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Antiferromagnetic metal phase in an electron-doped rare-earth nickelate

Long viewed as passive elements, antiferromagnetic materials have emerged as promising candidates for spintronic devices due to their insensitivity to external fields and potential for high-speed switching. Recent work exploiting spin and orbital effects has identified ways to electrically control and probe the spins in metallic antiferromagnets, especially in noncollinear or noncentrosymmetric spin structures. The rare earth nickelate NdNiO3 is known to be a noncollinear antiferromagnet where the onset of antiferromagnetic ordering is concomitant with a transition to an insulating state. Here, we find that for low electron doping, the magnetic order on the nickel site is preserved while electronically a new metallic phase is induced. We show that this metallic phase has a Fermi surface that is mostly gapped by an electronic reconstruction driven by the bond disproportionation. Furthermore, we demonstrate the ability to write to and read from the spin structure via a large zero-field planar Hall effect. Our results expand the already rich phase diagram of the rare-earth nickelates and may enable spintronics applications in this family of correlated oxides.

Long viewed as passive elements, antiferromagnetic materials have emerged as promising candidates for spintronic devices due to their insensitivity to external fields and potential for high-speed switching. Recent work exploiting spin and orbital effects has identified ways to electrically control and probe the spins in metallic antiferromagnets, especially in noncollinear or noncentrosymmetric spin structures. The rare earth nickelate NdNiO 3 is known to be a noncollinear antiferromagnet where the onset of antiferromagnetic ordering is concomitant with a transition to an insulating state. Here, we find that for low electron doping, the magnetic order on the nickel site is preserved while electronically a new metallic phase is induced. We show that this metallic phase has a Fermi surface that is mostly gapped by an electronic reconstruction driven by the bond disproportionation. Furthermore, we demonstrate the ability to write to and read from the spin structure via a large zero-field planar Hall effect. Our results expand the already rich phase diagram of the rare-earth nickelates and may enable spintronics applications in this family of correlated oxides.
In recent years, antiferromagnetic materials have become leading contenders for spintronic devices. In comparison with their ferromagnetic counterparts, more subtle methods to control the ordered spins (writing) and to probe such control (reading) are required 1 . The most widely used method in antiferromagnets is the same as that in ferromagnets -measuring a component of the anisotropic magnetoresistance (AMR) signal 2,3 . This signal strength is typically limited to just a couple percent of the sample's resistance, however, which limits high-density applications 4 . This has driven parallel attempts to discover additional read-out methods as well as to identify metallic antiferromagnets with larger AMR signals 5,6 .
Here we develop a metallic antiferromagnet and demonstrate nearly an order of magnitude stronger AMR signal over conventional antiferromagnets. We begin with the rare-earth nickelates (RNiO 3 ), transition metal oxides which sit at the boundary between localized and itinerant electron behaviors. With the exception of LaNiO 3 , an unconventional metal 7 with the largest rare-earth cation R, the RNiO 3 compounds undergo a metal-insulator transition (MIT) and a transition from a paramagnetic to a noncollinear antiferromagnetic state [8][9][10] .
In PrNiO 3 and NdNiO 3 bulk crystals, the onsets of the antiferromagnetic and insulating states are coincident (T M IT = T N ) [10][11][12][13] . In addition, at the MIT a breathing-mode distortion occurs where half of NiO 6 octahedra are expanded and half are compressed in an alternating pattern: a charge order sets in without any 3d 6 /3d 8 charge fluctuation on the nickel sites, known as "bond disproportionation" [14][15][16][17] (shown schematically in Fig. 1a).
