Ferro-type order of magneto-electric quadrupoles in the pseudo-gap phase of YBa2Cu3O6 + x unearthed by neutron diffraction

A theory that fully describes previously observed neutron Bragg spots indicative of magnetic order in the pseudo-gap phase of YBa2Cu3O6 + x is presented. Magnetic diffraction intensities, unveiled by polarization analysis, are explained by parity-violating magnetic (magneto-electric) quadrupoles at in-plane Cu sites arranged in a simple ferro-type motif. An absence of conventional spin and orbital angular momentum dipoles in the theory is compatible with the occurrence of superconductivity and strongly suggests, moreover, that magneto-electric quadrupoles are the primary order-parameter in the pseudo-gap phase.