In recent electron probe microanalysis of the samples described in our manuscript, the Sr content was found to be x = 0.33Ϯ 0.01 and not 0.30. The correct chemical formula is thus La 1.67 Sr 0.33 CuO 4 . This places the compound slightly further away from the superconducting region of the La 2−x Sr x CuO 4 phase diagram, but otherwise has no effect on any of the conclusions of the original paper. In a subsequent paper, 1 the sample labeled x = 0.33 refers to the same compound reported in this manuscript. In three other recent articles, the Hall, 2 Nernst, 3 and thermopower 4 data reported for x = 0.30 should be relabeled x = 0.33 . 1 R.

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Many physical properties of high-temperature (high-T c ) 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 longperiod 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 threedimensional magnetic couplings which survive into the superconducting state, and coexist with the crucial inter-layer couplings responsible for threedimensional 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.La 2 CuO 4 is the parent compound of the original high temperature superconductor La 2-x Ba x CuO 4 discovered by Bednorz and Muller 13 nearly two decades ago. Here we examine the related cuprate La 2-x Sr x CuO 4 (LSCO) with x=0.10 and a superconducting transition temperature of T c =29 K. Previous measurements indicate weak, long-period magnetic order derived from defects which differ from sample to sample, and stronger field-induced order with all of the hallmarks of an intrinsic effect 8 , including sample-independence and a sharp onset temperature indistinguishable from T c . While these measurements have stimulated theory 14,15,16 , they could only probe magnetism within the CuO 2 planes, and thus were insensitive to inter-planar interactions. The latter are ultimately responsible for technologically useful three-dimensional superconductivity and for key features of the competition between magnetism and superconductivity 16 . Apart from the inter-planar correlations, it is important to establish whether it is the coupling of the field to the spins or to the motion of the electrons which is responsible for the field-induced order. Clarification would permit rigorous scrutiny of the idea that the vortices in the superconductors nucleate the field-induced order, a phenomenon rather different from the Zeemaninduced pair-breaking likely to be responsible for the high-field superconductorinsulator transition characteristic of the underdoped cuprates 17,18 .The standard technique for measurement of antiferromagnetic order is neutron diffraction, the mag...

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