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A correlated ferromagnetic polar metal by design

Nature Materials (2024)Cite this article

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Abstract

Polar metals have recently garnered increasing interest because of their promising functionalities. Here we report the experimental realization of an intrinsic coexisting ferromagnetism, polar distortion and metallicity in quasi-two-dimensional Ca3Co3O8. This material crystallizes with alternating stacking of oxygen tetrahedral CoO4 monolayers and octahedral CoO6 bilayers. The ferromagnetic metallic state is confined within the quasi-two-dimensional CoO6 layers, and the broken inversion symmetry arises simultaneously from the Co displacements. The breaking of both spatial-inversion and time-reversal symmetries, along with their strong coupling, gives rise to an intrinsic magnetochiral anisotropy with exotic magnetic field-free non-reciprocal electrical resistivity. An extraordinarily robust topological Hall effect persists over a broad temperature–magnetic field phase space, arising from dipole-induced Rashba spin–orbit coupling. Our work not only provides a rich platform to explore the coupling between polarity and magnetism in a metallic system, with extensive potential applications, but also defines a novel design strategy to access exotic correlated electronic states.

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Fig. 1: Experimental realization of Ca3Co3O8.
Fig. 2: Magnetic and metallic properties of Ca3Co3O8.
Fig. 3: Evidence and mechanism of the polar state in Ca3Co3O8.
Fig. 4: Non-reciprocal electrical transport in Ca3Co3O8.
Fig. 5: Robust THE in Ca3Co3O8.

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Data availability

The data supporting the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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Acknowledgements

This study was financially supported by the Basic Science Center Project of National Natural Science Foundation of China (NFSC) under grant no. 52388201, the NFSC (52025024), the National Key R&D Program of China (2021YFE0107900, 2023YFA1406400, 2021YFA1400100 and 2021YFA1400300), the Beijing Natural Science Foundation (grant no. Z200007), the NFSC (52161135103 and U2032218), the Beijing Advanced Innovation Center for Future Chip (ICFC), the Army Research Office (ARO) under grant no. W911NF-15-1-0017 and the National Science Foundation (NSF) under grant no. DMR-2104397. N.N. was supported by JST CREST grant number JPMJCR1874 and JSPS KAKENHI grant number 18H03676. A portion of this work was performed on the Steady High Magnetic Field Facilities, High Magnetic Field Laboratory, CAS. We acknowledge the Users with Excellence Project of Hefei Science Center CAS, 2021HSC-UE007. The high-field XMCD measurement was performed under proposal no. 2019A1344 at SPring-8 BL25SU. This research used resources of the Advanced Light Source, a US DOE Office of Science User Facility under contract no. DE-AC02-05CH11231. We acknowledge the High-Performance Computing Modernization Program (HPCMP) of the DOD for providing computational resources that have contributed to the research results reported herein.

Author information

Author notes

  1. These authors contributed equally: Jianbing Zhang, Shengchun Shen, Danilo Puggioni, Meng Wang, Haozhi Sha.

Authors and Affiliations

  1. State Key Laboratory of Low Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, China

    Jianbing Zhang, Shengchun Shen, Meng Wang, Yingjie Lyu, Huining Peng, Yujia Wang, Tian Liang, Shuyun Zhou & Pu Yu

