Fig. 5. Strain-induced magnetism in rippled GdPtSb membranes.

a Magnetization of GdPtSb thin film directly grown on a sapphire substrate (green), exfoliated GdPtSb membrane adhered to polyimide (blue) and polyurethane (red). The applied field H is oriented out-of-the sample plane, i.e., the global [111] direction. Both membranes have a thickness of 14 nm. b Room-temperature magnetization at 0.4 Tesla versus ripple aspect ratio (height/width). Relaxed film (green), rippled membrane on polyimide (filled and open blue circles), rippled membrane on polyurethane (red). The ripple height and width are measured by phase-contrast optical microscopy. The error bar represents the distribution of aspect ratio over several regions of the rippled membranes. c–e Optical microscope images of the film c, rippled membrane on polyimide d, and rippled membrane on polyurethane e, respectively. The scale bar is 100 μm. f Estimate of the strain ϵ_s for a sinusoidal membrane with peak to peak width (wavelength) 20 micron, ridge to valley height 5 micron, and thickness 14 nm, consistent with the dimensions of the membrane on polyurethane. Details in Supplementary Fig. S8.