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We present evidence that the antiferromagnetic spin correlations in optimallydoped YBa_2Cu_3O_7 and underdoped YBa_2Cu_4O_8 develop a surprisingly stronganisotropy in the superconducting state. Comparing the ratio of the nuclearspin-lattice relaxation rates of the planar copper and oxygen, measured at thelowest and highest temperatures as well as at T_c, we conclude that theantiferromagnetic in-plane correlations vanish as the temperature goes to zero.This observation is corroborated by the measurement of the copper linewidth inYBa_2Cu_4O_8. In contrast, the out-of-plane correlations do not changeappreciably between T=T_c and T=0. Within a model of fluctuating fields thisextreme anisotropy of the antiferromagnetic correlations also explains theobserved temperature dependence of the anisotropy of the copper relaxationmeasured in a low external magnetic field.Comment: Minor revisions. Accepted for publication in J. Phys.: Condens.  Matter as a Lette

journal of physics. condensed matter

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