  Understanding the pseudo-gap phase from which a superconducting state emerges
is a central problem in the physics of cuprates. The phase exists below a
temperature T* for less than optimal doping of holes, and no clear jump in the
specific heat or change in lattice symmetry is observed on crossing T*. Here we
show that, two sets of intriguing experimental results in the literature
concerning magnetic properties of underdoped YBCO are united in a single theory
based on Cu quadrupole moments. The quadrupole is a product of spin and the
electric dipole, so there is no magnetic dipole moment, and standard
crystallography describes the magnetic motif. One experiment employed the Kerr
effect and the second Bragg diffraction of polarized neutrons, and both are
shown to imply an order-parameter for the pseudo-gap phase composed of
magneto-electric quadrupoles at in-plane Cu sites in a ferro-type order.
  The successful interpretation of neutron diffraction data for YBCO yields the
first experimental evidence that neutrons are deflected by magneto-electric
multipoles. Predicted in 2014, our verification of the effect validates a new
application for the experimental technique of choice in studies of magnetic
motifs and excitations.
