuss our experimental results regarding the possibility of a spin-multipolar state close to saturation.
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