Stability of ferrons in antiferromagnets: The role of zero-point fluctuations

A free carrier of spin (1/2, placed in a Heisenberg antiferromagnet, may form a ferron, which is a quasiparticle in which the free carrier is surrounded by a localized region with a net magnetic moment. Type-I ferrons (core not fully saturated) are unstable in lattices with dimensionality D≥2, although they are stable for D<2, in mean-field theory. With D=2 in mind, we examine the influence of zero-point spin fluctuations on the stability of ferrons, to find they oppose the formation of type-I ferrons, although scaling relations for various contributions to the binding energy are unaffected. We comment on the possible relevance of these results to the high-$T_c$ superconductors; the ground state for a single hole may be a type-II ferron (saturated core), if this picture is applied to these materials.