X-ray scattering study of the incommensurate phase in Mg-doped ${\mathrm{CuGeO}}_3$

We present results of a systematic x-ray scattering study of the effects of Mg doping on the high-field incommensurate phase of ${\mathrm{CuGeO}}_3.$ Lorentzian-squared line shapes, the changing of the first-order transition to second order, and the destruction of long-range order with infinitesimal doping are observed, consistent with random-field effects in a three-dimensional $\mathrm{XY}$ system. Values for the soliton width in pure and lightly doped ${\mathrm{CuGeO}}_3$ are deduced. We find that even a very small doping has a drastic effect on the shape of the lattice modulation.