Weak ferromagnetism accompanying loop current order in underdoped cuprate superconductors

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 underdoped 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.