Anisotropy of the antiferromagnetic spin correlations in the superconducting state of YBa₂Cu₃O₇ and YBa₂Cu₄O₈

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We present evidence that the antiferromagnetic spin correlations in optimally doped YBa₂Cu₃O₇ and underdoped YBa₂Cu₄O₈ develop a surprisingly strong anisotropy in the superconducting state. Comparing the ratio of the nuclear spin-lattice relaxation rates of the planar copper and oxygen, measured at the lowest and highest temperatures as well as at Tc, we conclude that the antiferromagnetic in-plane correlations vanish as the temperature goes to zero. This observation is corroborated by the measurement of the copper linewidth in YBa₂Cu₄O₈. In contrast, the out-of-plane correlations do not change appreciably between T=Tc and T=0. Within a model of fluctuating fields this extreme anisotropy of the antiferromagnetic correlations also explains the observed temperature dependence of the anisotropy of the copper relaxation measured in a low external magnetic field.