The local and nonlocal magnetization of impurities in linear antiferromagnetic chains

Abstract

Some organic free radicals represent linear antiferromagnetic chains in which the low-temperature susceptibility is dominated by impurities. The impurities appear to be coupled via exchange to their neighbors and yet still give rise to a paramagnetic contribution to the magnetization. Previously, 1,2 an Ising model with ferromagnetically coupled, randomly distributed impurities was presented to interpret the magnetization. Simple assumptions permit this model to be generalized to other anisotropies. It is shown that for a small concentration of impurities there are two contributions to the low-temperature magnetization. One is a local contribution and is proportional to the number of impurities q. It is largest and least localized for Heisenberg coupling. The local contribution is given by gβ(2Σi= 0∞ Si)1/2/2 where the Si's were defined in a previous work.3 The other contribution is nonlocal, depends upon the zero-temperature long-range order ωinfty, and probably can be represented as a single spin of magnitude gβ(ω ∞q)1/2/2. Near the Ising limit the system acts like a superparamagnet. The magnetic field dependence of the magnetization can be used to separate the two contributions. For Heisenberg coupling, the magnetization will be paramagnetic and this paramagnetism persists as kT/ | J | → 0. This is a direct consequence or alternatively a measure of whether ω∞=0 in the case of Heisenberg coupling. The interaction between spins in the organic free radicals is better represented by Heisenberg coupling than Ising coupling. The low-temperature experimental results agree with the paramagnetism predicted in the case of Heisenberg coupling. © 1967 The American Institute of Physics.