Local magnetizations in impure two-dimensional antiferromagnets

Abstract

The local magnetizations near dilute substitutional impurities in the quadratic-layer antiferromagnet ${\mathrm{K}}_{2}$Mn${\mathrm{F}}_{4}$ are studied both experimentally and theoretically. The impurities considered are the nonmagnetic Zn and Mg, as well as Ni. The magnetizations are probed through the positions of the impurity-associated satellites in the nuclear magnetic resonance of the out-of-layer and in-layer $^{19}\mathrm{F}$ nuclei adjacent to the magnetic ions. It is discussed in which way the effects of lattice deformations can be eliminated in order to obtain the variations of the local magnetizations with temperature. The theoretical treatment is based on Green's-function techniques. The decoupling employed is within the local spin-deviation operators and accounts for correlation between nearest neighbors. It reduces the renormalized spin-wave Hamiltonian to an effective quadratic form, rendering decoupling of Green's functions unnecessary. The spectral distributions of the excitations are calculated including local modes. The theory is subsequently applied to the 13-site cluster consisting of the impurity and the first three shells of Mn around it. Good agreement is found. The magnetization is significantly modified in the first shell. The further shells are only weakly affected, however somewhat stronger than in comparable three-dimensional systems. For nonmagnetic impurities the thermal spin deviation in the first shell is about $\frac{1}{3}$ larger than that of the host; in the Ni-doped system the additional deviations are within 1%. The zero-point deviation of the Ni is 0.11 units of spin, as compared to 0.17 in the host. A further experimental result is a uniform shift, increasing with concentration, of the sublattice magnetization at large distance from the impurity. It must be related to the finite density of states near the zone center in two-dimensional systems. Finally, some data are presented on the local susceptibilities.