Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic

Journal name:
Nature
Volume:
537,
Pages:
523–527
Date published:
DOI:
doi:10.1038/nature19343
Received
Accepted
Published online

Materials that exhibit simultaneous order in their electric and magnetic ground states hold promise for use in next-generation memory devices in which electric fields control magnetism1, 2. Such materials are exceedingly rare, however, owing to competing requirements for displacive ferroelectricity and magnetism3. Despite the recent identification of several new multiferroic materials and magnetoelectric coupling mechanisms4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, known single-phase multiferroics remain limited by antiferromagnetic or weak ferromagnetic alignments, by a lack of coupling between the order parameters, or by having properties that emerge only well below room temperature, precluding device applications2. Here we present a methodology for constructing single-phase multiferroic materials in which ferroelectricity and strong magnetic ordering are coupled near room temperature. Starting with hexagonal LuFeO3—the geometric ferroelectric with the greatest known planar rumpling16—we introduce individual monolayers of FeO during growth to construct formula-unit-thick syntactic layers of ferrimagnetic LuFe2O4 (refs 17, 18) within the LuFeO3 matrix, that is, (LuFeO3)m/(LuFe2O4)1 superlattices. The severe rumpling imposed by the neighbouring LuFeO3 drives the ferrimagnetic LuFe2O4 into a simultaneously ferroelectric state, while also reducing the LuFe2O4 spin frustration. This increases the magnetic transition temperature substantially—from 240 kelvin for LuFe2O4 (ref. 18) to 281 kelvin for (LuFeO3)9/(LuFe2O4)1. Moreover, the ferroelectric order couples to the ferrimagnetism, enabling direct electric-field control of magnetism at 200 kelvin. Our results demonstrate a design methodology for creating higher-temperature magnetoelectric multiferroics by exploiting a combination of geometric frustration, lattice distortions and epitaxial engineering.

At a glance

Figures

  1. HAADF-STEM images.
    Figure 1: HAADF-STEM images.

    a, End-members LuFe2O4 (left) and LuFeO3 (right). b, (LuFeO3)m/(LuFe2O4)1 superlattice series for 1 ≤ m ≤ 10. Samples are imaged along the LuFeO3 P63cm [100] zone axis. LuFe2O4 is imaged down the equivalent zone axis, which, owing to the primitive unit cell of LuFe2O4, is the [120] zone axis. Schematics of the LuFe2O4 and LuFeO3 crystal structures are shown in a with lutetium (Lu), iron (Fe) and oxygen (O) in turquoise, yellow and brown, respectively.

  2. Magnetic and ferroelectric characterization of (LuFeO3)m/(LuFe2O4)n superlattices.
    Figure 2: Magnetic and ferroelectric characterization of (LuFeO3)m/(LuFe2O4)n superlattices.

    a, MT curves for a series of (LuFeO3)m/(LuFe2O4)1 superlattices cooled in a 1-kOe field. M0, magnetization at 1.8 K. b, Loops of the magnetization as a function of the magnetic field for the (LuFeO3)9/(LuFe2O4)1 superlattice, at various temperatures. c, The ferromagnetic Curie temperatures TC,mag extracted from the MT curves (some of which are shown in a) plotted as a function of the fraction of iron ions that sit in the LuFeO3 layers, m/(m + 2n). Regions I and II show data for the (LuFeO3)1/(LuFe2O4)n and (LuFeO3)m/(LuFe2O4)1 series, respectively. The Curie temperature reaches a maximum of 281 K for the (LuFeO3)9/(LuFe2O4)1 compound. d, The total moment per iron cation in LuFe2O4 at 50 K assuming the moment of LuFeO3 remains constant. The measured moment of end-member LuFe2O4 is displayed as a horizontal line for reference. e, Average polarization from HAADF-STEM for superlattice layering plotted as a function of composition. Ferroelectric distortions are observed for the (LuFeO3)m/(LuFe2O4)1 superlattices with m ≥ 2 (m/(m + 2n) ≥ 0.5). Error bars are s.e.m. f, Temperature-dependent XLD for a series of (LuFeO3)m/(LuFe2O4)1 superlattices. The drop in the dichroic signal corresponds to the ferroelectric transition in the m= 3 and m= 5 films; the transition in the m= 9 film is above the measurement limit. Error bars are discussed in Methods; a.u., arbitrary units. g, Out-of-plane PFM images of the (LuFeO3)9/(LuFe2O4)1 superlattice following electrical poling using a d.c. bias applied to the proximal tip. The ‘up’ and ‘down’ c-oriented domains appear in turquoise and red, respectively. The written domain structure is still apparent after 100 h, demonstrating the retention of the poling. Scale bars, 5 μm.

