We argue that recent neutron scattering measurements by Lake et. al. (Science 291, 1759 (2001)) of the spin excitation spectrum of LSCO in a magnetic field can be understood in terms of proximity to a phase with co-existing superconductivity and spin density wave order. We present a general theory for such quantum transitions, and argue that their low energy spin fluctuations are controlled by a singular correction from the superflow kinetic energy, acting in the region outside the vortex cores. We propose numerous experimental tests of our theory.
@article{arxiv.cond-mat/0103192,
title = {Spin ordering quantum transitions of superconductors in a magnetic field},
author = {Eugene Demler and Subir Sachdev and Ying Zhang},
journal= {arXiv preprint arXiv:cond-mat/0103192},
year = {2009}
}