Ferroelectric nanodomains in the uniaxial relaxor system ${\mathrm{Sr}}_{0.61-x}{\mathrm{Ba}}_{0.39}{\mathrm{Nb}}_2{\mathrm{O}}_6{:\mathrm{C}\mathrm{e}}_x^{3+}$

The domain morphology of the disordered relaxor ferroelectric strontium barium niobate doped with cerium, ${\mathrm{Sr}}_{0.61-x}{\mathrm{Ba}}_{0.39}{\mathrm{Nb}}_2{\mathrm{O}}_6{:\mathrm{C}\mathrm{e}}_x^{3+},$ has been investigated by piezoelectric force microscopy. The evolution of natural and written domains above the phase-transition temperature $T_C$ reveals a very slow relaxation into a depolarized multicluster state. This hints at strong pinning forces due to quenched random fields. Below $T_C$ zero-field-cooled nanodomains are observed to show fractal-like shapes. Their size distribution can be described by a power law with exponential cutoff in accordance with the random-field Ising model.