Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

# Sign-tunable anomalous Hall effect induced by two-dimensional symmetry-protected nodal structures in ferromagnetic perovskite thin films

### Subjects

An Author Correction to this article was published on 13 October 2021

This article has been updated

## Abstract

Magnetism and spin–orbit coupling are two quintessential ingredients underlying topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by spin–orbit coupling, the nodal structures become a source of Berry curvature, leading to a large anomalous Hall effect. However, two-dimensional systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that two-dimensional spin-polarized band structures of perovskite oxides generally support symmetry-protected nodal lines and points that govern both the sign and the magnitude of the anomalous Hall effect. To demonstrate this, we performed angle-resolved photoemission studies of ultrathin films of SrRuO3, a representative metallic ferromagnet with spin–orbit coupling. We show that the sign-changing anomalous Hall effect upon variation in the film thickness, magnetization and chemical potential can be well explained by theoretical models. Our work may facilitate new switchable devices based on ferromagnetic ultrathin films.

## Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from\$8.99

All prices are NET prices.

## Data availability

The data that support the findings of this study are available from the corresponding authors on request.

## References

1. 1.

Burkov, A. A. Anomalous Hall effect in Weyl metals. Phys. Rev. Lett. 113, 187202 (2014).

2. 2.

Ye, L. et al. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555, 638–642 (2018).

3. 3.

Groenendijk, D. J. et al. Berry phase engineering at oxide interfaces. Phys. Rev. Res. 2, 023404 (2020).

4. 4.

Chang, G. et al. Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in half-metallic Heusler Co2TiX (X = Si, Ge, or Sn). Sci. Rep. 6, 38839 (2016).

5. 5.

Chang, G. et al. Magnetic and noncentrosymmetric Weyl fermion semimetals in the RAlGe family of compounds (R = rare earth). Phys. Rev. B 97, 041104 (2018).

6. 6.

Kim, K. et al. Large anomalous Hall current induced by topological nodal lines in a ferromagnetic van der Waals semimetal. Nat. Mater. 17, 794–799 (2018).

7. 7.

Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).

8. 8.

Zeng, C., Yao, Y., Niu, Q. & Weitering, H. H. Linear magnetization dependence of the intrinsic anomalous Hall effect. Phys. Rev. Lett. 96, 037204 (2006).

9. 9.

Wang, Q. et al. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions. Nat. Commun. 9, 3681 (2018).

10. 10.

Fang, Z. et al. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92–95 (2003).

11. 11.

Chen, Y., Bergman, D. & Burkov, A. Weyl fermions and the anomalous Hall effect in metallic ferromagnets. Phys. Rev. B 88, 125110 (2013).

12. 12.

Vazifeh, M. M. & Franz, M. Electromagnetic response of Weyl semimetals. Phys. Rev. Lett. 111, 027201 (2013).

13. 13.

Zyuzin, A. A. & Tiwari, R. P. Intrinsic anomalous Hall effect in type-II Weyl semimetals. JETP Lett. 103, 717–722 (2016).

14. 14.

Young, S. M. & Kane, C. L. Dirac semimetals in two dimensions. Phys. Rev. Lett. 115, 126803 (2015).

15. 15.

Niu, C. et al. Two-dimensional topological nodal line semimetal in layered X2Y (X = Ca, Sr, and Ba; Y = As, Sb, and Bi). Phys. Rev. B 95, 235138 (2017).

16. 16.

Zhang, H., Huang, H., Haule, K. & Vanderbilt, D. Quantum anomalous Hall phase in (001) double-perovskite monolayers via intersite spin-orbit coupling. Phys. Rev. B 90, 165143 (2014).

17. 17.

Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

18. 18.

Neumeier, J. et al. Magnetic, thermal, transport, and structural properties of Sr2RuO4+δ: enhanced charge-carrier mass in a nearly metallic oxide. Phys. Rev. B 50, 17910 (1994).

19. 19.

Puchkov, A., Shen, Z.-X., Kimura, T. & Tokura, Y. ARPES results on Sr2RuO4: Fermi surface revisited. Phys. Rev. B 58, R13322 (1998).

20. 20.

Damascelli, A. et al. Fermi surface, surface states, and surface reconstruction in Sr2RuO4. Phys. Rev. Lett. 85, 5194–5197 (2000).

21. 21.

Mackenzie, A. P. et al. Quantum oscillations in the layered perovskite superconductor Sr2RuO4. Phys. Rev. Lett. 76, 3786–3789 (1996).

22. 22.

Mackenzie, A. P. et al. The Fermi surface topography of Sr2RuO4. J. Phys. Soc. Jpn 67, 385–388 (1998).

23. 23.

Chang, S. H. et al. Thickness-dependent structural phase transition of strained SrRuO3 ultrathin films: the role of octahedral tilt. Phys. Rev. B 84, 104101 (2011).

24. 24.

Sohn, B. et al. Stable humplike Hall effect and noncoplanar spin textures in SrRuO3 ultrathin films. Phys. Rev. Res. 3, 023232 (2021).

25. 25.

Singh, D. & Mazin, I. Electronic structure and magnetism of Sr3Ru2O7. Phys. Rev. B 63, 165101 (2001).

26. 26.

Chang, Y. J. et al. Fundamental thickness limit of itinerant ferromagnetic SrRuO3. Phys. Rev. Lett. 103, 057201 (2009).

27. 27.

Jeong, D. W. et al. Temperature evolution of itinerant ferromagnetism in SrRuO3 probed by optical spectroscopy. Phys. Rev. Lett. 110, 247202 (2013).

28. 28.

Zhang, P. et al. A precise method for visualizing dispersive features in image plots. Rev. Sci. Instrum. 82, 043712 (2011).

29. 29.

