Polarization Switching in Ferroelectric Thin Films Undergoing First-Order Phase Transitions

Figure 3

Dependence of the switching current 𝑗 on time 𝑡 (in units of 𝛾𝜂/𝛽²) at polarization reversal process (transition from the stable state to the second stable state or from the first metastable state to the second one) in the 2D system. Calculations are carried out for temperatures in the vicinity of the phase transition (𝛿=1.017, 𝛿=0.9835) and for the values of the applied field in the vicinity of coercive field 𝐸_𝑐 (𝐸=0.95⋅𝐸_𝑐,  𝐸=1.05⋅𝐸_𝑐): (1)  𝛿=1.017, 𝐸=0.95⋅𝐸_𝑐; (2)  𝛿=0.9835, 𝐸=0.95⋅𝐸_𝑐; (3)  𝛿=0.9835, 𝐸=1.05⋅𝐸_𝑐. At 𝛿=1.017, the two minima corresponding to the ferroelectric metastable domains are above the minima corresponding to the paraelectric stable phase at zero electric field, while at 𝛿=0.9835 the situation is reversed. The number of dipoles is 64 × 64. The initial state corresponds to the ferroelectric state with a nucleus of the second domain of polarization oriented in the opposite direction (the size of the nucleus is 4×4). The values of coefficients 𝐷 and 𝜈 correspond to those for 𝐵𝑎𝑇𝑖𝑂₃, 𝐷=200, 𝜈=40.