Lateral piezoresponse force microscopy (LPFM) images, before (a) and after (b) the application of a 18-kOe magnetic field, show obvious changes in ferroelectric domain states. In both (a,b) the same region of the PZTFT single-crystal lamella has been scanned. In each case, the left and middle panels are amplitude images, showing variations in the local in-plane piezoelectric activity, with the cantilever orientation in each scan given by the blue schematic tip shape. The directions of tip distortion contributing to the amplitude images are given by the black arrows superposed onto the schematic cantilevers. Domains or packets of domains are clearly distinguished. The right panels are simple in-plane vector maps of the local polarization direction, inferred from the phase signal associated with the amplitude images presented in the middle and left panels. Polar directions are assigned to one of four quadrant directions (grey: left and up; lime green: left and down; purple: right and up; brown: right and down). The magnetic field has caused obvious growth in the domains with polar orientations represented by the lime green colour. Scale bar, 2 μm.