Extended Data Fig. 2: Calibration of CrSBr strain response using a strain gauge heterostructure.

a, Diagram of a hBN/CrSBr/graphene strain gauge heterostructure deposited on a Si/SiO₂ pillar. When the pillar is strained, the strain is transferred to the heterostructure on top. In our experiments, the strain is aligned with the a crystal axis of the CrSBr, which is the magnetic intermediate axis orthogonal to the easy (b) axis. The red and blue arrows on the CrSBr depict the AFM interlayer coupling which produces an A-type layered AFM structure. b, Finite element analysis modelling using parameters similar to those of our experiment (see Methods). The modelling shows that the surface of the pillar has a highly uniform strain profile (< 0.01% total variation) over the length scale of the sample across the middle of the pillar. c, Raman spectra of the graphene 2D peak (top) and CrSBr Raman mode centered around 346 cm⁻¹ (bottom) with 0 (black) and 100 (red) volts applied to the strain cell. d, Full strain dependence of the graphene 2D peak. The grey line represents a linear fit of the peak position as a function of piezo voltage determined by Lorentzian fits. The strain values are then calculated using a previously reported^28,38 Raman shift rate of graphene. e, Energy of the silicon Raman peak as a function of piezo voltage. Using the previously reported³⁷ strain shift rate yields a calibration which is essentially the same as that determined from the graphene spectra. In order to determine the amount of built-in strain due to preparation of the silicon substrate and differences in thermal expansion coefficients, we also measured a freestanding silicon chip glued next to the strained chip. Comparing the strained silicon pillar at zero volts to the freestanding chip right next to it, we found that the built-in strain on this particular pillar was negligible. f, CrSBr Raman peak extracted from Lorentzian fits as a function of strain along with linear fits to the data (blue line) and the first-principles calculated Raman shift rate (green line, shifted vertically to ~ 346 cm^-1 at V = 0). Error bars in e-f represent the uncertainty of the Lorentzian fits.