  2. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, USA

    Danilo Puggioni, Lauren N. Walters & James M. Rondinelli

  3. State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing, China

    Haozhi Sha, Wandong Xing, Linhan Liu, Di Yi, Ce-Wen Nan & Rong Yu

  4. MOE Key Laboratory of Advanced Materials, Tsinghua University, Beijing, China

    Haozhi Sha, Wandong Xing, Linhan Liu & Rong Yu

  5. High Magnetic Field Laboratory, HFIPS, Anhui, Chinese Academy of Sciences, Hefei, China

    Xueli Xu, De Hou, Chuanying Xi, Li Pi & Zhigao Sheng

  6. Department of Physics, Tokyo Institute of Technology, Tokyo, Japan

    Hiroaki Ishizuka

  7. Center for Synchrotron Radiation Research, Japan Synchrotron Radiation Research Institute, Hyogo, Japan

    Yoshinori Kotani

  8. Institute of Materials Research, Tohoku University, Sendai, Japan

    Motoi Kimata & Hiroyuki Nojiri

  9. International Center for Synchrotron Radiation Innovation Smart, Tohoku University, Sendai, Japan

    Tetsuya Nakamura

  10. RIKEN Center for Emergent Matter Science (CEMS), Wako, Japan

    Tian Liang, Naoto Nagaosa, Yoshinori Tokura & Pu Yu

  11. Frontier Science Center for Quantum Information, Beijing, China

    Tian Liang, Shuyun Zhou & Pu Yu

  12. School of Integrated Circuits, Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing, China

    Tianxiang Nan

  13. Department of Physics and Astronomy, University of New Hampshire, Durham, NH, USA

    Jiadong Zang

  14. Department of Physics, Durham University, Durham, UK

    Qing He

  15. Department of Applied Physics, University of Tokyo, Tokyo, Japan

    Naoto Nagaosa & Yoshinori Tokura

Authors
  1. Jianbing Zhang
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  2. Shengchun Shen
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  3. Danilo Puggioni
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Contributions

P.Y. conceived the project and coordinated the studies. Jianbing Z. and M.W. fabricated the samples and performed the structural and magnetic measurements. S.S. and Jianbing Z. performed all the electrical transport measurements. D.P. and J.M.R. formulated the theoretical models, carried out the first-principles calculations and did the group theoretical analysis with L.N.W. Q.H., Y.W., Y.L. and H.P. carried out the synchrotron spectroscopy measurements. H.P. carried out the MFM measurements. H.S., W.X. and L.L. carried out high-resolution STEM and ptychography experiments and reconstructions under the supervision of R.Y. X.X. carried out the SHG measurements under the supervision of Z.S. C.X. and L.P. provided support in high magnetic field electrical transport measurements. Y.K., M.K., H.N. and Tetsuya N. provided support for the high magnetic field X-ray circular dichroism measurements. H.I., T.L., D.Y., Tianxiang N., Jiadong Z., S.Z., N.N., C.-W.N. and Y.T. provided scientific insights. Jianbing Z., S.S., D.P. and P.Y. wrote the manuscript, and all authors discussed results and commented on the manuscript.

Corresponding authors

Correspondence to Rong Yu, James M. Rondinelli or Pu Yu.

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Extended data

Extended Data Fig. 1 Extended structural characterizations.

a-b, Reciprocal space mappings of Ca2Co2O5 (a) and Ca3Co3O8 (b) thin films around the (103)pc crystalline plane of the LSAT substrate, in which qx and qz represent the projected directions in reciprocal space. The diffraction spots of both Ca2Co2O5 and Ca3Co3O8 were denoted based on a pseudocubic notation. c-d, Rocking curves around Ca2Co2O5 (001)pc (c) and Ca3Co3O8 (001)pc (d) diffraction peaks. e, STEM image of Ca3Co3O8 thin film with a large field of view. f, STEM HAADF images obtained at different locations of e. The images in red, orange, and blue boxes correspond to regions close to the surface, in the middle region, and at the Ca3Co3O8 film-substrate interface, respectively. A buffered layer (about one pseudocubic unit cell) can be identified at the interface, which is essential to match the different lattice constants between LSAT substrate and the newly formed Ca3Co3O8. g-h, High-resolution STEM HAADF (g) and ABF (h) images of Ca3Co3O8 thin films. The zone axis was set along the oxygen vacancy channels of Ca3Co3O8, which is equivalent to the [110]pc direction of the LSAT substrate. The schematic of the atomic-scale crystalline structure is shown as reference in g. i-j, Simulated HAADF (i) and ABF (j) patterns for Ca3Co3O8.

Extended Data Fig. 2 Extended magnetic measurements of Ca3Co3O8.