  3. First-principles calculations of the spin configuration of LuFe2O4.
    Figure 3: First-principles calculations of the spin configuration of LuFe2O4.

    a, b, Monoclinic structures of the LuFe2O4 system for the Fe2+/Fe3+ antiferroelectric charge-ordered (COI) state (a; space group C2/m) and the ferroelectric charge-ordered (COII) state (b; space group Cm). The saturation magnetization per iron cation was calculated as a function of temperature (right panels). For the COII configuration (b), the temperature-dependent saturation magnetization per iron cation is calculated as a function of Q, the amplitude of the atomic distortions from the high-symmetry structure. In the COII state, the magnetic transition temperature increases with the magnitude of the structural distortion associated with the ferroelectric state.

  4. Magnetoelectric coupling in the (LuFeO3)9/(LuFe2O4)1 superlattice.
    Figure 4: Magnetoelectric coupling in the (LuFeO3)9/(LuFe2O4)1 superlattice.

    a, Out-of-plane PFM image at 300 K of the domain structure following electrical poling using a d.c. bias applied to the proximal tip. The ‘up’ and ‘down’ c-oriented domains appear in turquoise and red, respectively. Scale bar, 3 μm. b, c, XMCD PEEM ratio images from the Fe L3 edge acquired at 200 K (b) and 320 K (c). The correlation between the electrical poling and magnetic imaging demonstrates electric-field control of ferrimagnetism at 200 K. d, Comparison of the dichroic signals along the yellow lines in b and c.

  5. X-ray diffraction characterization of the (LuFeO3)m/(LuFe2O4)n superlattices.
    Extended Data Fig. 1: X-ray diffraction characterization of the (LuFeO3)m/(LuFe2O4)n superlattices.

    a, θ–2θ XRD scans for the (LuFeO3)m/(LuFe2O4)n films for which either n or m is equal to 1. The composition is labelled (m-n) on the right. The asterisk (*) indicates the 111 XRD peak from the (111) YSZ substrate. b, Rocking-curve XRD scan of the 005 film peak of the (LuFeO3)1/(LuFe2O4)1 film (blue) compared with the 111 peak of the YSZ substrate (black). FWHM, full-width at half-maximum.

  6. Relation between the lutetium displacements and polarization.
    Extended Data Fig. 2: Relation between the lutetium displacements and polarization.

    The magnitude of the lutetium displacement d can be measured by HAADF-STEM. Using first-principles calculations, this displacement can be directly related to the polarization of the structure. Lutetium is shown in turquoise, iron in yellow and oxygen in brown.

  7. Magnetic characterization of the (LuFeO3)m/(LuFe2O4)n superlattices.
    Extended Data Fig. 3: Magnetic characterization of the (LuFeO3)m/(LuFe2O4)n superlattices.

    a, MT curves for a series of (LuFeO3)m/(LuFe2O4)1 superlattices cooled in a 1-kOe field. b, MT curves for a series of (LuFeO3)1/(LuFe2O4)n superlattices cooled in a 1-kOe field. c, The “excess magnetization” is found by subtracting the bulk magnetization of the LuFe2O4 and LuFeO3 from the measured moment. It is plotted normalized to the number of iron atoms in the LuFe2O4 layers in the sample. The composition is plotted according to the fraction of iron atoms in the LuFeO3 layers in the (LuFeO3)m(LuFe2O4)n structure. d, Loops of the magnetization M as a function of the magnetic field H for the (LuFeO3)9/(LuFe2O4)1 superlattice. The MH loop at 300 K has a distinctly different shape that is more reminiscent of the 250-K loop, demonstrating that ferromagnetic (or ferrimagnetic) fluctuations still exist at 300 K even if the entire film is not ferromagnetic (or ferrimagnetic). e, The saturation magnetization of the (LuFeO3)9/(LuFe2O4)1 superlattice at 70 KOe as a function of temperature. Although the remanent magnetization, as measured by the field-cooled curve, disappears around the Curie temperature of 281 K, ferromagnetic (or ferrimagnetic) fluctuations remain in this sample to temperatures above room temperature.

