  We study the mixing problem of the determinant like operators in ABJM theory
to two loop order in the scalar sector. The gravity duals of these operators
are open strings attached to the maximal giant graviton, which is a D4-brane
wrapping a $\mathbb{CP}^2$ inside $\mathbb{CP}^3$ in our case. The anomalous
dimension matrix of these operators can be regarded as an open spin chain
Hamiltonian. We provide strong evidence of its integrability based on
coordinate Bethe ansatz method and boundary Yang-Baxter equation.
