Pseudospin Approach to Linear Antiferromagnetic Chains

Abstract

The generalized linear antiferromagnetic chain with two spins per unit cell $J>\mathrm{}0\mathrm{}$, and $a, b, d, e>~0$, ${\mathcal{H}}_G=\Sigma \stackrel{\frac{N}{2}}{j=1\mathrm{}}J\{a{S_{2j}}^z{S_{2j+1}}^z+b({S_{2j}}^x{S_{2j+1}}^x+{S_{2j}}^y{S_{2j+1}}^y)+d{S_{2j}}^z{S_{2j-1}}^z+e({S_{2j}}^x{S_{2j-1}}^x+{S_{2j}}^y{S_{2j-1}}^y\left)\right\},$ is solved in the pseudospin approximation. The pseudospin method is compared with the exactly soluble special case of the Heisenberg-Ising antiferromagnet ($a=b=1+\delta$, $d=1-\delta$, $e=0\mathrm{}$) and good agreement is obtained even for a sensitive property like the long-range order. It is suggested that the pseudospin approach provides a single, systematic approximation scheme, not only for describing the magnetic properties of a class of solid free radicals, but also as a check for widely used many-body techniques.