a-f, In-plane (IP) and out-of-plane (OOP) magnetic hysteresis loops measured at 5 K, 10 K, 50 K, 125 K, 150 K, 175 K, respectively. For the IP results, the coercive field as well as the residual- and the saturated moments decrease systematically with increasing temperature. As for OOP, the coercive field and residual magnetic moment remain almost zero for all temperatures probed. g, Comparison of XMCD spectra at Co L-edges for Ca2Co2O5, Ca3Co3O8 and SrCoO3 samples. The signal from SrCoO3 is scaled by a factor of 1/3 for better comparison. h, XMCD spectra at oxygen K-edges for Ca2Co2O5 and Ca3Co3O8. The evident contribution to magnetization from oxygen ions indicates a strong hybridization between O 2p and Co 3d states in Ca3Co3O8. The inset shows the experimental configuration, in which μ+ and μ- denote right and left circularly polarized X-rays. The spectra were taken at 78 K with a magnetic field of 4 T applied along the incident light direction. The XMCD spectral feature for Ca3Co3O8 resembles nicely that of SrCoO3, with the characteristic dip- and peak- features located around L3- and L2- edges, respectively. Because SrCoO3 is ferromagnetic with all Co ions parallelly coupled, the suppressed XMCD in Ca3Co3O8 suggests that only a portion of Co ions is coupled ferromagnetically. While the rest Co ions must be antiferromagnetically coupled and canceled with each other, otherwise a peak (dip) feature would be observed at the L3 (L2) edge. Based on the extended similarity of XMCD peak features and positions between Ca3Co3O8 and SrCoO3, we deduce that all Co ions within octahedral layers are coupled ferromagnetically, while the Co ions within tetrahedra are coupled antiferromagnetically, and furthermore the double peak features around the L3 edge suggests a different electronic state of the Co ions within the octahedra. These are strongly supported by our first-principles calculations (Extended Data Figs. 7b, c).

Extended Data Fig. 3 Magnetization measurements for films with different thickness.

a, Temperature dependent in-plane magnetization. The measurements were performed in a heating process at a magnetic field of 0.3 T after field cooling with a magnetic field of 7 T. b, Field dependence of in-plane magnetization at 50 K.

Extended Data Fig. 4 Transport measurements for films with different thickness.

All curves show similar metallic behaviors with clear kink feature at the magnetic transition temperature of ~150 K.

Extended Data Fig. 5 Electron ptychography characterizations of Ca2Co2O5 and Ca3Co3O8 samples.

a, Modulus of reconstructed orthogonal probe states at the object plane. Ratios of each state are 50.1%, 15.2%, 10.4%, 9.0%, 8.4% and 7.0%. b, Initial (light grey) and refined (orange) scan positions. c, Modulus of the Fourier transformation of the total phase images of Ca3Co3O8 (left) and Ca2Co2O5 (right). The information limits are 0.33 Å and 0.34 Å for Ca3Co3O8 and Ca2Co2O5, respectively, which are marked out with orange dotted circles. Image contrast is adjusted to show the information limit clearly. Scale bars, 0.5 nm−1. d-e, Ptychographic phase images of Ca2Co2O5 (d) and Ca3Co3O8 (e). In the schematics, the yellow circles denote Co atoms, the red circles denote O atoms, and the purple circles denote Ca atoms. f-g, Displacements of Co atoms relative to two nearest neighbor equatorial O atoms within CoO6 octahedral layers of Ca2Co2O5 (f) and Ca3Co3O8 (g). Each pixel represents a Co atomic column with its displacement (dCo-O) along the c axis. In Ca3Co3O8, there are two octahedral layers between tetrahedral layers, and the displacements in the neighboring octahedral layers are summed.

Extended Data Fig. 6 Crystalline structure and atomic displacements of Ca3Co3O8.

a-c, Schematic crystalline structures of Ca3Co3O8 for the centrosymmetric orthorhombic Pbam phase (a), centrosymmetric monoclinic P21/c phase (b), and noncentrosymmetric monoclinic Pc phase (c), respectively. The different colors indicate the distinct Co Wyckoff sites. d-e, In-plane (d) and out-of-plane (e) atomic displacements of \({\Gamma }_{2}^{-}\) polar mode.

Extended Data Fig. 7 Representative spin configurations and theoretically calculated density of states (DOS) for Ca3Co3O8.

a-b, Schematic illustrations of ferromagnetic orders among the whole lattice (FM1) (a) and ferromagnetic order only in the octahedral layers (FM2) (b). In FM2, the spins within the tetrahedral layers are coupled antiferromagnetically, and therefore have negligible contribution to the magnetization. Spin orientations on the Co sites are indicated by the solid black arrows. c, Site-projected DOS for Ca3Co3O8 in FM2 Pc phase. The Co cations are in a Co3+L state (d6 intermediate-spin) for the Oh1 site, and in a Co2+L state (d7 high-spin) for both the Oh2 and Td sites. Based on the calculations, we find an average local magnetic moment of ~2.7 μB for the Td sites and an average local magnetic moment of ~1.2 and ~2.6 μB for the Oh1 and Oh2 sites, respectively. d, DOS for Ca3Co3O8 in the Pc phase with FM2 magnetic state, which indicates the metallic nature. The atomic and angular momentum decomposed (DOS) is performed for Co atoms in octahedral (Oh) and tetrahedral (Td) sites. e, DOS for Ca3Co3O8 in the G-type antiferromagnetic Pc phase.

