INTRODUCTION

Complex oxide materials exhibit a wide range of correlated electron behavior representing the delicate balance of charge, spin, orbital, and lattice degrees of freedom. External parameters such as electric field, magnetic field, or strain can tune the material to exhibit correlated phenomena, including ferromagnetism1,2,3,4 and superconductivity5,6. In a few complex oxide materials, the ferromagnetic order has been stabilized in thin film form, although the bulk phase has no long-range magnetic order. LaCoO3 thin films exhibit ferromagnetism (Tc = 70 K)1,7,8,9, while bulk phases are diamagnetic at low temperatures and paramagnetic at higher temperatures. Similar stabilization of a ferromagnetic ground state is found in PrCoO32,10. Despite various experimental studies, the origin of this emergent ferromagnetism is still not well understood.

LaNiO3 (LNO), a paramagnetic metal at all temperatures in the bulk, has elicited attention because theory predicts interesting topological phases in (111)-oriented LNO grown on LaAlO3 (LAO)11,12,13,14. Unlike LNO, other rare-earth nickelates of the form RENiO3 (RE = rare earth) have temperature-dependent metal–insulator and magnetic transitions. While a suppression of metallicity has been achieved in (001)-oriented LNO films with thicknesses of t = 2 − 4 unit cells (u.c.)15,16,17,18,19,20,21,22, no magnetic order has ever been observed. Recently, there has been a report of ferromagnetism in a 10-u.c.-thick (111)-oriented LNO film23, but the underlying mechanisms of this ferromagnetism were not clear. Understanding the origin of the emergent long-range magnetic order in LNO(111) films would enable us to design and tune such correlated behavior and explore interactions in possible topological phases.

Here, we report the emergence of long-range magnetic order in LNO films grown on LAO(111) in a wide range of thicknesses (t = 8 − 26 u.c.), in both insulating and metallic samples. The anomalous Hall effect and hysteretic magnetoresistance (MR) indicate long-range magnetic order only present in the (111) direction. The (111) interface limits the strain relaxation required by the lattice mismatch between substrate and film, causing a distortion of the NiO6 octahedra. An expansion near the substrate–film interface is observed via x-ray diffraction measurements and dynamical x-ray diffraction simulations. X-ray absorption spectroscopy reveals an increased concentration of Ni2+ ions in ultrathin films, replacing Ni3+ ions observed in thicker films and bulk LNO. Together, the structural changes at the LNO/LAO(111) interface and the increased concentration of Ni2+ ions in ultrathin LNO films likely facilitate ferromagnetic superexchange interactions among Ni2+ and Ni3+ ions. The emergent magnetic order in ultrathin LNO(111) films, therefore, relies both on the growth constraints imposed by lattice mismatch in the (111) interface geometry and on the presence of Ni2+ ions.

RESULTS

Structural characterization

In order to determine the underlying mechanism responsible for the emergent magnetic ordering, we performed careful structural, chemical, and transport characterization. Structural characterization via laboratory and synchrotron x-ray diffraction measurements confirm the excellent crystalline quality and fully coherent growth of all films. Figure 1a shows symmetrical x-ray diffraction scans around LNO/LAO(222) Bragg peaks. The LNO(222) peak, on the left of the LAO(222) substrate peak, signifies the expected overall compressive in-plane strain. The thickness fringes extending around the LNO(222) Bragg peak indicate high crystalline quality of the films and the uneven fringe intensity distribution imply that there is a variable out-of-plane interatomic spacing along the film thickness24.

Fig. 1: Structural characterization of (111)-oriented LaNiO3.
figure 1

a Experimental x-ray diffraction profiles of ultrathin LaNiO3 (LNO) films around the (222) peak. b Representative x-ray diffraction fits of LNO films. The 8 and 26 u.c. films are modeled as three layers, with the largest distortion of the unit cell in the interfacial layer. c Results of the dynamical x-ray diffraction simulations, highlighting the distortions of the NiO6 octahedra, the thickness of the distorted layers, and the overall thickness of the films. Numerical values are listed in Supplemental Table 2. Schematic diagram of oxygen octahedra connectivity and LNO layer buildup along d [0 0 1] and e [1 1 1] direction. Right: two monolayers of LaNiO3. The light blue indicates Ni atoms in the first monolayer, and dark blue indicates Ni atoms in the second monolayer. Note La atoms are not pictured here. Strong coupling of oxygen bonds across the LNO/LAO(111) interface imposes restrictions on NiO6 octahedra in the first few LNO monolayers that are controlled by the underlying symmetry of the LAO lattice.