  8. Neutron diffraction of the (LuFeO3)6/(LuFe2O4)2 superlattice.
    Extended Data Fig. 4: Neutron diffraction of the (LuFeO3)6/(LuFe2O4)2 superlattice.

    a, Magnetic reflections for the (LuFeO3)6/(LuFe2O4)2 superlattice were observed in neutron diffraction by scanning along the [10L] direction in reciprocal space at several temperatures between 5 K and 325 K. A single peak is observed showing considerable change in intensity between 5 K and room temperature. The offset from the 101 position is due to a slight misalignment of the sample. r.l.u. in a denotes reciprocal lattice units. b, Integrated intensity of the 101 magnetic reflection for the (LuFeO3)6/(LuFe2O4)2 superlattice as a function of temperature. The solid line is the mean-field fit. Error bars in a and b represent one standard deviation.

  9. HAADF-STEM images of the (LuFeO3)m/(LuFe2O4)1 superlattices.
    Extended Data Fig. 5: HAADF-STEM images of the (LuFeO3)m/(LuFe2O4)1 superlattices.

    ad, Coloured overlays represent the local polarization for m= 1 (a), m= 3 (b), m= 7 (c) and m= 9 (d). Turquoise atoms have positive polarization and red atoms have negative polarization, as indicated by the colour bars. For each row of lutetium atoms, the mean lutetium displacement is plotted, with the bar representing the 20%–80% spread of the root-mean-square displacement. The colour of the bar indicates the direction of polarization.

  10. Quantification of the ferroelectric displacements from HAADF-STEM images.
    Extended Data Fig. 6: Quantification of the ferroelectric displacements from HAADF-STEM images.

    After identifying the position of the lutetium atom with sub-ångström precision, it is compared to the neighbouring atoms and the displacement is calculated. a, Schematics of the ‘down’, ‘up’ and non-polar polarization states. b, Average displacement of the lutetium atoms as a function of the number of LuFeO3 layers m in the (LuFeO3)m/(LuFe2O4)1 structure. The displacement of the end-member LuFeO3 is shown for reference; this displacement of 29 pm corresponds to approximately 4.3 μC cm−2. Error bars in a and b are s.e.m. c, A comparison of the distortion observed in the middle of the LuFeO3 block to those in the edge layers, for example, those adjacent to the LuFe2O4 bilayers. d, In situ TEM heating experiment of the (LuFeO3)m/(LuFe2O4)n superlattices. We infer the ferroelectric phase from where distortions in the lutetium rows are resolved. With increasing temperature, ferroelectricity disappears starting with lower m. Above T= 675 K, we see no ferroelectric distortions; however, the electrical noise in the images at these temperatures is quite large.

  11. X-ray linear dichroic spectroscopy of the Fe L2,3 edge.
    Extended Data Fig. 7: X-ray linear dichroic spectroscopy of the Fe L2,3 edge.

    a, b, The X-ray adsorption spectra for in-plane (blue) and out-of-plane (red) linearly polarized radiation are plotted in the top panels for the (LuFeO3)9/(LuFe2O4)1 (a) and (LuFeO3)1/(LuFe2O4)3 (b) superlattices at 300 K. The difference between the normalized spectra (black, bottom panels) is also plotted for each case. For the (LuFeO3)9/(LuFe2O4)1 sample, the peak dichroism is about 40% whereas the peak dichroism is only about 20% for the (LuFeO3)1/(LuFe2O4)3 superlattice.

  12. Exchange interactions in the COII structure of LuFe2O4.
    Extended Data Fig. 8: Exchange interactions in the COII structure of LuFe2O4.

    a, Schematic of the COII LuFe2O4 structure with intra-layer, inter-layer and in-plane interactions labelled. The Fe–O–Fe bond angles in the undistorted structure are indicated by the black arrows. The red arrows demonstrate the change to the bond angles as the distortions turn on. Lutetium, Fe3+, Fe2+ and oxygen are shown in turquoise, yellow, green and brown, respectively. b, Calculated exchange interactions as a function of the lutetium distortion Q. Circles, squares and diamonds denote the DFT-estimated value of the exchange interactions between two Fe2+ spins, two Fe3+ spins and Fe2+–Fe3+ spins, respectively. We considered in-plane interactions, intra-bilayer interactions and the interaction between two FeO2 bilayers.

