Imaging and control of critical fluctuations in two-dimensional magnets

Abstract

Strong magnetization fluctuations are expected near the thermodynamic critical point of a continuous magnetic phase transition. Such critical fluctuations are highly correlated and in principle can occur at any time and length scales1; they govern critical phenomena and potentially can drive new phases2,3. Although critical phenomena in magnetic materials have been studied using neutron scattering, magnetic a.c. susceptibility and other techniques4,5,6, direct real-time imaging of critical magnetization fluctuations remains elusive. Here we develop a fast and sensitive magneto-optical imaging microscope to achieve wide-field, real-time monitoring of critical magnetization fluctuations in single-layer ferromagnetic insulator CrBr3. We track the critical phenomena directly from the fluctuation correlations and observe both slowing-down dynamics and enhanced correlation length. Through real-time feedback control of the critical fluctuations, we further achieve switching of magnetic states solely by electrostatic gating. The ability to directly image and control critical fluctuations in 2D magnets opens up exciting opportunities to explore critical phenomena and develop applications in nanoscale engines and information science.

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Fig. 1: Polarization-enhanced MCD imaging of 2D CrBr3.
Fig. 2: Real-time imaging of critical fluctuations in 2D CrBr3.
Fig. 3: Spatial correlation function.
Fig. 4: Electrical control of the critical fluctuations.

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

We thank J. Sethna and J. Kent-Dobias for discussions. This work was supported by the National Science Foundation (NSF) (grant no. DMR-1807810) for the development of the magneto-optical imaging microscope, the ARO Award no. W911NF-17-1-0605 for sample and device fabrication, the Cornell Center for Materials Research with funding from the NSF MRSEC programme (grant no. DMR-1719875) for optical characterizations and the Air Force Office of Scientific Research under award no. FA9550-19-1-0390 for data analysis. The growth of hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan and CREST (grant no. JPMJCR15F3). K.F.M. acknowledges support from a David and Lucille Packard Fellowship. C.J. acknowledges support from a Kavli Postdoctoral Fellowship. Z.T. acknowledges support from the Watt W. Webb Graduate Fellowship in Nanoscience.

Author information

Affiliations

Authors

Contributions

C.J. conceived the experiment. C.J. and Z.T. developed the measurement technique and performed the experiment and analysis. Z.T. prepared the samples. K.K. fabricated the devices. K.W. and T.T. grew the bulk hBN crystals. C.J., K.F.M. and J.S. cowrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Chenhao Jin or Kin Fai Mak or Jie Shan.

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Competing interests

The authors declare no competing interests.

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

41563_2020_706_MOESM2_ESM.mov

Real-time imaging of thin bulk CrBr3 at temperature of 28 K. The video was taken and shown both at 10 f.p.s.

41563_2020_706_MOESM3_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.0 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM4_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.4 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM5_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.6 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM6_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.8 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM7_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.9 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM8_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.0 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM9_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.1 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM10_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.2 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM11_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.3 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM12_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.4 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM13_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.5 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM14_ESM.mov

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.7 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

41563_2020_706_MOESM15_ESM.mov

Real-time imaging of magnetic switching in monolayer CrBr3 S1 by controlling the critical fluctuations with light. The video was taken and shown both at 10 f.p.s.

Supplementary Information

Supplementary Notes 1–9 and Supplementary Figs. 1–7.

Supplementary Video 1

Real-time imaging of thin bulk CrBr3 at temperature of 28 K. The video was taken and shown both at 10 f.p.s.

Supplementary Video 2

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.0 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 3

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.4 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 4

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.6 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 5

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.8 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 6

Real-time imaging of monolayer CrBr3 S1 at temperature of 21.9 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 7

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.0 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 8

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.1 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 9

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.2 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 10

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.3 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 11

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.4 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 12

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.5 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 13

Real-time imaging of monolayer CrBr3 S1 at temperature of 22.7 K. The video was taken at 70 f.p.s. and shown at 30 f.p.s.

Supplementary Video 14

Real-time imaging of magnetic switching in monolayer CrBr3 S1 by controlling the critical fluctuations with light. The video was taken and shown both at 10 f.p.s.

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Jin, C., Tao, Z., Kang, K. et al. Imaging and control of critical fluctuations in two-dimensional magnets. Nat. Mater. (2020). https://doi.org/10.1038/s41563-020-0706-8

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