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We report a comprehensive polarized and unpolarized neutron scattering studyof the evolution of the dynamical spin susceptibility with temperature anddoping in three underdoped single crystals of the \YBCO{6+x} high temperaturesuperconductor: \YBCO{6.5} (Tc = 52 K), \YBCO{6.7} (Tc = 67 K), and \YBCO{6.85}(T_c = 87 K). Theoretical implications of these data are discussed, and acritique of recent attempts to relate the spin excitations to thethermodynamics of high temperature superconductors is given.Comment: minor revisions, to appear in PR

physical review. b, condensed matter

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Spin susceptibility in underdopedYBa2Cu3O6