Magnetization of ${\mathrm{Cu}}_2$${\left({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2\right)}_2$${\mathrm{Cl}}_4$: A Heisenberg spin-ladder system

We study the magnetization of a Heisenberg spin ladder using exact-diagonalization techniques, finding three distinct magnetic phases. We consider the results in relation to the experimental behavior of the copper compound ${\mathrm{Cu}}_2$${\left({\mathrm{C}}_5{\mathrm{H}}_{12}{\mathrm{N}}_2\right)}_2$${\mathrm{Cl}}_4$ and deduce that the compound is well described by such a model with a ratio of bond strengths ($\frac{J}{J^{\prime }}$) of the order of 0.2, consistent with results from the magnetic susceptibility. The effects of temperature, spin impurities, and additional diagonal bonds are presented and we give evidence that these diagonal bonds are indeed of a ferromagnetic nature.