Quenching of orbital momentum by crystalline fields in a multichannel Kondo impurity

We consider an impurity of spin S interacting via an isotropic spin exchange with conduction electrons of spin 1/2. The conduction electrons can be in n different orbital channels. We assume that crystalline fields split the orbital degrees of freedom into two multiplets, the one with lower energy consisting of n* orbitals and the one of higher energy of n-n* orbitals. The exchange coupling is the same for all channels. We derive the thermodynamic Bethe ansatz equations for this model and discuss the ground-state properties of the impurity as a function of the spin S and the magnetic field. The solution of the ground-state Bethe ansatz equations is obtained numerically. Three situations have to be distinguished when the magnetic field is small compared to the Kondo temperature: (i) If S=n/2 or S=n*/2 the conduction electrons exactly compensate the impurity spin into a singlet ground state, (ii) if S>n/2 the impurity is undercompensated, i.e., only partially compensated leaving an effective spin S-n/2 at low temperatures, and (iii) in all other cases the impurity spin is overcompensated giving rise to critical behavior. The quenching of the orbits by the crystalline field dramatically affects the cases S<n/2, i.e., the critical behavior of the overcompensated multichannel Kondo impurity and the singlet ground state with S=n*/2.