Absence of overscreened Kondo effect in a ferromagnetic host

We study the low-temperature behavior of a boundary magnetic impurity S' = 1/2 in an open ferromagnetic Takhatajian-Babujian spin-S chain. For antiferromagnetic Kondo coupling, it is shown via the Bethe ansatz solution that the impurity spin is always locked into the critical behavior of the bulk. At low temperatures, a local composite of spin-(S-1/2) forms near the impurity site and its contribution to specific heat is of simple power law T-1/2. The absence of the overscreened Kondo effect is due to the large correlation length of host spins which is divergent near the quantum critical point.