Full size image

To quantify the variation of the LNO interplanar spacing along the [1 1 1] direction, we have employed dynamical x-ray diffraction modeling of the X-ray powder diffraction profiles of LNO/LAO(111) thin films. X-ray diffraction calculations were carried out using the GID sl_program for simulating dynamical x-ray diffraction from strained crystals, multilayers, and superlattices, developed by Stepanov25. LNO(111) films can be fit by dynamical x-ray diffraction as three layers (see Fig. 1b): an interfacial layer with the largest out-of-plane d-spacing, followed by an intermediate layer with less expanded d111 spacing, and finally a bulk-like region where deformations of the NiO6 octahedra are diminished and the mismatch strain is accommodated by octahedral rotations. In order to accommodate coherent epitaxial strain, NiO6 octahedra are rotated differently than in bulk LNO in all three layers. Although the lattice parameter should change continuously and not form distinct layers, we were able to successfully fit the x-ray diffraction profiles using a three-layer model.

Our x-ray diffraction profiles show a dramatic change in the out-of-plane lattice parameter of the LNO films with depth. Bulk LNO has pseudocubic unit cell of aLNO = 3.86 Å and bulk LAO has a psuedocubic lattice parameter of aLAO = 3.79 Å giving an expected lattice mismatch of ~−1.8%. In this paper, we define one unit cell in a (111)-oriented film as the distance between two (111) planes, or as \({d}_{111}={a}_{001}/\sqrt{3}=2.23\) Å. Analysis of the (111)-oriented films show an interfacial layer with an average calculated thickness of 2 u.c. and a remarkable 16% expansion of the d111 interplanar distance as compared to the bulk-like thin film region. The next, intermediate layer has an average calculated thickness of 3 u.c. and a 3% d111 expansion. The topmost, most bulk-like layer has a pseudocubic out-of-plane lattice constant of about aLNO = 3.821 Å consistent across samples of all thicknesses. Representative x-ray diffraction simulations of the 8 and 26 u.c. samples are shown in Fig. 1b. Simulations that assume a lattice parameter change in the surface layer or a film of uniform lattice parameter did not fit as well to the experimental data. Fit parameters and plots for all samples are presented in Supplemental Table 1 and Supplemental Figure 1.

The large lattice distortion observed at the LNO/LAO interface is likely due to the nature of the interfacial bonding. Because the NiO6 octahedra are connected across the interface via three oxygen bonds, they are more constrained than those in (001)-oriented films (see Fig. 1d, e). The enhanced interfacial bonding at the (111) interface inhibits octahedral rotations that normally relieve the interfacial mismatch strain and instead favors a physical deformation of the octahedra, considerably expanding it along the [1 1 1] direction. In addition, there is much less octahedra connectivity within the single (111) plane (Fig. 1e); they are instead more directly affected by octahedra in the layer above and below them. By contrast, a synchrotron x-ray diffraction study of (001)-oriented LNO films by Fowlie et al. shows no enlargement of the out-of-plane lattice parameter for films 5 u.c. to 10 nm thick19, indicating effective strain accommodation by octahedral rotations. A dramatic change in film properties due to distortion of the unit cell fits well with the past work15,16,17,18,19,20,21,26,27. The structural model that we derive from dynamical x-ray diffraction simulations suggests that the LNO unit-cell symmetry is lowered at the interface due to octahedral deformations. It is known that the symmetry lowering at an interface can result in various emergent functionalities: piezoelectric28,29, pyroelectric30, and ferroelectric effects31,32. In fact, Doennig et al. predict the emergence of magnetic ordering in reduced symmetry LNO11.

