Molecular dynamics simulations of first-principles-based effective Hamiltonians for $\mathrm{Pb}({\mathrm{Sc}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_3$ under hydrostatic pressure and for $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_3$ at ambient pressure show clear evidence of a relaxor state in both systems. The Burns temperature is identified as the temperature below which dynamic nanoscale polar clusters form, pinned to regions of quenched chemical short-range order. The effect of pressure in $\mathrm{Pb}({\mathrm{Sc}}_{1/2}{\mathrm{Nb}}_{1/2}){\mathrm{O}}_3$ demonstrates that the stability of the relaxor state depends on a delicate balance between the energetics that stabilize normal ferroelectricity and the average strength of random local fields which promote the relaxor state.

• Received 10 May 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.137601