While the rare earth nickelates thus display coupled spin, charge and lattice degrees of freedom, as well as robust metallic and antiferromagnetic states, to date an antiferromagnetic metal phase has not yet been identified 18 . We choose NdNiO 3 , which displays a direct transition from a paramagnetic metal to a noncollinear antiferromagnetic insulator at the highest temperature within the RNiO 3 series [19][20][21] . Previous studies have found that strong compressive strain [22][23][24]  Here, we employ electron doping of epitaxial NdNiO 3 thin films through substitution of Ce 4+ on the Nd 3+ lattice site. We find that cerium substitution rapidly induces a metal-metal transition (MMT) where the low-temperature metallic phase retains the antiferromagnetism on the nickel sites of the parent NdNiO 3 . In contrast to the metallic phase above MMT and MIT, the Fermi surface below the MMT is largely gapped with spectral weight confined to discrete high-intensity spots. Moreover, in this low-temperature phase we demonstrate heat-assisted magnetic recording with a maximum measured amplitude of 18%, bringing a family of materials into the spintronics community and suggesting a pathway to stronger AMR readout signals in antiferromagnets.
Epitaxial films of Ce x Nd 1−x NiO 3 were synthesized by reactive oxide molecular-beam epitaxy (MBE) on (100) pc NdGaO 3 ((110) in orthorhombic notation for the Pnma space group), which provides 1% tensile strain (see Methods). All crystallographic directions referenced throughout this work follow the pseudocubic (pc) notation. Fig. 1b shows the high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image of the Ce 0.03 Nd 0.97 NiO 3 compound. Additional HAADF-STEM and electron energy loss spectroscopy (EELS) maps found in the supplement support the high structural quality and absence of cerium phase segregation or local lattice deformations in these samples (Supplementary Fig. S1, Fig. S5). X-ray absorption spectroscopy data on the Ce-M 4,5 , Nd-M 4,5 and O-K pre-peak edges confirm the prototypical Ce 4+ and Nd 3+ valence states, and indicate electron doping onto the nickel sites ( Supplementary Fig. S6).
As seen in Fig. 1c, cerium substitution results in qualitative changes in the transport properties of the films. The parent compound NdNiO 3 shows a MIT at ∼200 K with a resistivity increase of about five orders of magnitude 30 . For intermediate cerium doping (0.01 ≤ x < 0.06) the resistivity increases when cooling through the MMT but recovers a dρ/dT > 0 behavior, indicative of a metallic phase and a MMT as opposed to the MIT of the parent compound. These samples also demonstrate slight resistive upturns at sufficiently low temperature (below about 10 K), but we believe this to be due to weak localization effects, as suggested by the negative magnetoresistance shown in Supplementary Fig. S21. For higher doping (x > 0.06), the transition is fully suppressed and the films remain metallic at all temperatures. We note the emergence of this MMT transition and fully metallic samples was not observed in previous cerium-doped NdNiO  For the fully metallic Ce 0.1 Nd 0.9 NiO 3 , the band structure instead does not show any temperature variation or any noticeable difference with respect to the metallic phase of NdNiO 3 ( Supplementary Fig. S11). The existence of a unique low temperature Fermi surface in the Ce-doped samples hosting a metal-metal transition helps to dismiss concerns of phase coexistence as has been seen in prior nickelate research 30,35 .
In  To probe the antiferromagnetic order in this low-temperature metallic phase, we use neutron diffraction and site-specific resonant x-ray scattering (RXS). Neutron diffraction ( Supplementary Fig. S15) shows that the parent NdNiO 3 is antiferromagnetically ordered as reported in the literature 8,37 . Figure  From our data in Fig. 2b,c, we argue that in this low-temperature metallic phase the Peierls component of the MIT has taken place, but the additional electrons provided by the Ce 4+ atoms likely screen correlations just enough that the electron and hole bands are not pushed apart. In this respect, note also that no sizeable bandwidth reduction can be seen in Fig Figure S19). Figure 4b shows the spin structure of the parent compound NdNiO 3 schematically (as found in previous works 21,38 ) below the corresponding measurement angles in Fig. 4a The amplitude of the ZF-PHE for a given cooling field B F C is defined as the overall difference between the peak (at 45 o in Fig. 4a) and the trough (in Fig. 4a at 135 o ). We find a maximum amplitude of about 18%, which is roughly three times stronger than typically reported ZF-PHE magnitudes in antiferromagnets 4 and, to the best of our knowledge, about equal to the maximum ever reported 46 (see Supplementary Fig. S19). The dependence on Fig. 4c, roughly follows a simple quadratic up to our maximum used cooling field of 14 T, implying that with stronger fields even larger amplitudes are attainable. The temperature dependence, Fig. 4d, shows a gradual weakening of the effect as the system approaches its transition and a sudden suppression above the MMT (consistent with the Néel transition).

