Mechanical deformation of a crystal can have a profound effect on its physical properties. Notably, even small modifications of bond geometry can completely change the size and sign of magnetic exchange interactions and thus the magnetic ground state. Here we report the strain tuning of the magnetic properties of the A-type layered antiferromagnetic semiconductor CrSBr achieved by designing a strain device that can apply continuous, in situ uniaxial tensile strain to two-dimensional materials, reaching several percent at cryogenic temperatures. Using this apparatus, we realize a reversible strain-induced antiferromagnetic-to-ferromagnetic phase transition at zero magnetic field and strain control of the out-of-plane spin-canting process. First-principles calculations reveal that the tuning of the in-plane lattice constant strongly modifies the interlayer magnetic exchange interaction, which changes sign at the critical strain. Our work creates new opportunities for harnessing the strain control of magnetism and other electronic states in low-dimensional materials and heterostructures.
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We thank K. Seyler, D. Cobden and M. Yankowitz for their helpful discussions on the strain devices. The strain-induced magnetic phase transition project is mainly supported by the US Department of Energy (DOE), Basic Energy Sciences (BES), under award DE-SC0018171. Part of the strain setup and RMCD measurements are supported by the Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI) program via grant no. FA9550-19-1-0390 and the Gordon and Betty Moore Foundation’s EPiQS Initiative via grant GBMF6759 to J.-H.C. The first-principles calculation is mainly supported by NSF MRSEC DMR-1719797. K.X. acknowledges the Graduate Fellowship from Clean Energy Institute funded by the State of Washington. Z.L. and J.-H.C. acknowledge the support of the David and Lucile Packard Foundation. T.C. acknowledges support from the Micron Foundation. Computational resources were provided by HYAK at the University of Washington. CrSBr crystal synthesis is supported by the Center on Programmable Quantum Materials, an Energy Frontier Research Center funded by the US DOE, Office of Science, BES, under award DESC0019443.
The authors declare no competing interests.
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Extended Data Fig. 1 Photograph of strain cell and mounted CrSBr flake.
The strain cell consists of three piezoelectric actuators glued to a titanium flexure element. The white arrows indicate the direction of motion when a positive voltage is applied. Inset, optical micrograph showing a zoom-in on the CrSBr flake, which is indicated by the blue arrow. Scale bar: 30 µm.
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 reported28,38 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.
Extended Data Fig. 3 Photoluminescence (PL) intensity map of sample S2.
Spatial map of PL intensity integrated from 1.363 eV to 1.39 eV with 54 V applied to the piezo stacks. This spectral range captures PL from the highest energy exciton in the AFM state, but not in the FM state. That is, the dark regions in the PL map are the most strained, as they are in the FM state, whereas the brightest regions have the strongest AFM state and thus have the lowest strain. Scalebar: 10 µm. The data presented in the paper were taken in the center of the high strain region.
Extended Data Fig. 4 DFT scalar-relativistic calculations of strain effects on band gap and interlayer magnetic ordering.
a, DFT-LSDA calculated change of the band gap, ΔEgap-AFM, of bulk CrSBr in the interlayer AFM phase as the strain is applied along a-axis, while b- and c-axes are free to relax. ΔEgap-AFM is < 5 meV for < ±1% strain. b, DFT-LSDA calculation of energy difference Δ between the interlayer FM and AFM states as a function of strain applied along the a axis. The sign switching from positive to negative as strain increases indicates a strain-induced AFM to FM transition, denoted by the dashed black line. We found that the calculated Δ shows little difference between fixed- and free-boundary conditions, that is, if the lattice constants in b and c are kept constant (black) or free to relax (red). In the latter case, the change in lattice constant b and c are − 0.1% and − 0.4%, respectively, for a 1% strain along a, in bulk CrSBr. c, DFT-LSDA calculations of the energy difference of FM and AFM interlayer coupling as a function of strain applied along the c axis with lattice constants in a and b kept constant. CrSBr stays in the AFM phase within ± 2% strain. The results in both (b) and (c) suggest that the sign switching of the interlayer magnetic exchange interaction is not a result of changes to the interlayer spacing caused by the Poisson effect. d, Calculated total stacking-dependent energy of AFM bilayer CrSBr. A 4×4 grid is used to sample real-space shift vectors between one layer relative to the other. We find only one stable interlayer stacking configuration at (0, 0). Combined with the experimentally demonstrated reversible tunability, we rule out switching of the lateral layer-stacking arrangement as the cause of AFM-FM phase transition.
