Cubic ground state of field-cooled PbMg$_{1/3}$Nb$_{2/3}$O$_3$*

Neutron and x-ray diffraction techniques have been used to study the competing long and short-range polar order in the relaxor PbMg$_{1/3}$Nb$_{2/3}$O$_3$ (PMN) under the influence of an external [111]-oriented electric field. While the bulk unit cell remains cubic for electric fields up to 8\,kV/cm, a suppression of the diffuse scattering and a concomitant enhancement of the Bragg peak intensity is observed below $T_c=210$\,K, indicating a more ordered structure with increasing electric field yet an absence of a long-range ferroelectric ground state. The electric field strength has little effect on the diffuse scattering above $T_c$. The absence of hysteresis suggests that the ground state of PMN may not be a frozen glassy phase, but may be better understood in terms of random fields introduced through the presence of structural disorder.