Neutron-diffraction studies on modulated ${\mathrm{Rb}}_2$${\mathrm{ZnBr}}_4$, carried out under hydrostatic pressure, revealed two new commensurate phases characterized by wave vectors q=2/7${\mathit{b}}^{\mathrm{*}}$ and q=1/4${\mathit{b}}^{\mathrm{*}}$, respectively. The first-order phase transition between them is revealed by the coexistence of two distinct peaks in the diffraction pattern. The observed pressure-temperature phase diagram contains the above-mentioned phases, the ferroelectric commensurate phase q=1/3, and a region characterized by wave-vector values in the interval q=2/7– 1) / 3 . In this region the modulation wave vector exhibits stepwise behavior as a function of pressure but remains nearly constant in temperature runs. We have found in this region a characteristic memory effect in which two temperature runs performed at the same pressure lead to two different modulation wave-vector values, while only the thermal history of the sample is different in the two runs. At ambient pressure we confirm the presence of a multipeaked diffraction pattern just above the lock-in transition to the commensurate q=1/3 phase. At 122 K the phase transition from the 1/3 phase to the 1/4 phase is detected in pressure scans. The transition mechanism involves the q=2/7 phase, at least as a metastable intermediate phase.

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