Impurity entanglement through electron scattering in a magnetic field

We study the entanglement of magnetic impurities in an environment of electrons through successive scattering while an external magnetic field is applied. We show that the dynamics of the problem can be approximately described by a reduced model of three interacting spins, which reveals an intuitive view on how spins can be entangled by controlled electron scattering. The role of the magnetic field is rather crucial. Depending on the initial state configuration, the magnetic field can either increase or decrease the resulting entanglement but more importantly it can allow the impurities to be maximally entangled.