Three-dimensionality of field-induced magnetism in a high-temperature superconductor

Many physical properties of high-temperature superconductors are two-dimensional phenomena derived from their square-planar CuO 2 building blocks. This is especially true of the magnetism from the copper ions. As mobile charge carriers enter the CuO 2 layers, the antiferromagnetism of the parent insulators, where each copper spin is antiparallel to its nearest neighbours 1 , evolves into a fluctuating state where the spins show tendencies towards magnetic order of a longer periodicity. For certain charge-carrier densities, quantum fluctuations are sufficiently suppressed to yield static long-period order 2 , 3 , 4 , 5 , 6 , and external magnetic fields also induce such order 7 , 8 , 9 , 10 , 11 , 12 . Here we show that, in contrast to the chemically controlled order in superconducting samples, the field-induced order in these same samples is actually three-dimensional, implying significant magnetic linkage between the CuO 2 planes. The results are important because they show that there are three-dimensional magnetic couplings that survive into the superconducting state, and coexist with the crucial inter-layer couplings responsible for three-dimensional superconductivity. Both types of coupling will straighten the vortex lines, implying that we have finally established a direct link between technical superconductivity, which requires zero electrical resistance in an applied magnetic field and depends on vortex dynamics, and the underlying antiferromagnetism of the cuprates.