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A new mechanism for relaxing the nuclear magnetic moments, in which a pair of spin-polarized BCS quasiparticles is emitted or absorbed, and which dominates at low temperature, is identified in type-II d-wave superconductors in an external magnetic field above Hc1. The results of the theory are compared with the NMR experiments on YBCO in high magnetic fields and found to agree without invoking antiferromagnetic order in the vortex core.

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