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An anomalous Hall effect in altermagnetic ruthenium dioxide

Nature Electronics volume 5, pages 735–743 (2022)Cite this article

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Abstract

The anomalous Hall effect is a time-reversal symmetry-breaking magneto-electronic phenomenon originally discovered in ferromagnets. Recently, ruthenium dioxide (RuO2) with a compensated antiparallel magnetic order has been predicted to generate an anomalous Hall effect of comparable strength to ferromagnets. The phenomenon arises from an altermagnetic phase of RuO2 with a characteristic alternating spin polarization in both real-space crystal structure and momentum-space band structure. Here we report an anomalous Hall effect in RuO2 with an anomalous Hall conductivity exceeding 1,000 Ω−1 cm−1. We combine the vector magnetometry and magneto-transport measurements of epitaxial RuO2 films of different crystallographic orientations. We show that the anomalous Hall effect dominates over an ordinary Hall contribution, and a contribution due to a weak field-induced magnetization. Our results could lead to the exploration of topological Berry phases and dissipationless quantum transport in crystals of abundant elements and with a compensated antiparallel magnetic order.

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Fig. 1: Experimental method for detecting AHE in RuO2.
Fig. 2: Magnetization and magneto-transport measurements.
Fig. 3: Measurements of magnetization M components transverse to the applied magnetic field.
Fig. 4: Anomalous Hall resistivity from symmetry breaking by the antiparallel magnetic order on rutile crystal (ρL-AHE).

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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank J. M. D. Coey at Trinity College, Dublin, and C. Jiang at Beihang University for enlightening and helpful discussion during the preparation of the relevant early versions of this manuscript. Z.L. acknowledges financial support from the National Natural Science Foundation of China (NSFC; grant nos. 52271235 and 52121001). Z.L. and Z.Z. acknowledge financial support from the NSFC on the Science Foundation Ireland (SFI)–NSFC Partnership Programme (NSFC grant no. 51861135104). L.Š., J.S. and T.J. were supported in part by the Ministry of Education of the Czech Republic Grants LM2018110 and LNSM-LNSpin, by the Grant Agency of the Czech Republic grant no. 19-28375X and by the EU FET Open RIA grant no. 766566. L.Š. and R.G.-H. acknowledge the use of the supercomputer Mogon at Johannes Gutenberg Universität (https://hpc.uni-mainz.de/), the computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum provided under the programme Projects of Large Research, Development, and Innovations Infrastructures (CESNET LM2015042). L.Š. and J.S. acknowledge support from the Alexander von Humboldt Foundation and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—TRR 173-268565370 (project A03).

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Author notes

  1. These authors contributed equally: Zexin Feng, Xiaorong Zhou, Libor Šmejkal.

Authors and Affiliations

  1. School of Materials Science and Engineering, Beihang University, Beijing, China

    Zexin Feng, Xiaorong Zhou, Huixin Guo, Xiaoning Wang, Han Yan, Peixin Qin, Xin Zhang, Haojiang Wu, Hongyu Chen, Ziang Meng, Li Liu & Zhiqi Liu

  2. Institut für Physik, Johannes Gutenberg Universität Mainz, Mainz, Germany

    Libor Šmejkal, Rafael González-Hernández & Jairo Sinova

  3. Institute of Physics, Academy of Sciences of the Czech Republic, Staré Město, Czech Republic

    Libor Šmejkal, Jairo Sinova & Tomáš Jungwirth

  4. Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan, China

    Lei Wu, Zengwei Zhu & Zhengcai Xia

  5. School of Physics, Huazhong University of Science and Technology, Wuhan, China

    Lei Wu, Zengwei Zhu & Zhengcai Xia

  6. Grupo de Investigacíon en Física Aplicada, Departamento de Física, Universidad del Norte, Barranquilla, Colombia

    Rafael González-Hernández

  7. School of Physics and Astronomy, University of Nottingham, Nottingham, UK

    Tomáš Jungwirth

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  1. Zexin Feng
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Contributions

Z.F. and X.Zhou performed the sample growth, electrical, structural and magnetic measurements with assistance from L.W., Z.Z., H.G., X.W., H.Y., P.Q., X.Zhang, H.W., H.C., Z.M., L.L. and Z.X. The theoretical calculations were performed by L.Š., R.G.-H., J.S. and T.J. Data analysis was conducted by Z.L., Z.F., X.Zhou, L.Š., R.G.-H., J.S. and T.J. The manuscript was written by Z.L., Z.F., X. Zhou, L.Š., J.S. and T.J. All the authors commented on manuscript. This project was conceived and led by Z.L.

