Electric field effect on short-range polar orders in a relaxor ferroelectric system

Short-range polar orders in the relaxor ferroelectric material PbMg$_{1/3}$Nb$_{2/3}$O$_3$-$28\%$PbTiO$_3$ (PMN-28PT) have been studied using neutron diffuse scattering. An external electric field along [110] direction can affect the diffuse scattering in the low temperature rhombohedral/monoclinic phase. Diffuse scattering intensities associated with [110] short-range polarizations are partially suppressed, while those arising from [1$\bar{1}$0] polarizations are enhanced. On the other hand, short-range polar orders along other equivalent $\langle110\rangle$ directions, i.e. [101],[10$\bar{1}$], [011], and [01$\bar{1}$] directions, are virtually unaffected by the field. Our results, combined with previous work, strongly suggest that most part of short-range polar orders in PMN-$x$PT relaxor systems are robust in the low temperature phase, where they couple strongly to ferroelectric polarizations of the surrounding ferroelectric domains, and would only respond to an external field indirectly through ferroelectric domain rotation.