Competing Interests
The authors declare no competing interests.   (Fig. S3) substrates. The comparison of phase diagram of the films grown on NdGaO 3 and LaAlO 3 is shown in Fig. S4. Reciprocal space maps (RSMs) were generated by aligning to the signal peak after performing L-rod scans, and capturing fixed geometry CCD images for bins around the peak location.

Resonant x-ray scattering
Note that the deviation of the peak maximum from the expected L = 0.25 is small enough to be due to an alignment offset, and is not directly indicative of any incommensurate order. Reciprocal space maps were measured at a series of temperatures upon warming and cooling each sample and regions of interest were defined around the observed order peaks.
To extract integrated intensities, constant size regions of interest were defined around the peak in the RSMs and the total intensity contained was summed. Background intensities (used for background subtraction) were collected in the diffuse regions around the ordering peaks. Small Q x and Q y offsets were added relative to the location of the ( 1 4 , 1 4 , 1 4 ) peak to define a region of background intensity.

X-ray absorption spectroscopy
We use Beamlines 6.3.1 and 4.0.2 at the Advanced Light Source at Lawrence Berkeley National Laboratory to perform x-ray absorption spectroscopy (XAS). Measurements were conducted in the total electron yield geometry. Each spectra shown is the average of 4-16 individual scans. The Nd-M 4,5 and Ce-M 4,5 spectra were normalized to the pre-edge intensity. The O-K edge spectra were normalized to the integrated peak intensity.

Transport measurements
Cr(10 nm)/Au(100 nm) electrical contacts were deposited in the pattern shown by the cartoon of Fig. 4a with an electron-beam evaporator. Channels were etched in with a diamond scribe. A typical device was roughly 3mm x 5mm. Transport measurements were performed in a Quantum Design Dynacool Physical Property Measurement System (PPMS) for fields up to 9 T. In plane rotations were performed using the Quantum Design horizontal rotator option. Measurements performed at 12 T and 14 T were conducted in a 14 T Quantum Design PPMS. Hall coefficients were calculated from linear fits of antisymmetrized field sweeps measured from ± 9 T; a representative example is shown in Supplemental Figure S22. In Fig. 4e/f, a vertical offset due to contact misalignment was removed.

Angle-resolved photoemission
The ARPES data was measured at the beamline MAESTRO of the Advanced Light Source using a Scienta 4000 electron analyzer. The angular resolution is better than 0.1 • and the energy resolution varied between 10 meV and 25 meV depending on the setting chosen. The light polarization was set to p. In this configuration when the sample is facing the analyzer slit with the a axis in the horizontal (x) direction the electric field is even in the xz mirror plane plane containing the surface normal and therefore the measurement is sensitive to the d x 2 −y 2 and d z 2 orbitals along k x , which are both even in the same plane. Prior to the ARPES experiments, the films were annealed in a a partial oxygen pressure of 1 × 10 −5 with ∼10% ozone at a temperature of 420°C for approximately one hour.

