Influence of vortices on the magnetic resonance in cuprate superconductors

We investigate several theoretical possibilities for the suppression in a c-axis magnetic field of the magnetic resonance recently observed in inelastic neutron scattering experiments on ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}.$ We find that neither the Doppler shift of the quasiparticle states caused by supercurrents outside the vortex core, nor an assumed spatially uniform suppression of the coherence factors or spectral gap due to the applied field, can account for the observed effect. In contrast, suppressing the gap or the coherence factors in the vortex core to zero is consistent with the data, and an even simpler description of the data can be achieved by assuming that the resonance is not supported within the core. These three models can then be used to estimate the effective radius ${\xi }_{\mathrm{eff}}$ around each vortex, which we find to be larger than ${\xi }_{\mathrm{sc}}$ but smaller than ${\xi }_{\mathrm{sc}}+{\xi }_{\mathrm{mag}},$ where ${\xi }_{\mathrm{sc}}$ and ${\xi }_{\mathrm{mag}}$ are respectively the superconducting and spin-spin correlation lengths. We use this observation to predict the doping dependence of the field suppression.