Domain wall $^{p}$∞ g a$_{1}$ a$_{11}$ a$_{111}$ Tetragonal phase T180 { 001 } P$_{0}$ G$_{44}$ α$_{1}$ − $^{e}$‖q$_{11}$ − $^{e}$⊥q$_{12}$ + C 12 C $_{11}$( $^{e}$‖ + $^{e}$⊥ ) q$_{12}$ α ( e ) 11 − 1 2 q 2 12 C 11 α$_{111}$ T180 { 011 } P$_{0}$ G$_{44}$ α$_{1}$ − $^{e}$‖q$_{11}$ + C 12 C ′ $^{$_{11}$e}$‖ q$_{12}$ − 2 C 44 C ′ $^{$_{11}$e}$⊥ q$_{12}$ α ( e ) 11 − 1 2 q 2 12 C ′ 11 α$_{111}$ T90 P 0 √$_{2}$ G 11 − G 12 2 α r 1 + α rs 12$^{P}$$^{2}$ 0 2 + $_{α}$′ 112$^{P}$$^{4}$ 0 4 α r 11 + $_{α}$′ 112$^{P}$$^{2}$ 0 2 $_{α}$′ 111 Orthorhombic phase O180 { 1 ¯ 10 } P$_{0}$ G 11 − G 12 2 α$_{1}$ − e$_{b}$ ( $_{q}$′ 11 − $_{q}$′ $_{12}$) − e$_{c}$q$_{12}$ − e$_{a}$ ( $_{q}$′ 11 + $_{q}$′ $_{12}$) α ( e ) 11 2 + α ( e ) 12 4 − q ′ 2 12 2 C ′ 11 1 4 ( α$_{111}$ + α$_{112}$ ) + q ′ 2 12 C ′ $_{11}$P 2 0 O180 { 001 } P$_{0}$ G$_{44}$ α$_{1}$ − e$_{a}$ ( q$_{11}$ + q$_{12}$ ) − e$_{b}$q$_{44}$ + 2 e$_{a}$q$_{12}$ C 12 C 11 α ( e ) 11 2 + α ( e ) 12 4 − q 2 12 2 C 11 1 4 ( α$_{111}$ + α$_{112}$ ) O90 P 0 √$_{2}$ G$_{44}$ α r 1 + α (e) 12 P 2 0 2 + α$_{112}$ P 4 0 4 α ( e ) 11 + 1 2 [ α$_{112}$P 2 0 − q 2 12 C 11 ] α$_{111}$ O120 √$_{3}$$_{P}$$_{0}$ 2 G 11 − G $_{12}$+4 G 44 6 *** *** 2 α $_{111}$+21 α $_{112}$+2 α 123 108 Rhombohedral phase R180 { 1 ¯ 10 } P$_{0}$ G 11 − G $_{12}$+ G 44 3 α$_{1}$ + 1 6 C ′ $_{33}$[ C$_{12}$ ( e$_{a}$ ( q$_{11}$ + 2 q$_{12}$ − 4 q$_{44}$ ) − 6 e$_{b}$q$_{44}$ ) α ( e ) 11 + α ( e ) 12 3 − q ′ 2 13 2 C ′ 33 3 α $_{111}$+6 α $_{112}$+ α 123 27 − C$_{11}$ (6 e$_{b}$q$_{44}$ + 3 e$_{a}$$_{q}$′ $_{11}$) − 2 C$_{44}$ (3 e$_{a}$ ( q$_{11}$ + 2 q$_{12}$ ) + 6 e$_{b}$$_{q}$′ $_{11}$)] R180 { ¯ 211 } P$_{0}$ G 11 − G $_{12}$+ G 44 3 *** *** 3 α $_{111}$+6 α $_{112}$+ α 123 27 R109 P 0 √$_{3}$ G$_{44}$ α$_{1}$ + α ( e ) 12 P 2 0 3 + α 112 P 4 0 9 + 2 q 2 12 P 2 0 3 C 11 − q 2 44 P 2 0 6 C 44 α ( e ) 11 2 + α ( e ) 12 4 − q 2 12 2 C 11 α $_{111}$+ α 112 4 − e$_{a}$ ( q$_{11}$ + 2 q$_{12}$ ) − e$_{b}$q$_{44}$ + 1 12 (2 α$_{112}$ + α$_{123}$ ) P 2 0 R71 P 0 √$_{3}$ G$_{44}$ α$_{1}$ + 2 α ( e ) 12 P 2 0 3 + 2 α 112 P 4 0 9 + α 123 P 4 0 9 α ( e ) 11 + 2 α 112 P 2 0 3 − q 2 12 2 C ′ 33 α$_{111}$ − e$_{a}$ ( q$_{11}$ + 2 q$_{12}$ ) + q 2 12 P 2 0 3 C ′ 33 − q 2 44 P 2 0 3 C 44 Domain wall 2 ξ Σ U A $^{p}$∞ g a$_{1}$ a$_{11}$ a$_{111}$ Tetragonal phase (298 K) T180 { 001 } 0.63 5.9 6.41 1.43 0.265 2.0 -14.26 1.69 8.00 T180 { 011 } 0.63 5.9 6.41 1.43 0.265 2.0 -14.26 1.69 8.00 T90 3.59 7.0 1.45 1.09 0.188 26.5 -7.86 9.53 3.12 Orthorhombic phase (208 K) O180 { 1 ¯ 10 $_{}}$† 2.66 31.0 8.20 1.70 0.331 26.5 -9.71 -2.75 4.36 O180 { 001 } 0.70 8.9 8.95 1.64 0.331 2.0 -11.07 -2.13 4.36 O90 0.72 4.3 4.26 1.50 0.234 2.0 -11.62 -0.08 12.97 O60 3.62 5.3 1.09 1.08 0.166 26.1 -7.64 12.14 4.36 $_{O120}$† 1.70 13.7 5.82 1.47 0.287 10.2 -10.82 0.50 4.92 Rhombohedral phase (118 K) R180 { 1 ¯ 10 $_{}}$† 2.13 36.0 11.81 1.83 0.381 18.3 -9.53 -3.64 3.17 R180 { ¯ 211 $_{}}$† 2.13 36.0 11.81 1.83 0.381 18.3 -9.53 -3.64 3.17 $_{R109}$† 0.70 7.8 7.81 1.65 0.311 2.0 -10.84 -2.56 5.60 R71 0.74 3.7 3.52 1.58 0.220 2.0 -10.31 -2.42 17.94 TABLE II: Parameters characterizing various mechanically compatible and neutral domain wall species of BaTiO$_{3}$-like fer- roelectrics within the SPP treatment described in the Section IV. Results for O60, O120, and R180 { ¯ 211 } walls as well as a few other parameters are omitted because the corresponding analytical expressions through the GLD model parameters and spontaneous values of polarization and strain are too complicated. TABLE III: Predicted values of thickness and planar energy density of domain wall species illustrated in Fig. 2 together with the determining parameters appearing in the SPP treatment. Results are evaluated from the BaTiO$_{3}$-specific GLD model at three selected temperatures corresponding to the tetragonal, orthorhombic and rhombohedral phase, respectively. Domain walls for which relaxing of the P$_{t}$ component results in a lower-energy CPP solution (see in Section VI.) are denoted by †$_{. Numerical}$ values are in SI units (2 ξ in nm; Σ in mJ/m $^{2}$; U in MJ/m $^{3}$; $^{p}$∞ in C/m $^{2}$; g $_{in 10}$− 11 kg m 5 $_{s}$− 2 $_{C}$− $^{2}$; a$_{1}$ in 10 7 kg m 3 $_{s}$− 2 $_{C}$− $^{2}$; a$_{11}$ in 10 8 kg m 7 $_{s}$− 2 $_{C}$− $^{4}$; a$_{111}$ in 10 9 kg m 11 $_{s}$− 2 $_{C}$− $^{6}$). 7