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Correspondence to Zhiqi Liu.

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Extended data

Extended Data Fig. 1 Supporting DFT calculations.

a, Strongly momentum-dependent spin-split Fermi surface calculated without spin-orbit interaction and with Hubbard U = 1.6 eV. b, Strong crystal-momentum resolved Berry curvature in RuO2 calculated with spin-orbit interaction included and magnetic moments along [110] corresponding to the intrinsic anomalous Hall conductivity vector along [110]. The black contours mark Fermi surface. c, Anomalous Hall conductivity vs. energy calculated for the Néel vector along [110] crystal axis. Zero energy corresponds to the Fermi level position in stoichiometric RuO2. d, Magnetocrystalline anisotropy energy (MAE) E[110]-E[001] vs. energy. e, Anomalous Hall conductivity dependence on Hubbard U. f, Corresponding dependence of the magnitude of the sublattice magnetic moment Hubbard U.

Extended Data Fig. 2 Conductivity phase diagram of RuO2 thin films.

Conductivity phase diagram of RuO2 thin films fabricated on MgO substrates versus the deposition oxygen partial pressure and the substrate temperature. Each data point represents the mean conductivity value derived from the measurements of three repeating samples.

Extended Data Fig. 3 Exchange bias experiments.

The exchange bias measurements were performed after field cooling from 400 K by a + 500 mT field applied in plane. a. Coercivity fields of a Pt(2 nm)/CoFe(5 nm)/RuO2(27 nm)/TiO2(110) sample and a Pt(2 nm)/CoFe(5 nm)/TiO2(110) sample as a function of temperature. b. Normalized magnetization of the Pt(2 nm)/CoFe(5 nm)/RuO2(27 nm)/TiO2(110) sample at 50 K. c. Exchange bias field of the CoFe/RuO2 system versus temperature. d. Normalized magnetization of the post-annealed Pt(2 nm)/CoFe(5 nm)/RuO2(27 nm)/TiO2(110) sample at 200 K. e. Exchange bias field of the post-annealed sample as a function of temperature. The sample was annealed at 250 °C for 1 h in a vacuum furnace under an in-plane magnetic field of 500 mT.

Extended Data Fig. 4 Structural characterization of a RuO2/TiO2(100) heterostructure.

a. X-ray diffraction data. b. Cross-section transmission electron microscopy image of the RuO2 film.

Extended Data Fig. 5 Structural characterization of a RuO2/TiO2(001) heterostructure.

a. X-ray diffraction data. b. Cross-section transmission electron microscopy image of the RuO2 film.

Extended Data Fig. 6 Structure and exchange bias of a (110)-oriented RuO2/MgO thin film.

a, X-ray diffraction spectrum. Inset: Schematic of the RuO2/MgO heterostructure. b, Normalized in-plane magnetization of the Pt/CoFe/RuO2/MgO stack as a function of magnetic field at 50 K. c, Comparison of the in-plane coercivity field of Co90Fe10 (CoFe) films in a Pt/CoFe/RuO2/MgO heterostructure and a Pt/CoFe/MgO heterostructure. Inset: Schematic of a RuO2/MgO heterostructure capped by a 5-nm-thick CoFe layer and a 2-nm-thick Pt top layer. d, In-plane exchange bias field of the Pt/CoFe/RuO2/MgO heterostructure versus temperature.

Extended Data Fig. 7 X-ray diffraction of a RuO2/SrTiO3(001) heterostructure.

X-ray diffraction of a RuO2/SrTiO3(001) heterostructure.

Extended Data Fig. 8 Electrical transport of the (100)-oriented RuO2/SrTiO3 and the (110)-oriented RuO2/MgO sample.

a. Temperature-dependent resistivity. b. Hall resistivity as a function of pulsed magnetic fields for the (110)-oriented RuO2/MgO sample. c. Hall resistivity as a function of pulsed magnetic fields for the (100)-oriented RuO2/SrTiO3 sample.

Extended Data Fig. 9 High-field moments of substrates and substrates plus films.

High-field moments of substrates and substrates plus films.

Extended Data Fig. 10 Supporting DFT calculations in magnetic field.

a, Band structure calculated with moments along [110] crystal direction and without/with applied magnetic field along [110] direction implemented via a Zeeman term in the ELK code. b, Momentum resolved Berry curvature calculated in Wannier90 from the bands obtained in VASP code in zero magnetic field.

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Feng, Z., Zhou, X., Šmejkal, L. et al. An anomalous Hall effect in altermagnetic ruthenium dioxide. Nat Electron 5, 735–743 (2022). https://doi.org/10.1038/s41928-022-00866-z

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