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Understanding the pseudo-gap phase from which a superconducting state emergesis a central problem in the physics of cuprates. The phase exists below atemperature T* for less than optimal doping of holes, and no clear jump in thespecific heat or change in lattice symmetry is observed on crossing T*. Here weshow that, two sets of intriguing experimental results in the literatureconcerning magnetic properties of underdoped YBCO are united in a single theorybased on Cu quadrupole moments. The quadrupole is a product of spin and theelectric dipole, so there is no magnetic dipole moment, and standardcrystallography describes the magnetic motif. One experiment employed the Kerreffect and the second Bragg diffraction of polarized neutrons, and both areshown to imply an order-parameter for the pseudo-gap phase composed ofmagneto-electric quadrupoles at in-plane Cu sites in a ferro-type order.  The successful interpretation of neutron diffraction data for YBCO yields thefirst experimental evidence that neutrons are deflected by magneto-electricmultipoles. Predicted in 2014, our verification of the effect validates a newapplication for the experimental technique of choice in studies of magneticmotifs and excitations.

Ferro-type order of magneto-electric quadrupoles as an order-parameter for the pseudo-gap phase of a cuprate superconductor