Matsuno, J. et al. Interface-driven topological Hall effect in SrRuO3-SrIrO3 bilayer. Sci. Adv. 2, e1600304 (2016).

30. 30.

Sohn, B. et al. Hump-like structure in Hall signal from ultra-thin SrRuO3 films without inhomogeneous anomalous Hall effect. Curr. Appl. Phys. 20, 186–190 (2020).

31. 31.

Jin, L. et al. Two-dimensional Weyl nodal-line semimetal in a d0 ferromagnetic K2N monolayer with a high Curie temperature. Phys. Rev. B 102, 125118 (2020).

32. 32.

Jin, L. et al. Ferromagnetic two-dimensional metal-chlorides MCl (M = Sc, Y, and La): candidates for Weyl nodal line semimetals with small spin-orbit coupling gaps. Appl. Surf. Sci. 520, 146376 (2020).

33. 33.

Sun, K., Yao, H., Fradkin, E. & Kivelson, S. A. Topological insulators and nematic phases from spontaneous symmetry breaking in 2D Fermi systems with a quadratic band crossing. Phys. Rev. Lett. 103, 046811 (2009).

34. 34.

Chong, Y. D., Wen, X.-G. & Soljačić, M. Effective theory of quadratic degeneracies. Phys. Rev. B 77, 235125 (2008).

35. 35.

Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).

36. 36.

Go, D., Jo, D., Kim, C. & Lee, H.-W. Intrinsic spin and orbital Hall effects from orbital texture. Phys. Rev. Lett. 121, 086602 (2018).

37. 37.

Cho, S. et al. Experimental observation of hidden Berry curvature in inversion-symmetric bulk 2H-WSe2. Phys. Rev. Lett. 121, 186401 (2018).

38. 38.

Park, S. R. et al. Chiral orbital-angular momentum in the surface states of Bi2Se3. Phys. Rev. Lett. 108, 046805 (2012).

39. 39.

Schüler, M. et al. Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials. Sci. Adv. 6, eaay2730 (2020).

40. 40.

Schultz, M., Levy, S., Reiner, J. W. & Klein, L. Magnetic and transport properties of epitaxial films of SrRuO3 in the ultrathin limit. Phys. Rev. B 79, 125444 (2009).

41. 41.

Mathieu, R. et al. Scaling of the anomalous Hall effect in Sr1−xCaxRuO3. Phys. Rev. Lett. 93, 016602 (2004).

42. 42.

Zhang, D. et al. Origin of the anomalous Hall effect in SrCoO3 thin films. Phys. Rev. B 100, 060403 (2019).

43. 43.

Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

44. 44.

Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

45. 45.

Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

46. 46.

Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter 32, 165902 (2020).

47. 47.

Liechtenstein, A. I., Anisimov, V. I. & Zaanen, J. Density-functional theory and strong interactions: orbital ordering in Mott-Hubbard insulators. Phys. Rev. B 52, R5467–R5470 (1995).

48. 48.

Vaugier, L., Jiang, H. & Biermann, S. Hubbard U and Hund exchange J in transition metal oxides: screening versus localization trends from constrained random phase approximation. Phys. Rev. B 86, 165105 (2012).

49. 49.

Bezdicka, P., Wattiaux, A., Grenier, J., Pouchard, M. & Hagenmuller, P. Preparation and characterization of fully stoichiometric SrCoO3 by electrochemical oxidation. Z. Anorg. Allg. Chem. 619, 7–12 (1993).

Download references

## Acknowledgements

We gratefully acknowledge discussions with J. R. Kim. This work is supported by IBS-R009-D1 and IBS-R009-G2 through the Institute for Basic Science (IBS) Center for Correlated Electron Systems. B.-J.Y. was supported by the Institute for Basic Science in Korea (grant no. IBS-R009-D1), Samsung Science and Technology Foundation under project no. SSTF-BA2002-06, the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (no. 2021R1A2C4002773, and no. NRF-2021R1A5A1032996), and the US Army Research Office and Asian Office of Aerospace Research & Development (AOARD) under grant no. W911NF-18-1-0137. S.Y.P. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (no. 2021R1C1C1009494) and by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (no. 2021R1A6A1A03043957). The Advanced Light Source is supported by the Office of Basic Energy Sciences of the US Department of Energy under contract no. DE-AC02-05CH11231.

## Author information

Authors

### Contributions

B.S., E.L., B.-J.Y. and C.K. conceived the project. S.Y.P., B.-J.Y. and C.K. led the project. B.S. synthesized and characterized the materials with support from B.K. and T.W.N.; B.S., W.K. and J.H. conducted ARPES measurements with support from J.D.D., J.S.O., J.K.J., D.O. and Y.K.; B.S., H.R. and S.H. conducted spin-resolved ARPES measurements. B.S. performed transport measurements. B.S. and B.K. performed magnetic measurements. M.K. and D.K. performed ionic liquid gating. B.S. analysed the experimental data. E.L. conducted tight-binding calculations and symmetry analysis. S.Y.P. conducted first-principles calculations. B.S., E.L., B.-J.Y. and C.K. wrote the paper with contributions from other authors. All authors participated in the discussions and commented on the manuscript.

### Corresponding authors

Correspondence to Se Young Park, Bohm-Jung Yang or Changyoung Kim.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Additional information

Peer review information Nature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

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

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–21 and Discussion.

## Rights and permissions

Reprints and Permissions

## About this article

### Cite this article

Sohn, B., Lee, E., Park, S.Y. et al. Sign-tunable anomalous Hall effect induced by two-dimensional symmetry-protected nodal structures in ferromagnetic perovskite thin films. Nat. Mater. (2021). https://doi.org/10.1038/s41563-021-01101-4

Download citation

• Received:

• Accepted:

• Published:

## Search

### Quick links

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing