Screening of Point Charge Impurities in Highly Anisotropic Metals: Application to μ+-Spin Relaxation in Underdoped Cuprate Superconductors

We calculate the screening charge density distribution due to a point charge, such as that of a positive muon (mu(+)), placed between the planes of a highly anisotropic layered metal. In underdoped hole cuprates the screening charge converts the charge density in the metallic-plane unit cells in the vicinity of the mu(+) to nearly its value in the insulating state. The current-loop-ordered state observed by polarized neutron diffraction then vanishes in such cells, and also in nearby cells over a distance of order the intrinsic correlation length of the loop-ordered state. This strongly suppresses the magnetic field at the mu(+) site. We estimate this suppressed field in underdoped YBa2Cu3O6+x and La2-xSrxCuO4, and find consistency with the observed similar to 0.2 G field in the former case and the observed upper bound of similar to 0.2 G in the latter case. This resolves the controversy between the neutron diffraction and mu-spin relaxation experiments.