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

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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 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 $\propto 1/r^3$, and of the staggered magnetization $\propto 1/r$ with relevant logarithmic corrections. We demonstrate that the local spin at the impurity 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 the three dimensional systems in the vicinity of the QCP.