The magnetic neutron scattering resonance of high-Tc superconductors in external magnetic fields: an SO(5) study

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The magnetic resonance at 41 meV observed in neutron scattering studies of Y Ba₂ Cu₃ O₇ holds a key position in the understanding of high-Tc superconductivity. Within the SO(5) model for superconductivity and antiferromagnetism, we have calculated the effect of an applied magnetic field on the neutron scattering cross-section of the magnetic resonance. In the presence of vortices, the neutron scattering cross-section shows clear signatures of not only the fluctuations in the superconducting order parameter ψ, but also the modulation of the phase of ψdue to vortices. In reciprocal space we find that i) the scattering amplitude is zero at (pi/a,pi/a), ii) the resonance peak is split into a ring with radius pi/d centered at (pi/a,pi/a), d being the vortex lattice constant, and consequently, iii) the splitting pi/d scales with the magnetic field as sqrtB.