Figure 4: Z4 × Z2 domain with Z3 vortices in Ca3Ti2O7 and Ca3Mn2O7.
From: Domain topology and domain switching kinetics in a hybrid improper ferroelectric
(a,b) In-plane domain structures of Ca3Ti2O7 and Ca3Mn2O7 from phase-field simulations. The eight colours denote the eight domain variants as listed. Z3 vortices corresponding to loops i–iii are denoted by black circles in spite of different nature of FA domains in Ca3Ti2O7 and Ca3Mn2O7. (c) Schematic of the energy diagram in A3B2O7 compounds with eight vertices, representing eight domain variants. Each vertex is connected to seven edges that correspond to one of five types of DWs as shown in the right side. Loops i–iii depict possible vortex domains and domain walls (in fact, Z3 vortices). Note that non Z3-type vortex domains corresponding to loops connecting, for example, (1+, 3+, 3−, 1−, 1+) or (1+, 2+, 3+, 3−, 1+) have not been observed experimentally. (d–f) Experimental DF-TEM images demonstrate two Z3 vortices at a very short interval of 50 nm in a Ca3Ti2O7 crystal. Scale bar, 100 nm. (d) Image was taken under a Friedel’s-pair-breaking condition to reveal 180°-type domain contrast. Polarization directions were shown by white arrows. (e) Image was taken under a larger tilting angle to reveal boundary interference fringes clearly. The width of bent fringes indicates a broad DW interrupting the connection of 1+ (red) and 3− (pink) domains. (f) Image shows a schematic of the corresponding domain configuration. (g) Five possible Z3-vortex configurations derived from the energy diagram. The indicated domain states are examples. Type 1, the only Z3-vortex configuration appearing within a single orthorhombic twin. Type 2, the most common Z3 vortex across the orthorhombic twin boundaries. Type 3, Z3 vortex accompanying 90° ferroelectric switching at APB. Type 4, Z3 vortex accompanying ferroelectric switching in the absence of APB. Type 5, the least favoured Z3 vortex with two high energy FAtr walls.
