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Manipulation of Dirac band curvature and momentum-dependent g factor in a kagome magnet

Abstract

The Zeeman effect describes the energy change of an atomic quantum state in a magnetic field. The magnitude and direction of this change depend on the dimensionless Landé g factor. In quantum solids, the response of the Bloch electron states to the magnetic field also exhibits the Zeeman effect, with an effective g factor that was theoretically predicted to depend on the momentum1,2,3, and which may be particularly strong in topological and magnetic systems. However, the momentum dependence of the g factor is difficult to extract and it has not been directly measured. Here we report the experimental discovery of a momentum-dependent g factor in the kagome magnet YMn6Sn6. We map the evolution of a massive Dirac band in the vicinity of the Fermi level as a function of the magnetic field. We find that electronic states at different lattice momenta exhibit different Zeeman energy shifts, giving rise to an anomalous g factor that peaks around the Dirac point. Our work provides a momentum-resolved visualization of Dirac band curvature manipulated by a magnetic field, which will be relevant to other topological kagome magnets.

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Fig. 1: Crystal structure and different surface terminations.
Fig. 2: Magnetic field dependence of the spectral peak in the density of states.
Fig. 3: Spectroscopic imaging of the Mn plane.
Fig. 4: Determination of the k-dependent g factor.

Data availability

All data that support the findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The computer code used for data analysis is available upon request from the corresponding author.

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Acknowledgements

I.Z. gratefully acknowledges support from Army Research Office grant no. W911NF-17-1-0399. H. Lei acknowledges support by the National Key R&D Program of China (grant no. 2018YFE0202600), the Beijing Natural Science Foundation (grant no. Z200005) and the Fundamental Research Funds for the Central Universities and the Research Funds of Renmin University of China (grants nos. 18XNLG14 and 19XNLG17). K.L. acknowledges support from the National Key R&D Program of China (grant no. 2017YFA0302903), the National Natural Science Foundation of China (grant no. 12174443) and the Beijing Natural Science Foundation (grant no. Z200005). K.L. acknowledges the use of computational resources provided by the Physical Laboratory of High Performance Computing at Renmin University of China. Z.W. acknowledges support from the US Department of Energy, Basic Energy Sciences (grant no. DE-FG02-99ER45747) and the Cottrell SEED Award no. 27856 from the Research Corporation for Science Advancement.

Author information

Authors and Affiliations

Authors

Contributions

H.Li and H.Z. performed STM experiments. H.Li analysed the STM data. Q.W. and Q.Y. synthesized and characterized the samples under the supervision of H.Lei, K.J. and Z.W. performed orbital magnetization calculations. N.-N.Z. and K.L. performed simulations of the STM topographs. H.Li, H.Z., Z.W. and I.Z. wrote the manuscript, with input from all authors. I.Z. supervised the project.

Corresponding authors

Correspondence to Ziqiang Wang, Hechang Lei or Ilija Zeljkovic.

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The authors declare no competing interests.

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Nature Physics thanks Madhav Ghimire and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Other surface terminations observed in YMn6Sn6.

(a-d) STM topographs of other crystalline facets observed on surfaces with large slopes (approximate surface angle is shown in the upper left). The upper right corner in each panel shows the Fourier transform of the corresponding topograph, with the most prominent peaks circled in red. For comparison, all STM topographs of the ab-plane in the main text show nominal angle of approximately 2 degrees or less, a typical uncertainty of gluing the sample to the holder by silver epoxy. STM setup condition: (a, b) Iset = 10 pA, Vsample = 400 mV; (c) Iset = 70 pA, Vsample = 30 mV; (d) Iset = 10 pA, Vsample = 400 mV.

Extended Data Fig. 2 Surface identification based on step heights and theoretical simulations.

(a) STM topograph of consecutive steps. (b) Topographic line profile taken along the red line denoted in (a). The total height between the bottom layer and the top layer is 8.7 Å, which is a unit cell height. Based on the step heights and the nature of surface morphologies over each layer, surface terminations are identified as Mn, Sn1, Mn and Mn (the tallest to the shortest terrace). (c-e) Theoretical simulations of STM topographs of Mn, Sn1 and Sn2 terminations at 30 mV bias. (fh) Experimental STM topographs of Mn, Sn1 and Sn2 surface terminations. STM setup condition: (c-e) simulated Vsample = 30 mV. (f-h) Iset = 70 pA, Vsample = 30 mV.

Extended Data Fig. 3 Bias-dependent STM topographs.

STM topographs of (a-d) Mn and (e-h) Sn1 surface terminations as a function of bias. The lower right corner of (a,e) shows a Fourier transform of the topograph in that panel, with hexagonal Bragg peaks circled in red. STM topographs measured at different bias over the same region of the sample show qualitatively the same surface morphology, regardless of the bias. STM setup condition: (a) Iset = 100 pA, V sample = 1 V. (b) Iset = 100 pA, Vsample = 50 mV. (c) Iset = 100 pA, Vsample = −50 mV. (d) Iset = 100 pA, Vsample = −1 V. (e) Iset = 30 pA, Vsample = 1 V. (f) Iset = 30 pA, Vsample = 50 mV. (g) Iset = 30 pA, Vsample = −50 mV. (h) Iset = 30 pA, V sample = −1 V.

Supplementary information

Supplementary Information

Supplementary Figs. 1–12 and Discussions 1–6.

Source data

Source Data Fig. 1

Data from Fig. 1g,h,i.

Source Data Fig. 2

Data from Fig. 2a,c.

Source Data Fig. 4

Data from Fig. 4e,f,g,j.

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Li, H., Zhao, H., Jiang, K. et al. Manipulation of Dirac band curvature and momentum-dependent g factor in a kagome magnet. Nat. Phys. 18, 644–649 (2022). https://doi.org/10.1038/s41567-022-01558-3

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