Magnetotransport signatures of antiferromagnetism coexisting with charge order in the trilayer cuprate HgBa(2)Ca(2)Cu(3)O(8+δ)

Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO(2) planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa(2)Ca(2)Cu(3)O(8+δ) and we report quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. The presence of an ordered antiferromagnetic metallic state that extends deep in the superconducting phase is a key ingredient that supports magnetically mediated pairing interaction in cuprates.