Universal spin screening clouds in local moment phases

When a local impurity spin interacts with conduction electrons whose density of states (DOS) has a (pseudo)gap or diverges at the Fermi energy, a local moment (LM) phase can be favored over a Kondo phase. Theoretically studying quantum entanglement between the impurity and conduction electrons, we demonstrate that conduction electrons form an LM spin cloud in general LM phases, which corresponds to, but has a fundamental difference from, the Kondo cloud screening the impurity spin in the Kondo phase. The LM cloud algebraically decays over the distance from the impurity when the DOS has a pseudogap or divergence, and exponentially when it has a hard gap. We find an LM cloud length, a single length scale characterizing a universal form of the LM cloud. The findings are supported by both analytic theories and numerical computations.