Extended Data Fig. 8 XMCD studies of Ca3Co3O8 at high magnetic field.

a, Schematic illustration of XAS and XMCD measurements. b, Normalized XAS spectroscopy for Co L-edges in Ca3Co3O8 under different magnetic fields. The identical spectra under different magnetic fields exclude the spin-state transition during the application of a high magnetic field. c, Comparison of XMCD spectra of Co L-edges in Ca3Co3O8 at different magnetic fields. The red and blue curves with solid lines represent XMCD signals measured with the application of 30 T magnetic field along the c-axis, and its remnant state with zero field. The black dashed line represents the XMCD signal measured with a magnetic field of 4 T with an incident angle of 60°, which probes mainly the in-plane magnetization. d, Summary of field dependent magnetization in Ca3Co3O8. The high field (up to 30 T) data (colored curves) represent the magnetic contribution of spin- (red curve), orbital- magnetic moments (blue curve) and their combination (purple curve) for Co ions, as obtained from the XMCD sum rule. Both the IP (black solid curve) and OOP (black dashed curve) magnetizations were given for the purpose of comparison. The stark differences among the high-field (purple curve) and low-field (dash line) magnetizations along the c-axis, as well as the saturated in-plane magnetization (black curve), demonstrate an enhanced total magnetization through a field-induced spin-flop transition. All data were measured at 100 K.

Extended Data Fig. 9 Extended magneto-transport measurements for Ca3Co3O8.

a-b, Hall resistivity (a) and magnetoresistance (b) measured at several temperature points. The ordinary Hall contribution was removed from the Hall signal by fitting the linear background at the high field region. The Hall signal at 125 K is magnified for the purpose of clarity. c, Topological Hall effect (hump feature) obtained for the tilted magnetic fields. The measurements were carried out at 125 K. θ is the angle between the magnetic field and the normal (c) direction. The circles at the lowest Hall amplitude denote the contribution of the topological Hall signal ρRyx. The results clearly reveal that the topological Hall signal is profoundly suppressed with the presence of an in-plane magnetic field. d, Evolution of topological Hall resistivity and in-plane magnetization as a function of the in-plane magnetic field, measured at 125 K. The topological Hall contribution decreases rapidly as the in-plane magnetization approaches saturation, which indicates the hump feature originates from noncollinear/noncoplanar spin configuration.

Extended Data Fig. 10 Correlations between the topological Hall effect and the microscale magnetic domain structure.

a-b, Magnetic force microscopy (MFM) images measured at (a) 120 K and (b) 10 K with different magnetic-field strengths. The magnetic field was applied along the c axis. c-d, Comparison of the topological Hall resistivity (ρxy-ρ0B, hump features of blue and red lines with increasing and decreasing magnetic field), domain density (n, black circles) and magnetization (M, gray line) as a function of the magnetic field at (c) 120 K and (d) 10 K. e, MFM intensity profile across an isolated domain as outlined by the yellow line in the rightmost image of (b). The completely suppressed MFM signal in the domain wall region indicates the formation of a Néel-type magnetic domain wall in Ca3Co3O8. Since the Ca3Co3O8 film shows large Dzyaloshinskii-Moriya interaction (DMI) strength (Supplementary Information Note 3) to stabilize Néel domain wall with chirality, while classical bubbles do not have any preferred chirality and are stabilized solely by dipolar interactions.

Supplementary information

Supplementary Information

Supplementary Notes 1–5, Figs. 1–3 and Table 1.

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Source Data Fig. 1

Source data for the plots in Fig. 1e.

Source Data Fig. 2

Source data for the plots in Fig. 2a–d.

Source Data Fig. 3

Source data for the plots in Fig. 3a–c.

Source Data Fig. 4

Source data for the plots in Fig. 4b–d.

Source Data Fig. 5

Source data for the plots in Fig. 5a–d.

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Zhang, J., Shen, S., Puggioni, D. et al. A correlated ferromagnetic polar metal by design. Nat. Mater. (2024). https://doi.org/10.1038/s41563-024-01856-6

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