  13. Spin configurations of the COI and COII structures of LuFe2O4.
    Extended Data Fig. 9: Spin configurations of the COI and COII structures of LuFe2O4.

    a, Left, calculated density of states (DOS) for LuFe2O4 with the COI magnetic ground state, along with the occupancy of the iron 3d channel. Upper and lower panels show the DOS for the Fe2+ and Fe3+ ions, respectively. Oxygen 2p states are plotted in each case. Right, the crystal field splitting from the trigonal bipyramid symmetry and occupancy of the iron 3d channel. b, Low-energy spin configurations of COI and COII states labelled with the corresponding magnetization. Although the ground states of COI and COII have magnetizations of 0.5μB/Fe and 1.17μB/Fe, respectively, each has additional low-energy configurations with M ranging from 0μB/Fe to 1.17μB/Fe. Lutetium, Fe3+, Fe2+ and oxygen are shown in turquoise, yellow (spins in red), green (spins in blue) and brown, respectively. c, Low-energy spin configurations of hole-doped COI and COII states labelled with the corresponding magnetization.

  14. Calculated stable structures for LuFe2O4 and the (LuFeO3)3/(LuFe2O4)1 superlattice.
    Extended Data Fig. 10: Calculated stable structures for LuFe2O4 and the (LuFeO3)3/(LuFe2O4)1 superlattice.

    Monoclinic structures of the LuFe2O4 system containing charge-ordered Fe2+/Fe3+. a, The antiferroelectric charge-ordered state (COI); b, the ferroelectric charge-ordered state (COII); and c, the non-polar charge-ordered state (COIII). Panels a and b are shown in Fig. 3a and b, respectively. df, Single-domain (d) and undoped-type (e) and doped-type structures of the (LuFeO3)3/(LuFe2O4)1 structure. Electrons transfer from the LuFe2O4 layers to the LuFeO3 layers in the doped-type configuration (orange arrows). The doped-type configuration also stabilizes charged ferroelectric domain walls. The density of states for the Fe3+ and Fe2+ ions are plotted in f in yellow and green, respectively. Lutetium, Fe3+, Fe2+ and oxygen are shown in turquoise or red (depending on the ferroelectric polarization), yellow, green and brown, respectively.

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Author information

  1. These authors contributed equally to this work.

    • Julia A. Mundy,
    • Charles M. Brooks &
    • Megan E. Holtz

Affiliations

  1. School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, USA

    • Julia A. Mundy,
    • Megan E. Holtz,
    • Hena Das,
    • Alejandro F. Rébola,
    • Robert Hovden,
    • Elliot Padgett,
    • Qingyun Mao,
    • Lena F. Kourkoutis,
    • Craig J. Fennie &
    • David A. Muller
  2. Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, USA

    • Charles M. Brooks,
    • John T. Heron,
    • Rainer Held,
    • Hanjong Paik &
    • Darrell G. Schlom
  3. Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

    • Jarrett A. Moyer &
    • Peter Schiffer
  4. Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48103, USA

    • John T. Heron
  5. Department of Materials Science and Engineering, University of California, Berkeley, California 94720, USA

    • James D. Clarkson,
    • Zhiqi Liu &
    • Ramamoorthy Ramesh
  6. NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    • Steven M. Disseler,
    • Julie A. Borchers &
    • William D. Ratcliff
  7. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    • Alan Farhan,
    • Elke Arenholz &
    • Andreas Scholl
  8. Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

    • Rajiv Misra
  9. Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA

    • Lena F. Kourkoutis,
    • David A. Muller &
    • Darrell G. Schlom
  10. Department of Physics, University of California, Berkeley, California 94720, USA

    • Ramamoorthy Ramesh
  11. Materials Sciences Division, Lawrence Berkeley National Laboratory, California 94720, USA

    • Ramamoorthy Ramesh

Contributions

The thin films were synthesized by C.M.B. and J.A.Mu. with assistance from R.He. and H.P. DFT calculations were performed by H.D., A.F.R. and C.J.F. The films were characterized by SQUID by J.A.Mo., R.M. and P.S.; by STEM by M.E.H., J.A.Mu., R.Ho., E.P., L.F.K. and D.A.M.; by variable-temperature STEM by Q.M., M.E.H. and D.A.M.; by neutron scattering by S.M.D., J.A.B. and W.D.R.; by transport by J.T.H.; by PFM by J.D.C., J.T.H. and R.R.; by X-ray spectroscopy by J.A.Mu., Z.L. and E.A.; by PEEM by A.F., Z.L., J.D.C., R.R. and A.S. J.A.Mu., C.J.F. and D.G.S. wrote the manuscript. The study was conceived and guided by D.G.S. All authors discussed results and commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Reviewer Information Nature thanks M. Fiebig, T. Kimura and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author details

