Susceptibility of an impure Heisenberg linear chain: Measurement of impurity-host exchange and anisotropy crossover

The magnetic susceptibility $\chi$ has been measured in samples of y${\left({\mathrm{CH}}_3\right)}_4\mathrm{N}{\mathrm{Mn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cl}}_3(\mathrm{TMMC}:\mathrm{Cu})$ for $x=0.026\mathrm{}\mathrm{and} 0.22$. Previous theory of other authors for the susceptibility of a classical chain with classical or diamagnetic impurities is extended here to include quantum spin impurities with arbitrary impurity-host exchange interaction but negligible impurity-impurity interaction. Fits of the data to this theory yield a ferromagnetic impurity-host interaction $\frac{J^{\prime }}{K_B}=1.6\mathrm{}$°K compared with the accepted antiferromagnetic host-host coupling $\frac{J}{k_B}\approx -7\mathrm{}$°K. The anisotropy of $\chi$ is unusual in that ${\chi }_{\perp }>{\chi }_{\parallel }$ at the lowest temperatures whereas ${\chi }_{\parallel }>{\chi }_{\perp }$ in pure TMMC. (${\chi }_{\parallel }$ and ${\chi }_{\perp }$ are susceptibilities for the field parallel and perpendicular to the chain axis.) We show by a first-order calculation of the susceptibility of a finite anisotropic classical chain that such a crossover in the relative values of ${\chi }_{\parallel }$ and ${\chi }_{\perp }$ is expected at a temperature $\frac{T_0\sim 2JS(S+1\mathrm{})x}{k_B}$.