Leggett's modes in magnetic systems with Jahn-Teller distortion

Leggett's mode is a collective excitation corresponding to the oscillation of the relative phase of the order parameters in a two band superconductor, with frequency proportional to interband coupling. We report on the existence of modes, similar to Leggett's mode, in magnetic systems with Jahn-Teller distortion. The minimal Kugel-Khomskii model, which describes simultaneously both the spin and the orbital order, is studied. The dynamical degrees of freedom are spin-s operators of localized spins and pseudospin-τ operators, which respond to the orbital degeneracy and satisfy the similar commutation relation with those of the spin operators. In the case of “G-type antiferro” spin and pseudospin order the system possesses two antiferromagnetic magnons with equal spin-wave velocities and two Leggett's modes with equal gaps proportional to the square root of the spin-pseudospin interaction constant. In the case of “ferro” spin and pseudospin order the system possesses one ferromagnetic magnon and one Leggett's mode with gap proportional to the spin-pseudospin interaction constant. We conclude that Leggett's modes, in the spectrum of the magnetic systems with Jahn-Teller distortion, are generic features of these systems.