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Strain is powerful for discovery and manipulation of new phases of matter; however, elastic strains accessible to epitaxial films and bulk crystals are typically limited to small ( < 2 %), uniform, and often discrete values. This Perspective highlights emerging directions for strain and strain gradient engineering in free-standing single-crystalline membranes of quantum materials. Membranes enable large ( ∼ 10 %), continuously tunable strains and strain gradients via bending and rippling. Moreover, strain gradients break inversion symmetry to activate polar distortions, ferroelectricity, chiral spin textures, superconductivity, and topological states. Recent advances in membrane synthesis by remote epitaxy and sacrificial etch layers enable extreme strains in transition metal oxides, intermetallics, and Heusler compounds, expanding beyond the natively van der Waals (vdW) materials like graphene. We highlight emerging opportunities and challenges for strain and strain gradient engineering in membranes of non-vdW materials. 

Hybrid MBE produces epitaxial SrTiO 3 free-standing nanomembranes using remote epitaxy in an adsorption-controlled manner. 

Abstract Remote epitaxy is a promising approach for synthesizing exfoliatable crystalline membranes and enabling epitaxy of materials with large lattice mismatch. However, the atomic scale mechanisms for remote epitaxy remain unclear. Here we experimentally demonstrate that GaSb films grow on graphene-terminated GaSb (001) via a seeded lateral epitaxy mechanism, in which pinhole defects in the graphene serve as selective nucleation sites, followed by lateral epitaxy and coalescence into a continuous film. Remote interactions are not necessary in order to explain the growth. Importantly, the small size of the pinholes permits exfoliation of continuous, free-standing GaSb membranes. Due to the chemical similarity between GaSb and other III-V materials, we anticipate this mechanism to apply more generally to other materials. By combining molecular beam epitaxy with in-situ electron diffraction and photoemission, plus ex-situ atomic force microscopy and Raman spectroscopy, we track the graphene defect generation and GaSb growth evolution a few monolayers at a time. Our results show that the controlled introduction of nanoscale openings in graphene provides an alternative route towards tuning the growth and properties of 3D epitaxial films and membranes on 2D material masks. 

Abstract Single-crystalline membranes of functional materials enable the tuning of properties via extreme strain states; however, conventional routes for producing membranes require the use of sacrificial layers and chemical etchants, which can both damage the membrane and limit the ability to make them ultrathin. Here we demonstrate the epitaxial growth of the cubic Heusler compound GdPtSb on graphene-terminated Al₂O₃substrates. Despite the presence of the graphene interlayer, the Heusler films have epitaxial registry to the underlying sapphire, as revealed by x-ray diffraction, reflection high energy electron diffraction, and transmission electron microscopy. The weak Van der Waals interactions of graphene enable mechanical exfoliation to yield free-standing GdPtSb membranes, which form ripples when transferred to a flexible polymer handle. Whereas unstrained GdPtSb is antiferromagnetic, measurements on rippled membranes show a spontaneous magnetic moment at room temperature, with a saturation magnetization of 5.2 bohr magneton per Gd. First-principles calculations show that the coupling to homogeneous strain is too small to induce ferromagnetism, suggesting a dominant role for strain gradients. Our membranes provide a novel platform for tuning the magnetic properties of intermetallic compounds via strain (piezomagnetism and magnetostriction) and strain gradients (flexomagnetism).