Extended Data Fig. 5 Strain-induced phase transition in a second suspended sample.
a, Strain dependent PL measurements of a second exfoliated CrSBr sample. The spectra are normalized to he maxima at each strain. The nominal sample temperature is 15 K. b, PL spectra at strains below (black) and above (blue) the phase transition reveal a ~ 12 meV redshift between the two.
Extended Data Fig. 6 Hysteresis in the strain-induced magnetic phase transition.
a, Intensity plot of PL as a function of strain as the piezo voltage is swept down from a high strain state. b, Integrated intensity of the entire spectral range as the strain is swept up (blue) and down (orange). To account for hysteresis in the piezostacks, we calibrated the strain using Raman sweeps in the same direction.
Extended Data Fig. 7 Magneto-photoluminescence measurements with the field swept along the hard (c) axis.
Magnetic field dependent PL measurement of unstrained CrSBr as the field is swept along the c crystal axis (magnetic hard axis).
Extended Data Fig. 8 Comparison of photoluminescence at select magnetic fields and integrated intensity of unstrained and highly strained CrSBr.
a-b, PL spectrum of unstrained (a) and highly strained (b) CrSBr at zero (black) and saturating (blue) magnetic field µoH applied along the easy b-axis. c-d, Extracted center of mass (COM) of the entire spectra range as a function of µoH || b-axis in the unstrained (c) and highly strained (d) samples.
Extended Data Fig. 9 Fully-relativistic Kohn-Sham DFT band structures of bulk CrSBr with 1.5% uniaxial strain applied along the a axis.
a, AFM CrSBr with magnetic moment constrained along the easy b axis. b, c, d, FM CrSBr with magnetic moment constrained along the b, a, and c axes, respectively. Due to the stronger interlayer hybridization in the FM phase, the top valence band and bottom conduction band at Gamma split into subband groups, resulting in a smaller Kohn-Sham band gap than that of the AFM phase. Once in the FM phase, the bandgap shows no appreciable difference when the magnetic moment is aligned along the different axes. These features agree well with our strain and magnetic field dependent measurements. We note, however, that Kohn-Sham DFT at the mean-field level has been known to underestimate the band gaps of semiconductors, and the band gaps presented here should not be directly compared to the PL energy levels in the present work. Optimized norm-conserving Vanderbilt pseudopotentials are employed in the fully-relativistic calculations with similar generation parameters to the scalar-relativistic pseudopotentials.
Extended Data Fig. 10 Effects of strain on exchange pathways and magnetic anisotropic energy in CrSBr.
a, The interlayer magnetic exchange coupling J1, J2, J3 and J4 for the 1st, 2nd, 3rd, and 4th nearest-neighbor (NN) interlayer Cr pairs. The strain-induced magnetic phase transition is likely driven by a significant enhancement in the 1st NN interlayer Cr-Cr coupling which favors ferromagnetism. b, Two interlayer magnetic exchange pathways between closest Cr-Cr interlayer pairs in side view. c, Schematics of the first exchange pathway, giving weaker magnetic exchange coupling. Due to the nearly orthogonal Br p orbitals in the super-super exchange pathway, the magnetic coupling is mediated by the weak on-site interaction between the p orbitals (Hund’s rule) in both Br. d, Schematics of the second exchange pathway that favors AFM coupling when α goes closer to 180° (compressive strain along a), and FM coupling when α approaches 90° (tensile strain along a), in agreement with the first principles calculation. Since this pathway allows for direct hopping in one of the Br, it should dominate the interlayer magnetic coupling between closest Cr-Cr interlayer pairs. e, Magnetic anisotropic energies as a function of uniaxial strain along a, obtained from fully-relativistic calculations, with the free boundary condition. The black and red points correspond, respectively, to the energy difference between the hard- and easy-axis AFM phase, and the energy difference between the hard-axis FM phase and the easy-axis AFM phase. The decreasing anisotropic energies agree with the observed decrease of saturating field in the spin canting process upon straining.
Source Data Fig. 1
Source data for Fig. 1c,d.
Source Data Fig. 2
Source data for Fig. 2a–d.
Source Data Fig. 3
Source data for Fig. 3a–d.
Source Data Fig. 4
Source data for Fig. 4a–c.
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Cenker, J., Sivakumar, S., Xie, K. et al. Reversible strain-induced magnetic phase transition in a van der Waals magnet. Nat. Nanotechnol. 17, 256–261 (2022). https://doi.org/10.1038/s41565-021-01052-6
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