Chemical valence characterization

Chemical valence characterization, performed using x-ray absorption spectroscopy (XAS), indicates that the valence of ultrathin (111) LNO films differs from bulk LNO. We see an increase in Ni2+ cations as films get thinner (see Fig. 2), as shown by an increase in the Ni L3 edge peak at ~852 eV and a splitting of the Ni L2 edge peak near 870 eV. The increasing intensity of the Ni2+ peak (852 eV) compared to the Ni3+ peak (854 eV) qualitatively shows that there is a higher concentration of Ni2+ near the substrate–film interface. Previous work by Anada et al. does not reveal any evidence of Ni2+ ions in LNO films grown on (001)-oriented LAO, although they observe a high concentration of Ni2+ ions in corresponding LNO films grown on (001)-oriented SrTiO333. The increased concentration of Ni2+ ions is likely due to either oxygen vacancies or oxygen ligand holes, which have been linked to insulating behavior in LNO films34. Although these two potential sources of Ni2+ ions are distinct, they are difficult to differentiate. Here, we do not have sufficient evidence to suggest which one dominates in ultrathin LNO films. In any case, XAS data show that the LNO/LAO(111) interface is populated with an increased concentration of Ni2+ ions.

Fig. 2: X-ray absorption spectroscopy results of (111)-oriented LaNiO3 films taken at ALS beamline 6.3.1.
figure 2

Note that the La peak located at 849 eV has been subtracted out using peak fitting software. Splitting of the Ni L2 peak indicates an increased concentration of Ni2+ ions in the LaNiO3 films.

Full size image

Electronic transport characterization

We also observe a change in the electronic properties in the thinnest samples: resistivity measurements of LNO(111) films reveal a thickness-dependent metal–insulator transition when the film thickness decreases <8 u.c. (t = 17.8 Å), see Fig. 3. The 6- and 8-u.c.-thick film resistivity can be modeled with thermally activated behavior at higher temperatures and 3D variable-range hopping at lower temperatures (see Fig. 3b, c). This indicates that the distorted LNO at the interface is insulating.

Fig. 3: Temperature-dependent electronic transport data for (111)-oriented LaNiO3.
figure 3

a Resistivity versus temperature for 6 u.c. to 13-nm-thick films. b Arrhenius thermal activation of carriers fit the high-temperature data for insulating samples. c 3D variable-range hopping fit to low-temperature data for insulating samples. The samples became too insulating to measure at 125 K for the 6 u.c. sample and at 25 K for the 8 u.c. sample.

Full size image

For the 6- and 8-u.c.-thick samples, the thermally activated behavior is described by an Arrhenius relation for carriers:

$$\sigma ={\sigma }_{0}\exp (-{{\Delta }}E/kT)$$
(1)

where σ0 is Drude conductivity, and ΔE is the thermal activation energy. See Supplemental Table 2 for the values obtained from the fit.

At lower temperatures, the 8 u.c. sample fits well to a variable-range hopping model where conduction occurs through inelastic hopping to states closer in energy35:

$$\sigma ={\sigma }_{0}\exp {(-{T}_{0}/T)}^{1/(d+1)}$$
(2)

where T0 is related to the density of states at the Fermi level and the spread of the wavefunction of the localized state, and d is the dimensionality of the system. Our sample fits best when d = 3, indicating that the transport behavior is not due to strong localization from a dimensional shift (d = 2) as has been observed in other (001)-oriented LNO films17,20,22,33. Because of instrument limitations, the 6 u.c. sample became too resistive to measure at 125 K. We propose that this insulating LNO is present in all our samples, but as the film thickens, the undistorted, bulk-like LNO dominates the transport. Additional details about these fits can be found in Supplemental Table 2.

In the 10, 13, and 26 u.c. samples, we observe an upturn in the resistivity at ~150, 70, and 25 K, respectively. Previous work on (001)-oriented LNO samples show a similar upturn in resistivity17,18. Moon et al. were able to fit the resistivity data from (001)-oriented LNO grown on various substrates to a model of weak localization described by a localization interaction model for a disordered metal in the 3D limit17, but our resistivity data lack the characteristic curvature and does not fit well to this model.

In addition to interfacial Ni2+ and structural distortions noted above, we observe magnetic ordering through the anomalous Hall effect and hysteretic MR in samples 8–26 u.c. thick (Fig. 4). The Hall effect signal can be described using the equation:

$${\rho }_{xy}={R}_{0}B+4\pi {R}_{S}M$$
(3)