Neutron Scattering Measurements
Elastic neutron scattering data were collected at the SPINS cold triple-axis spectrometer at the NIST Center for Neutron Research (NCNR) and at the CORELLI elastic diffuse scattering spectrometer 50 at the Oak Ridge National Laboratory Spallation Neutron Source (SNS). The SPINS measurements were taken at a fixed neutron energy of 5 meV with a collimation and filter setup of 80'-Be-80'-Be using a standard closed cycle refrigerator for sample temperature control.
CORELLI is a quasi-Laue time-of-flight instrument with an incident neutron wavelength band between 0.65 and 2.9Å. The two-dimensional detector array of CORELLI spans from -19 • to 147 • in the horizontal plane and from -27 • to 29 • vertically. Therefore, a large threedimensional volumetric reciprocal space is surveyed for a single sample orientation. The sample was mounted to an Al pin at the bottom of a close cycle refrigerator, which provided a base temperature of 3 K at NCNR and 6 K at CORELLI. The sample was mounted with the (h k 0) o plane horizontal, and the vertical rotation axis was along the (0 0 l) o axis.
The experiments were conducted by first rotating the film through 120 • in 1 • step to survey features in the large reciprocal space, and then data were collected for an extended time with particular sample orientations optimized for the selected reciprocal regions.

Scanning Transmission Electron Microscopy
High-angle annular dark-field STEM measurements were performed either on a JEOL ARM 200F (on the Ce 4% sample) or a Thermo-Fisher Scientific Titan Themis Z G3 (on the Ce 12% sample) both operating at 200 kV. The convergence angle was either 19.6 or 22 mrad and the collection angle range was 68 mrad-280 mrad. Fast-acquisition frames were collected, aligned and summed to minimize drift and obtain high signal-to-noise-ratio. The interfacial strain maps were extracted using the method described in the reference 51 .

Electron Energy Loss Spectroscopy
Electron energy loss spectroscopy (EELS) were performed on the Thermo-Fisher Scientific Titan Themis Z G3 equipped with a Gatan Continuum spectrometer and imaging filter. The microscope was operated at 200 kV and 100 pA current. Dual (zero-loss and core-loss) EELS spectrum images were acquired simultaneously to correct for energy drift. After determining a region of interest in a zone axis, the electron beam was blocked for 15 minutes to stabilize and minimize the stage drift. The total spectrum image time was maintained between 30 to 100 seconds to minimize stage drifting. EELS maps were acquired with a 6Å pixel-size sampling, a 30 ms pixel dwell time and 0.75 eV/channel electron dispersion.
To extract the elemental composition maps, EELS spectra were background subtracted up to the relevant elemental edge and then integrated. The background was modelled as a linear combination of power laws and the background window was selected to be as wide as possible to obtain good fits. The energy windows were as follows: Ni-L 2,3 edge (851-878 eV), Ce-M 4,5 edge (881-913 eV), Nd-M 4,5 edge (975-1010 eV).

Computational Methods
Density functional theory (DFT)-based calculations were performed using the all-electron, full potential code wien2k based on the augmented plane wave plus local orbital (APW+lo) basis set 52 . For the exchange-correlation functional, we have used the Perdew-Burke-Ernzerhof (PBE) implementation of the generalized gradient approximation (GGA) 53 . In the spin-polarized calculations, in order to treat the correlated Ni−d states, we added static mean-field correlations as implemented in the DFT+U framework 54 with an on-site Coulomb U repulsion ranging from 2 to 5 eV and a non-zero Hund's coupling J = 0.7 eV to account for the anisotropies of the interaction 55 . The results we present are consistent for this range of U values.
Phonon calculations were performed using Vienna Ab-initio Software Package (VASP) 57,58 which implements projector augmented waves formalism of DFT with an interface to Phonopy 56 for plotting the phonon dispersion. The same DFT+U framework as above was added to the GGA/PBE functionals. We employed an electronic energy tolerance of 10 −8 eV and a force tolerance of 10 −3 eV/Å for structural relaxations, with a Gaussian smearing of 0.005 eV, and an electronic momentum k-point mesh of 2 × 2 × 2 for a 4 × 4 × 4 supercell structure. We obtain similar phonon instabilities with an electronic momentum k-point mesh of 5 × 5 × 5 for a 2 × 2 × 2 supercell structure.

Data Availability
The data presented in the figures and other findings of this study are available from the