Intensity Spectrum of the Anisotropic Magnetic Chain

The transverse and longitudinal intensity spectrum pertaining to the lowest (one-cluster) multiplet of the linear anisotropic spin-ferromagnetic chain is obtained analytically in the absence of transverse mean exchange ($j^x+j^y=0\mathrm{}$) and neglecting coupling to higher multiplets. The magnetic susceptibilities, which have the form of continued fractions, are expressed in terms of Bessel functions. At high fields the susceptibilities have the form of quotients of power-series expansion in $\frac{j^a}{H_0}$, where $j^a$ is the transverse anisotropy parameter ($j^a=\frac{(j^x-j^y)}{2}$) and $H_0$ is the magnetic field. At low field the total intensity is evenly shared among the energy levels. At zero field the intensity spectra are bounded and continuous and assume the shape of a semiellipse about the degeneracy point. A magnetic intensity spectrum of that character has recently been observed by Nicoli and Tinkham in the magnetic salt Co${\mathrm{Cl}}_2$ · 2${\mathrm{H}}_2$O.