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# Exchange magnetostriction in two-dimensional antiferromagnets

## Abstract

Magnetostriction, coupling between the mechanical and magnetic degrees of freedom, finds a variety of applications in magnetic actuation, transduction and sensing1,2. The discovery of two-dimensional layered magnetic materials3,4,5,6,7,8 presents a new platform to explore the magnetostriction effects in ultrathin solids. Here we demonstrate an exchange-driven magnetostriction effect in mechanical resonators made of two-dimensional antiferromagnetic CrI3. The mechanical resonance frequency is found to depend on the magnetic state of the material. We quantify the relative importance of the exchange and anisotropy magnetostriction by measuring the resonance frequency under a magnetic field parallel and perpendicular to the easy axis, respectively. Furthermore, we show efficient strain-tuning of the internal magnetic interactions in two-dimensional CrI3 as a result of inverse magnetostriction. Our results establish the basis for mechanical detection and control of magnetic states and magnetic phase transitions in two-dimensional layered materials.

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## Data availability

The data that support the findings of this study are available within the paper and its Supplementary Information. Additional data are available from the corresponding authors upon request.

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## Acknowledgements

This work was primarily supported by the Air Force Office of Scientific Research under award FA9550-18-1-0480 (development of the experimental setup) and FA9550-19-1-0390 (optical characterizations). It was partially supported by the National Science Foundation under DMR-1807810 (modelling) and the Cornell Center for Materials Research with funding from the NSF MRSEC programme under DMR-1719875 (sample and device fabrication). This work was performed in part at Cornell NanoScale Facility, an NNCI member supported by NSF Grant NNCI-1542081. K.F.M. acknowledges support from a David and Lucille Packard Fellowship.

## Author information

Authors

### Contributions

S.J., K.F.M., J.S. and H.X. designed the study, discussed the results and co-wrote the manuscript. H.X. and S.J. developed the experimental setup and fabricated the devices. S.J. performed the bulk of the measurements and data analysis, assisted by H.X.

### Corresponding authors

Correspondence to Jie Shan or Kin Fai Mak.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

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## Extended data

### Extended Data Fig. 1 Mechanical resonance of 2D CrI3 under an out-of-plane magnetic field.

a,b, Field dependence of the amplitude (a) and linewidth (b) of the fundamental resonance of bilayer CrI3 resonator 1. The field dependence of the resonance frequency is shown in Fig. 2b. The red (blue) symbols correspond to the measurement for the positive (negative) field sweeping direction. c, Field dependence of the reflectance at 633 nm normalized by the reflectance at zero field.

### Extended Data Fig. 2 Summary of six CrI3-resonators under an out-of-plane magnetic field.

For each device, the contour plot shows the vibration amplitude versus driving frequency under an out-of-plane field that sweeps from the top to the bottom value. The other two panels compare the field dependence of the resonance frequency (upper panel) and MCD (lower panel) of the membrane. The two colours denote the two field sweeping directions. ac, Bilayer CrI3 resonator 1 (radius 2 μm), same as Fig. 2a–c. df, Bilayer CrI3 resonator 2 (radius 2 μm). gi, Trilayer CrI3 resonator (radius 3 μm). jl, Six-layer CrI3 resonator 1 (radius 3 μm), same as Fig. 2d–f. mo, Six-layer CrI3 resonator 2 (radius 3 μm). pr, Six-layer CrI3 resonator 3 (radius 3 μm). MCD of the trilayer resonator shows a ferromagnetic hysteresis loop centred at zero magnetic field (i), to which the mechanical resonance is not sensitive (h). The insets in i show the spin configuration of the system at given fields.

### Extended Data Fig. 3 Summary of 2 CrI3-resonators under an in-plane magnetic field.

For each device, the contour plot shows the vibration amplitude versus driving frequency under an in-plane field that sweeps from the top to the bottom value. The other panel is the field dependence of the resonance frequency. The two colours denote the two field sweeping directions. a,b, Six-layer CrI3 resonator 1 (same as Fig. 3). c, d, Six-layer CrI3 resonator 3.

### Extended Data Fig. 4 Inverse magnetostriction in six-layer CrI3 resonator 2.

a, Normalized MCD versus out-of-plane magnetic field that sweeps from 2.2 T to –2.2 T (only 2 T to 0.5 T and –0.5 T to –2 T is shown for clarity) at different values of Vg. b, c, Strain dependence of the two spin-flip transition fields (symbols). The error bars correspond to the spin-flip transition widths. The solid lines are linear fits.

### Extended Data Fig. 5 Calibration of gate-induced strain and determination of resonator parameters.

a, Reflection contrast of bilayer CrI3 resonator 1 from 1.6–1.9 eV as a function of gate voltage. The main feature is a dip (around 1.75 eV at Vg = 0V), which corresponds to the fundamental exciton resonance of monolayer WSe2. The feature redshifts slightly with Vg up to about 40 V followed by a larger redshift with further increase of Vg. b, Representative spectra at selected Vgs. c, Exciton resonance energy extracted from a (left axis) and gate-induced strain calibrated from the exciton resonance energy (right axis) as a function of $$V_{\mathrm{g}}^4$$ for Vg up to 39 V. The solid line is a linear fit. The built-in stress σ0 was determined from the slope.

### Extended Data Fig. 6 2D CrI3 resonators under high out-of-plane fields.

Normalized vibration amplitude versus driving frequency under an out-of-plane magnetic field up to 5 T for six-layer CrI3 resonator 2. The resonance frequency, amplitude and linewidth basically do not change up to 5 T except at the spin-flip transitions.

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### Cite this article

Jiang, S., Xie, H., Shan, J. et al. Exchange magnetostriction in two-dimensional antiferromagnets. Nat. Mater. 19, 1295–1299 (2020). https://doi.org/10.1038/s41563-020-0712-x

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