Field dependence of the magnetization for the spin-ladder material ${\mathrm{Cu}}_2$(${\mathrm{C}}_5$${\mathrm{H}}_{12}$${\mathrm{N}}_2$${)}_2$${\mathrm{Cl}}_4$

We have developed a series expansion method for calculating the uniform magnetization M as a function of the applied field h for Heisenberg systems at T=0. The method involves introducing Ising anisotropy along the z axis together with an applied uniform field along the x axis. On extrapolation to the isotropic limit, one recovers the magnetization for the Heisenberg system with an applied field along the x axis. This method circumvents the difficulties in developing perturbation theory associated with the commuting nature of the uniform field. The results developed for two-chain ladders appropriate for the material ${\mathrm{Cu}}_2$(${\mathrm{C}}_5$ ${\mathrm{H}}_{12}$ ${\mathrm{N}}_2$ ${)}_2$ ${\mathrm{Cl}}_4$ are in good agreement with the experimental data. In addition, uniform susceptibility is calculated by high-temperature expansions and also compared with the experimental data.