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Field induced spin exciton doublet splitting in d_{x^2-y^2}-wave 115-heavy electron superconductors

We investigate the spin-exciton modes in the superconducting d_{x^2-y^2} state of CeMIn_5 heavy fermion compounds found at the antiferromagnetic wave vector by inelastic neutron scattering. We present a theoretical model that explains the field dependence for both field directions. We show that the recently observed splitting of the spin exciton doublet in CeCoIn_5 into two non-degenerate modes for in-plane field appears naturally in this model. This is due to the spin anisotropy of g- factors and quasiparticle interactions which lead to different resonant conditions for the dynamic susceptibility components. We predict that the splitting of the spin resonance doublet becomes strongly nonlinear for larger fields when the energy of both split components decreases. For field along the tetragonal axis no splitting but only a broadening of the resonance is found in agreement with experiment.