Extended data figures and tables

Extended Data Figures

  1. Extended Data Figure 1: X-ray diffraction characterization of the (LuFeO3)m/(LuFe2O4)n superlattices. (358 KB)

    a, θ–2θ XRD scans for the (LuFeO3)m/(LuFe2O4)n films for which either n or m is equal to 1. The composition is labelled (m-n) on the right. The asterisk (*) indicates the 111 XRD peak from the (111) YSZ substrate. b, Rocking-curve XRD scan of the 005 film peak of the (LuFeO3)1/(LuFe2O4)1 film (blue) compared with the 111 peak of the YSZ substrate (black). FWHM, full-width at half-maximum.

  2. Extended Data Figure 2: Relation between the lutetium displacements and polarization. (122 KB)

    The magnitude of the lutetium displacement d can be measured by HAADF-STEM. Using first-principles calculations, this displacement can be directly related to the polarization of the structure. Lutetium is shown in turquoise, iron in yellow and oxygen in brown.

  3. Extended Data Figure 3: Magnetic characterization of the (LuFeO3)m/(LuFe2O4)n superlattices. (355 KB)

    a, MT curves for a series of (LuFeO3)m/(LuFe2O4)1 superlattices cooled in a 1-kOe field. b, MT curves for a series of (LuFeO3)1/(LuFe2O4)n superlattices cooled in a 1-kOe field. c, The “excess magnetization” is found by subtracting the bulk magnetization of the LuFe2O4 and LuFeO3 from the measured moment. It is plotted normalized to the number of iron atoms in the LuFe2O4 layers in the sample. The composition is plotted according to the fraction of iron atoms in the LuFeO3 layers in the (LuFeO3)m(LuFe2O4)n structure. d, Loops of the magnetization M as a function of the magnetic field H for the (LuFeO3)9/(LuFe2O4)1 superlattice. The MH loop at 300 K has a distinctly different shape that is more reminiscent of the 250-K loop, demonstrating that ferromagnetic (or ferrimagnetic) fluctuations still exist at 300 K even if the entire film is not ferromagnetic (or ferrimagnetic). e, The saturation magnetization of the (LuFeO3)9/(LuFe2O4)1 superlattice at 70 KOe as a function of temperature. Although the remanent magnetization, as measured by the field-cooled curve, disappears around the Curie temperature of 281 K, ferromagnetic (or ferrimagnetic) fluctuations remain in this sample to temperatures above room temperature.

  4. Extended Data Figure 4: Neutron diffraction of the (LuFeO3)6/(LuFe2O4)2 superlattice. (174 KB)

    a, Magnetic reflections for the (LuFeO3)6/(LuFe2O4)2 superlattice were observed in neutron diffraction by scanning along the [10L] direction in reciprocal space at several temperatures between 5 K and 325 K. A single peak is observed showing considerable change in intensity between 5 K and room temperature. The offset from the 101 position is due to a slight misalignment of the sample. r.l.u. in a denotes reciprocal lattice units. b, Integrated intensity of the 101 magnetic reflection for the (LuFeO3)6/(LuFe2O4)2 superlattice as a function of temperature. The solid line is the mean-field fit. Error bars in a and b represent one standard deviation.

  5. Extended Data Figure 5: HAADF-STEM images of the (LuFeO3)m/(LuFe2O4)1 superlattices. (482 KB)

    ad, Coloured overlays represent the local polarization for m= 1 (a), m= 3 (b), m= 7 (c) and m= 9 (d). Turquoise atoms have positive polarization and red atoms have negative polarization, as indicated by the colour bars. For each row of lutetium atoms, the mean lutetium displacement is plotted, with the bar representing the 20%–80% spread of the root-mean-square displacement. The colour of the bar indicates the direction of polarization.