where the first term representing the ordinary Hall effect is proportional to the external magnetic field (with R0 as the ordinary Hall coefficient) and the second term representing the anomalous Hall effect is proportional to the film magnetization (with RS as the anomalous Hall coefficient (AHC)). The AHC represents both intrinsic contributions from the Berry phase curvature and extrinsic skew-scattering or side-jump mechanisms36. We observe nonlinearity in Hall effect measurements, with hysteretic behavior in 8–26 u.c. <~30 K, suggesting the emergence of spontaneous magnetization. The consistent onset temperatures support the idea of a magnetic phase of the same origin in all films. Figure 4a shows the behavior of the 10 u.c. film from T = 2 to 50 K. After subtracting the linear ordinary Hall effect contribution, we are left with clear loops (see Fig. 4b). The increase in coercivity and saturation resistance with decreasing temperature follows the expected behavior for a ferromagnet. Because the measured signal decreases with increasing film thickness (see Fig. 4c), it is likely that this magnetic phase is isolated to the distorted, insulating layer present in all films at the interface. As films get thicker, more current passes through the conducting bulk-like portion of the film, thus diminishing the transport contribution from the interface.

Fig. 4: Field-dependent electronic transport measurements of (111)-oriented LaNiO3.
figure 4

a Hall effect results at various temperatures for 10-u.c.-thick LNO(111). Scans are shifted for visibility and arrows indicate the direction of scan, field cooled at H = 9 T, b anomalous Hall effect loops at various T = 12, 30 K, linear ordinary Hall effect has been subtracted, c anomalous Hall effect loops for t = 10, 26 u.c., linear ordinary Hall effect has been subtracted, d magnetoresistance at various temperatures of 10 u.c., (111)-oriented LaNiO3, field cooled at H = 9 T. Magnetoresistance (ΔRxx = (R(H) − R0)/R0) results are shifted for visibility and arrows indicate the direction of scan.

Full size image

In addition, we observe a change in the sign of the AHC (RS) in the 26-u.c.-thick LNO(111) film compared to thinner films. Studies of other systems that observe a thickness-dependent change in the AHC attribute the change in sign to either extrinsic skew-scattering and side-jump mechanisms37,38,39 or to intrinsic changes in the band structure and the k-space Berry curvature of the material40,41. Simulations predict topological features in LNO grown on (111)-oriented LAO11,12,13,14, so it is possible that the negative AHC results from an evolution of band structure with thickness in ultrathin LNO films. However, we are unable to determine the cause of this change in the AHC and leave that to future work.

Longitudinal MR measurements, taken with the field out of plane, show hysteresis at T = 30 K and a crossover from positive to negative MR as temperature decreases. A representative set of curves for a t = 10 u.c. sample is shown in Fig. 4d. At high temperatures, the MR has the expected parabolic form of ordinary MR. As the temperature decreases, we observe an increasingly negative contribution to the longitudinal MR, which we attribute to the emergence of ferromagnetism. Negative MR is reported for (001)-oriented LNO films on SrTiO320 and (LaAlO3)0.3 (Sr2AlTaO6)0.7 (LSAT)15 and is attributed to the suppression of weak localization by a magnetic field, but our resistivity data suggest that weak localization, associated with a simple, negative parabolic MR, alone does not explain the data.

Interestingly, below ~20–25 K the 10–26 u.c. samples show a suppression in resistivity after the external field switches sign (Fig. 4d). We would expect scattering from magnetic domain walls to be a source of spin-dependent scattering, thereby increasing resistivity. Notably, LNO(111) grown on LAO has been observed to be an improper ferroelectric31. Ferroelectric domain walls have exhibited increased conductivity42,43,44 that is attributed to carrier accumulation at domain walls to screen polarization discontinuities and to the local modification of band structure44. This suppression of MR after the applied field changes sign is consistent with the results published by Asaba et al.23 and with domain wall switching observed in antiferromagnetic Nd2Ir2O7 thin films45. Similar behavior has been attributed to edge-state transport via chiral conducting modes in the topological insulator SmBi646 and Bi2Te3 − ySey47. However, further evidence of the emergence of Dirac electrons is needed to justify such conclusions in ultrathin LNO(111) films.

