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

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