Electrically reversible cracks in an intermetallic film controlled by an electric field

Cracks in solid-state materials are typically irreversible. Here we report electrically reversible opening and closing of nanoscale cracks in an intermetallic thin film grown on a ferroelectric substrate driven by a small electric field (~0.83 kV/cm). Accordingly, a nonvolatile colossal electroresistance on–off ratio of more than 108 is measured across the cracks in the intermetallic film at room temperature. Cracks are easily formed with low-frequency voltage cycling and remain stable when the device is operated at high frequency, which offers intriguing potential for next-generation high-frequency memory applications. Moreover, endurance testing demonstrates that the opening and closing of such cracks can reach over 107 cycles under 10-μs pulses, without catastrophic failure of the film.

site change of Mn+ and Mn-will cause the more stability of the FM with respect to the AF structure. 7. We also tested other defects, such as Mn vacancy, Pt vacancy, and anti-site of Mn and Pt.
These defects will decrease the energy difference between the AF0 phase and the FM phase, but, a significant decrease of their energy difference will be the Mn defects (such as anti-site of Mn+ and Mn-) within the Mn sublattice as shown in Fig. S1.
The calculated structural, elastic and magnetic parameters for the three different magnetic structures are shown in Tabs. S1-S3.

Supplementary Note 2
Mechanical tests of MnPt films. In order to assess the mechanical behavior of MnPt films, nanoindentation was utilized. A three-sided pyramidal Berkovich tip with a radius of about 100 nm was used to indent the surface of a 35 nm thick MnPt film on a silicon substrate on a Hysitron TriboScope (Minneapolis, MN, USA). Thirty indents were performed within a maximum displacement range between 5-80 nm (Fig. S2a). The representative load-displacement curves illustrate permanent plastic deformation and no pop-ins that would indicate thin film fracture events. From the initial unloading slopes of the load-displacement curves the elastic modulus using the Oliver-Pharr method 6 was calculated as well as the hardness (Fig. S2b). The mechanical properties of the MnPt film should be taken near the surface (5-30 nm) to avoid influence from the substrate. The elastic modulus of the MnPt film was measured to be approximately 155-160 GPa (close to the calculated bulk modulus B = 177 GPa) and the hardness was 5 GPa. A significant increase in the hardness after 30 nm of displacement is an indication of the substrate influence on the measured value.

Supplementary Methods
First-principles calculations. In the present work, all density functional theory (DFT) based first-principles calculations were performed by VASP code 12 with the electron-ion interaction described by the projector augmented wave method 13 and the exchange-correlation functional described by the generalized gradient approximation 14 . The L1 0 -type low energy antiferromagnetic (AFM) and the ferromagnetic (FM) structures were employed for MnPt, see details reported previously 15 . Single crystal elastic constants of AFM and FM MnPt were calculated by an efficient strain-stress method 3 with the employed non-zero strains of ±0.01. The same VASP settings as used previously 15 , 5,000 (or 8,000) k-points per reciprocal atom and plane wave energy cutoff of 270 eV (or 337 eV) were used for structural relaxations (or final static calculations) to calculate elastic constants using VASP. Note that the final static calculations were performed by the tetrahedron method with Blöchl correction 16 for accurate stress results.
In addition, the mentioned energy vs. volume equation of state (EOS) fittings were performed by a 4-paramter Birch-Murnaghan equation 2 in terms of about eight energy vs. volume firstprinciples data points for each structure. Based on the obtained single crystal elastic constants, aggregative elastic properties were estimated using the Hill approach 5 , including bulk modulus (B), shear modulus (G), Young's modulus, and Poisson ratio (ν).