DISCUSSION

We can describe the electronic and magnetic behavior of the 8–26 u.c. LNO samples in terms of a strained, magnetic, insulating layer close to the film/substrate interface and a paramagnetic conducting layer on top. The first few unit cells of highly distorted LNO(111) have a modified symmetry and altered bond lengths and angles (e.g., Ni–O–Ni). These structural changes at the interface result in modifications of the exchange interactions among Ni2+–Ni3+ ions, leading to a spontaneous magnetic moment. The Goodenough–Kanamori rules dictate that a low-spin Ni2+(3d8)–Ni3+(3d7) exchange can give ferromagnetic ordering for 180° superexchange48. Together, the negative MR and the large hysteresis in the anomalous Hall effect suggest long-range magnetic order in LNO(111) films, and could indicate either ferromagnetic or antiferromagnetic ordering. We were unable to detect a ferromagnetic signal in the films above the noise level of a superconducting quantum interference device magnetometer and x-ray magnetic circular dichroism (XMCD) measurement at ALS. The limitations due to background noise of these measurement techniques mean that the absence of magnetic signal does not preclude ferromagnetism in the samples. Because of this, Hall measurements are an ideal probe for our LNO(111) samples because the magnitude of the signal is inversely proportional to the thickness.

In summary, we have observed the emergence of long-range magnetic ordering at the film–substrate interface in ultrathin (111)-oriented LNO thin films up to 26 u.c. Synchrotron x-ray diffraction and dynamical x-ray diffraction simulations indicate substantial elongation of the unit cell in the [1 1 1] direction near the interface. An increased presence of Ni2+ ions at the interface, insulating behavior in films t ≤ 8 u.c., the anomalous Hall effect, and negative hysteretic MR indicate the presence of a distinct phase in LNO(111) in this region at the interface that hosts both insulating and magnetic behavior. This magnetic phase has a magnetic transition temperature of 30 K and likely comes from superexchange interactions among Ni2+ and Ni3+ ions. Such emergent magnetism provides a model system for the understanding of magnetic ordering in low dimensions and future spin-based architecture. These results also suggest that the particular distortions present in (111)-oriented films allow us to access emergent functionalities in materials that are unavailable in bulk or (001)-oriented thin films.

METHODS

Growth

LNO thin films were grown with thicknesses from 6 to 26 u.c. thick on 5 × 5 × 0.5 mm3 LaAlO3 (111) single crystal substrates. In this paper, we define 1 u.c. as the distance between (111) planes, or \({d}_{111}={a}_{\text{LNO}}/\sqrt{3}=2.23\) Å, where aLNO is the pseudocubic lattice parameter of LNO. Films were deposited using pulsed laser deposition with a 248-nm KrF laser operating at a fluence of 0.8 mJ/cm2 and in an oxygen partial pressure of 20 mTorr on substrates heated to 780 °C. To achieve smooth (111)-oriented films, we used an interval pulsed laser deposition technique, where one deposits ~1 u.c. worth of material quickly (10 Hz) and then waits for the in situ reflective high-energy electron diffraction signal intensity to recover and stabilize. Thin film surface morphology was characterized by an atomic force microscope and exhibited low root mean square roughness (0.064–0.285 nm). A typical scan is shown as Supplemental Figure 2.

Characterization

Experimental x-ray diffraction data from ultrathin LNO(111) films were collected at beamline 7-2 at the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory. X-ray diffraction profiles were matched with the profiles calculated using dynamical x-ray diffraction simulations, allowing us to precisely evaluate variations of the out-of-plane lattice parameter throughout the entire film thickness.

X-ray absorption spectroscopy measurements in total electron yield (TEY) mode were carried out at beamlines 4.0.2 and 6.3.1 at the Advanced Light Source, Lawrence Berkeley National Lab. Data were collected with a flying scan, where measurements were taken as the photon energy was continuously varied. Spectra were recorded with both positive and negative photon helicity, and XMCD spectra were calculated from their difference. These measurements enabled us to probe cation valence in samples within the TEY probe depth of ~5 nm. Because of the proximity of the La M4,5 edge to the Ni L3 peak, we fitted and subtracted the La peak from the collected data. Comparison of the peak location, shape, and relative intensity among peaks with the reference data allowed us to probe how the concentration of Ni2+ and Ni3+ ions differs between samples.

Transport measurements were performed on a Quantum Design Physical Property Measurement system using van der Pauw and Hall bar configurations. Resistivity versus temperature data were collected while cooling. Hall measurements and longitudinal MR measurements were performed on samples patterned into a Hall bar structure using photolithography and Ar ion milling. AuPd contacts were deposited via sputtering. In the patterned Hall bars, the current is applied along the [\(1\,{\bar{1}}\,0\)] or [\(\bar{1}\,\bar{1}\,2\)] direction and the field along the out-of-plane [1 1 1] direction.