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(Color online) 2D energy landscape for a tetragonal monodomain single crystal without electric field (a), showing four equivalent energy minima at P = (P 0, 0) and P = (0, P 0). G 0 and G 1 are located at (P = 0, 0) and , respectively. Upon increasing the electric field along the orthorhombic crystallographic direction there is a corresponding polarization rotation, until at a critical electric field the stable polarization direction is found along the 〈110〉 orientation.
(Color online) Unipolar electric field induced polarization at various off-axis angles to the 〈110〉-crystallographic orientation, as shown schematically in the inset figure. Polarization and electric field are normalized by the spontaneous polarization at zero applied load and the coercive electric field Ec, respectively. With increasing off-axis angle there is a change in the simulated hysteresis and initial linear piezoelectric properties.
(Color online) The critical phase transformation field in relation to the coercive electric field as a function of the fitting parameters q, which defines the path of polarization rotation during a 90° domain switch, and the ratio of energy barriers for 90° and 180° switching (G 1/G 0).
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