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Room-temperature flexible manipulation of the quantum-metric structure in a topological chiral antiferromagnet

Nature Physics volume 20, pages 1110–1117 (2024)Cite this article

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Abstract

The quantum metric and Berry curvature are two fundamental and distinct factors that describe the geometry of quantum eigenstates. Although the role of the Berry curvature in governing various condensed-matter states has been investigated extensively, the quantum metric, which has also been predicted to induce topological phenomena, has rarely been studied, particularly at ambient conditions. Here we demonstrate the room-temperature manipulation of the quantum-metric structure of electronic states through its interplay with the interfacial spin texture in a topological chiral antiferromagnet/heavy metal Mn3Sn/Pt heterostructure, which is manifested in a time-reversal-odd second-order Hall effect. We also show the flexibility in controlling the quantum-metric structure with moderate magnetic fields. Our results open the possibility of building applicable nonlinear devices by harnessing the quantum-metric structure.

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Fig. 1: Schematics and characterization of the MgO (111) substrate/MgO (1.3 nm)/Ru (5 nm)/Mn3Sn (15 or 30 nm)/MgO sample.
Fig. 2: Measurement of the ScHE in the (0001)-oriented Mn3Sn/Pt at room temperature.
Fig. 3: Theoretical modelling of the manipulation of the quantum-metric structure and the intrinsic ScHE.
Fig. 4: Temperature dependence of the ScHE and the AHE in (0001)-oriented Mn3Sn/Pt.

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Data availability

The data that support the findings of this study are shown in the main text figures and the extended data figures. Source data are provided with this paper.

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Simulation codes in this paper are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank T. Dietl for valuable discussions. A portion of this work was supported by the Japan Society for the Promotion of Science (JSPS; KAKENHI Grant Nos. 19H05622 to S.F., 22K03538 to Y.A. and 22KF0035 to J.H.), the Initiative to Establish Next-Generation Novel Integrated Circuits Centers (X-NICS) funded by the Ministry of Education, Culture, Sports, Science and Technology (Grant No. JPJ011438 to S.F.) and the Casio Science and Technology Foundation (Grant No. 40-4 to Y.T.). J.H. acknowledges support from the JSPS Postdoctoral Fellowship for Research in Japan. T.U. and J.-Y.Y. acknowledge support from GP-Spin at Tohoku University.

Author information

Author notes

  1. These authors contributed equally: Jiahao Han, Tomohiro Uchimura.

Authors and Affiliations

  1. Laboratory for Nanoelectronics and Spintronics, Research Institute of Electrical Communication, Tohoku University, Sendai, Japan

    Jiahao Han, Tomohiro Uchimura, Ju-Young Yoon, Yuta Yamane, Shun Kanai, Hideo Ohno & Shunsuke Fukami

  2. Advanced Institute for Materials Research, Tohoku University, Sendai, Japan

    Jiahao Han, Yutaro Takeuchi, Shun Kanai, Hideo Ohno & Shunsuke Fukami

  3. Graduate School of Engineering, Tohoku University, Sendai, Japan

    Tomohiro Uchimura, Ju-Young Yoon, Shun Kanai, Hideo Ohno & Shunsuke Fukami

  4. Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Japan

    Yasufumi Araki & Jun’ichi Ieda

  5. Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, Japan

    Yuta Yamane

  6. PRESTO, Japan Science and Technology Agency, Kawaguchi, Japan

    Shun Kanai

  7. Division for the Establishment of Frontier Sciences of the Organization for Advanced Studies at Tohoku University, Tohoku University, Sendai, Japan

    Shun Kanai

  8. Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan

    Shun Kanai, Hideo Ohno & Shunsuke Fukami

  9. National Institutes for Quantum Science and Technology, Takasaki, Japan

    Shun Kanai

  10. Center for Innovative Integrated Electronic Systems, Tohoku University, Sendai, Japan

    Hideo Ohno & Shunsuke Fukami

  11. Inamori Research Institute for Science, Kyoto, Japan

    Shunsuke Fukami

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Contributions

S.F. and J.H. planned the study. T.U. prepared and characterized the stacks and fabricated the devices with input from J.H., J.-Y.Y. and Y.T. J.H. and T.U. performed the transport measurements and analysed the data with input from Y.Y., S.K. and S.F. Y.A. performed the theoretical modelling with input from J.I. All authors discussed the results. J.H., Y.A. and S.F. wrote the paper with input from T.U., J.I. and H.O.

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Correspondence to Jiahao Han or Shunsuke Fukami.

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Extended data

Extended Data Fig. 1 Six degenerate configurations of the chiral-spin structure of Mn3Sn and corresponding directions of the applied magnetic field.

The Mn atoms in red and yellow locate in two neighboring kagome planes, respectively.

Extended Data Fig. 2 ScHE measured at different frequencies of the applied current I = 4 mA.

The applied magnetic field of 0.4T is along the +x axis of Fig. 2a. The solid line indicates that we do not observe a frequency dependence of \({V}_{{\rm{H}}}^{\;2{\rm{\omega }}}\).

Source data

Extended Data Fig. 3 Longitudinal angle-dependent magnetoresistance of the (0001)-oriented Mn3Sn/Pt measured by a d.c. of 4 mA and magnetic fields of 0.4 and 4 T.

The solid lines are fits to 180°-periodic sinusoidal functions.

Source data

Extended Data Fig. 4 ScHE and AHE of the (0001)-oriented Mn3Sn/MgO or Ta.

a, ScHE measured by applying an a.c. of 4 mA and rotating an in-plane magnetic field of 0.4 T. No field angle dependence is observed at even higher fields. b, Hall resistance measured by applying a d.c. of 0.5 mA and sweeping a magnetic field along the film normal. The linear background is kept here.

Source data

Extended Data Fig. 5 AHE and ScHE of the \(({\mathbf{1}}{\mathbf{\bar{1}}}{\mathbf{00}})\) -oriented Mn3Sn/Pt.

a, Measurement configuration. The current is applied along the \([11\bar{2}0]\) direction. β and γ scans correspond to the field rotation in zx and yz planes, respectively. b, Hall resistance measured by applying a d.c. of 0.5 mA as well as sweeping a magnetic field perpendicular to the film plane or rotating a magnetic field of 4 T for β scan. A large field of 4 T overcomes the perpendicular magnetic anisotropy and ensures a coherent rotation of the chiral-spin structure with the field. c, ScHE measured by applying an ac current of 4 mA and rotating a magnetic field of 4 T for β and γ scans. The β scan of 0.4 T has the same trend as that of 4 T but even smaller bumps. The result of the (0001)-oriented Mn3Sn/Pt at 4 mA and 0.4 T (α scan) is accompanied for comparison.

Source data

Extended Data Fig. 6 Structure of the effective model used in the theoretical calculations.

a, Kagome bilayer lattice. A unit cell contains six sites, (Ab, Bb, Cb) on the bottom layer and (At, Bt, Ct) on the top layer. The black dot represents the inversion center of the unit cell. b, c, Directions of the DMI vectors Dij (red arrows) for the nearest neighboring sites. If one takes i and j as the starting and end points of each link, Dij points to the direction shown as the small red arrow. Panels b and c denote \({{\bf{D}}}_{{ij}}^{{\rm{loc}}}\) and \({{\bf{D}}}_{{ij}}^{\mathrm{int}}\), respectively. The directions of the spin-orbit field vectors νij for the nearest neighboring sites follow the red arrows in panel b. The brown and grey arrows denote the displacement from one atom site to another.

Extended Data Fig. 7 Momentum-space distributions of the built-in Berry curvature \({[{{\boldsymbol{\Omega }}}_{\boldsymbol{n}}({\bf{k}})]}^{\boldsymbol{z}}\), the electrically induced Berry curvature \({[{{\boldsymbol{\Omega }}}_{\boldsymbol{n}}^{{\boldsymbol{(E\;)}}}({\bf{k}})]}^{\boldsymbol{z}}\), and its symmetric part \({[{{\boldsymbol{\Omega }}}_{\boldsymbol{n}}^{{\boldsymbol{(E\;)}}}({\bf{k}})]}_{{\mathbf{symm}}}^{\boldsymbol{z}}\) (unit: \({\boldsymbol{a}}_{\mathbf{0}}^{\mathbf{2}}\)) under the inverse triangular chiral-spin structure, calculated from the kagome bilayer model (\({\bf{E}}{\boldsymbol{\parallel}} +{\boldsymbol{x}}\) and \({\boldsymbol{\alpha}} ={\mathbf{0}}^{\boldsymbol{\circ}}\)).

a–c, Results without out-of-plane spin canting. d, e, f, Results with out-of-plane spin canting of the top layer due to the i-DMI. The solid-line hexagons correspond to the first Brillouin zone of the kagome lattice. Panels c and f have been shown in Fig. 3c. These results are calculated from the third lowest band in Fig. 3b.

Extended Data Fig. 8 ScHE in the (0001)-oriented Mn3Sn/Pt device with the applied current along \({\boldsymbol{y}}{\boldsymbol{\parallel}} {\boldsymbol{[}}{\mathbf{1}}{\mathbf{\bar{1}}}{\mathbf{00}}{\boldsymbol{]}}\).

a, Theoretical modeling. b, Experiment.

Source data

Extended Data Fig. 9 Theoretically calculated second-order longitudinal and transverse conductivity \({\boldsymbol{\sigma }}_{{\mathbf{s}}}^{\;\boldsymbol{xxx}}\) and \({\boldsymbol{\sigma }}_{{\bf{s}}}^{\;\boldsymbol{yxx}}\) under two mechanisms.

a, Scattering on the asymmetric Fermi surface. b, Intrinsic quantum-metric structure.

Source data

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Source data for Fig. 3a,b,d,e.

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Source data for Fig. 4a–d.

Source Data for Extended Data Fig. 2

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Source Data for Extended Data Fig. 9

Source data for Extended Data Fig. 9.

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Han, J., Uchimura, T., Araki, Y. et al. Room-temperature flexible manipulation of the quantum-metric structure in a topological chiral antiferromagnet. Nat. Phys. 20, 1110–1117 (2024). https://doi.org/10.1038/s41567-024-02476-2

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