Weak Ferromagnetism Accompanying Loop current order in Underdoped Cuprates

We discuss the necessary symmetry conditions and the different ways in which they can be physically realized for the occurrence of ferromagnetism accompanying the loop current orbital magnetic order observed by polarized neutron-diffraction experiments or indeed any other conceivable principal order in the under-doped phase of cuprates. We contrast the Kerr effect experiments in single crystals observing ferromagnetism with the direct magnetization measurements in large powder samples, which do not observe it. We also suggest experiments to resolve the differences among the experiments, all of which we believe to be correct.

Screening of point charge impurities in highly anisotropic metals: application to $mu^+$ spin relaxation in underdoped cuprates

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 in turn strongly suppresses the loop-current field at the $mu^+$ site. We estimate this suppressed field in underdoped YBa$_2$Cu$_3$O$_{6+x}$ and La$_{2-x}$Sr$_x$CuO$_4$, and find consistency with the observed 0.2--0.3 G field in the former case and the observed upper bound of $sim$0.2 G in the latter case. This resolves the controversy between the neutron diffraction and $mu$SR experiments. The screening calculation also has relevance for the effect of other charge impurities in the cuprates, such as the dopants themselves.