Magnetism in the cuprates induced by an external magnetic field

The proximity of antiferromagnetism and superconductivity in the phase diagram common to all the high temperature superconductors has long suggested an interaction between antiferromagnetism and superconductivity. In the vortex state, where a large magnetic field destroys superconductivity in the vortex cores, a number of theories have suggested that antiferromagnetism or spin density waves may be recovered in the cores. Recent experiments seem to indicate that the application of a large magnetic field can induce magnetism. In this contribution, we review theoretical arguments for vortex state magnetism and recent experimental evidence. In particular, we focus on evidence from muon spin rotation for vortex core magnetism in underdoped YBCO.