Within the kinetic energy driven superconducting mechanism, the dynamical spin response of the bilayer cuprate superconductors is studied. It is shown that there are two nondegenerate magnetic modes with odd and even symmetries, respectively, due to the bilayer interaction in the bilayer cuprate superconductors. Although the magnetic scattering in both odd and even symmetries shows an hour-glass-shaped dispersion, the commensurate magnetic resonance energy in the odd symmetry has a domelike shape of the doping dependence, while the commensurate magnetic resonance energy in the even symmetry decreases with increasing doping.
Quasiclassical Theory of Spin Dynamics in Superfluid
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He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States