Coupled-bilayer two-dimensional magnetic order of the Dy ions in ${\mathrm{Dy}}_2$${\mathrm{Ba}}_4$${\mathrm{Cu}}_7$${\mathrm{O}}_{15}$

Neutron scattering has been used to investigate the magnetic ordering of the Dy ions in the superconducting (${\mathit{T}}_{\mathit{c}}$≊60 K) ${\mathrm{Dy}}_2$ ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_7$ ${\mathrm{O}}_{15}$ (2:4:7) material. A modulated saw-tooth scattering profile is observed, indicative of a coupled-bilayer two-dimensional (2D) system in which the nearest-neighbor Dy spins within the a-b plane are coupled antiferromagnetically, with the moment direction along the c axis. The a-b-plane spin configuration is identical to the one which has been observed for the related ${\mathrm{DyBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ (1:2:3) and ${\mathrm{Dy}}_2$ ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_8$ ${\mathrm{O}}_{16}$ (2:4:8) materials. The Néel temperature in the present system is found to be ∼1.3 K, while no three-dimensional (3D) long-range order is seen to the lowest temperature measured (∼90 mK). The 2D behavior of this system originates from two sources. First, the c-axis spacing of the magnetic ions is ∼3 times the a-b spacing, and this structural anisotropy renders the c-axis interaction much weaker than the interactions within the a-b plane. Indeed we find that the calculated dipolar interaction between layers varies exponentially with distance, and is reduced by a factor of 7000 compared with the intralayer interactions. Second, every other a-b layer is shifted along the b axis by b/2, which causes a cancellation of the magnetic interplane interactions between the shifted and unshifted layers. Hence the magnetic system consists of sets of isolated bilayers. We anticipate that a similar coupled-bilayer 2D behavior should occur in other ${\mathit{scrR}}_2$ ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_7$ ${\mathrm{O}}_{15}$ systems (scrR= rare-earth element, except Er) which exhibit the same a-b-plane spin configuration as the Dy.