Ordered state of magnetic charge in the pseudo-gap phase of a cuprate superconductor (HgBa2CuO4+δ)

A symmetry-based interpretation of published experimental results demonstrates that the pseudo-gap phase of underdoped HgBa2CuO4+δ (Hg1201) possesses an ordered state of magnetic charge epitomized by Cu magnetic monopoles. Magnetic properties of one-layer Hg1201 and two-layer YBa2Cu3O6+x (YBCO) cuprates have much in common, because their pseudo-gap phases possess the same magnetic space-group, e.g. both underdoped cuprates allow the magneto-electric (Kerr) effect. Differences in their properties stem from different Cu site symmetries, leaving Cu magnetic monopoles forbidden in YBCO. Resonant x-ray Bragg diffraction experiments can complement the wealth of information available from neutron diffraction experiments on five Hg1201 samples on which our findings are based. In the case of Hg1201 emergence of the pseudo-gap phase, with time-reversal violation, is accompanied by a reduction of Cu site symmetry that includes loss of a centre of inversion symmetry. In consequence, parity-odd x-ray absorption events herald the onset of the enigmatic phase, and we predict dependence of corresponding Bragg spots on magneto-electric multipoles, including the monopole, and the azimuthal angle (crystal rotation about the Bragg wavevector).