  6. Extended Data Figure 6: Quantification of the ferroelectric displacements from HAADF-STEM images. (293 KB)

    After identifying the position of the lutetium atom with sub-ångström precision, it is compared to the neighbouring atoms and the displacement is calculated. a, Schematics of the ‘down’, ‘up’ and non-polar polarization states. b, Average displacement of the lutetium atoms as a function of the number of LuFeO3 layers m in the (LuFeO3)m/(LuFe2O4)1 structure. The displacement of the end-member LuFeO3 is shown for reference; this displacement of 29 pm corresponds to approximately 4.3 μC cm−2. Error bars in a and b are s.e.m. c, A comparison of the distortion observed in the middle of the LuFeO3 block to those in the edge layers, for example, those adjacent to the LuFe2O4 bilayers. d, In situ TEM heating experiment of the (LuFeO3)m/(LuFe2O4)n superlattices. We infer the ferroelectric phase from where distortions in the lutetium rows are resolved. With increasing temperature, ferroelectricity disappears starting with lower m. Above T= 675 K, we see no ferroelectric distortions; however, the electrical noise in the images at these temperatures is quite large.

  7. Extended Data Figure 7: X-ray linear dichroic spectroscopy of the Fe L2,3 edge. (168 KB)

    a, b, The X-ray adsorption spectra for in-plane (blue) and out-of-plane (red) linearly polarized radiation are plotted in the top panels for the (LuFeO3)9/(LuFe2O4)1 (a) and (LuFeO3)1/(LuFe2O4)3 (b) superlattices at 300 K. The difference between the normalized spectra (black, bottom panels) is also plotted for each case. For the (LuFeO3)9/(LuFe2O4)1 sample, the peak dichroism is about 40% whereas the peak dichroism is only about 20% for the (LuFeO3)1/(LuFe2O4)3 superlattice.

  8. Extended Data Figure 8: Exchange interactions in the COII structure of LuFe2O4. (244 KB)

    a, Schematic of the COII LuFe2O4 structure with intra-layer, inter-layer and in-plane interactions labelled. The Fe–O–Fe bond angles in the undistorted structure are indicated by the black arrows. The red arrows demonstrate the change to the bond angles as the distortions turn on. Lutetium, Fe3+, Fe2+ and oxygen are shown in turquoise, yellow, green and brown, respectively. b, Calculated exchange interactions as a function of the lutetium distortion Q. Circles, squares and diamonds denote the DFT-estimated value of the exchange interactions between two Fe2+ spins, two Fe3+ spins and Fe2+–Fe3+ spins, respectively. We considered in-plane interactions, intra-bilayer interactions and the interaction between two FeO2 bilayers.

  9. Extended Data Figure 9: Spin configurations of the COI and COII structures of LuFe2O4. (700 KB)

    a, Left, calculated density of states (DOS) for LuFe2O4 with the COI magnetic ground state, along with the occupancy of the iron 3d channel. Upper and lower panels show the DOS for the Fe2+ and Fe3+ ions, respectively. Oxygen 2p states are plotted in each case. Right, the crystal field splitting from the trigonal bipyramid symmetry and occupancy of the iron 3d channel. b, Low-energy spin configurations of COI and COII states labelled with the corresponding magnetization. Although the ground states of COI and COII have magnetizations of 0.5μB/Fe and 1.17μB/Fe, respectively, each has additional low-energy configurations with M ranging from 0μB/Fe to 1.17μB/Fe. Lutetium, Fe3+, Fe2+ and oxygen are shown in turquoise, yellow (spins in red), green (spins in blue) and brown, respectively. c, Low-energy spin configurations of hole-doped COI and COII states labelled with the corresponding magnetization.

  10. Extended Data Figure 10: Calculated stable structures for LuFe2O4 and the (LuFeO3)3/(LuFe2O4)1 superlattice. (691 KB)

    Monoclinic structures of the LuFe2O4 system containing charge-ordered Fe2+/Fe3+. a, The antiferroelectric charge-ordered state (COI); b, the ferroelectric charge-ordered state (COII); and c, the non-polar charge-ordered state (COIII). Panels a and b are shown in Fig. 3a and b, respectively. df, Single-domain (d) and undoped-type (e) and doped-type structures of the (LuFeO3)3/(LuFe2O4)1 structure. Electrons transfer from the LuFe2O4 layers to the LuFeO3 layers in the doped-type configuration (orange arrows). The doped-type configuration also stabilizes charged ferroelectric domain walls. The density of states for the Fe3+ and Fe2+ ions are plotted in f in yellow and green, respectively. Lutetium, Fe3+, Fe2+ and oxygen are shown in turquoise or red (depending on the ferroelectric polarization), yellow, green and brown, respectively.

Additional data