Impurity-induced magnetization in a three-dimensional antiferromagnet at the quantum critical point

We consider a single impurity with spin S embedded in a three-dimensional antiferromagnetic system which is close to the quantum critical point (QCP) separating magnetically ordered and disordered phases. Approaching the QCP from the disordered phase, we study the spatial distribution of the spin density and staggered magnetization induced by the impurity. Using two methods (self-consistent Born approximation and renormalization group), we found a power-law decay of the spin density [is proportional to]1/r3, and of the staggered magnetization [is proportional to]1/r with relevant logarithmic corrections. We demonstrate that the local spin at the impurity's site, r=0, approaches to zero at the QCP. We show that in the semiclassical limit of large S the problem is equivalent to the exactly solvable independent boson model. Our results demonstrate existence of spin-charge separation in three-dimensional systems at the QCP.