Introduction

Misfit strain has been a key control parameter to tune physical properties and to search for new emergent phenomena in transition-metal-oxide (TMO) films1,2,3,4,5,6,7,8,9. Recently, rare-earth nickelate films, RNiO3 (R = rare-earth element), have attracted much interest to control their metal-insulator transitions or peculiar ‘up-up-down-down’ spin orderings by misfit strain10,11,12,13. Among them, LaNiO3 (LNO) was considered to be less interesting, because its bulk is a paramagnetic metal at all temperatures14. However, after theoretical proposals that it could become an electronic analogue to high-Tc cuprates by strain and layer-thickness control15,16,17, a lot of studies have been devoted to realize it18,19,20,21,22,23,24,25,26,27,28. Though its final goal has not been achieved yet, the LNO heterostructures revealed various intriguing properties such as metal-insulator or antiferromagnetic (AFM) transitions by dimensionality control21,22,23,24,25,26,27 and a signature of charge disproportionation (CD), absent in bulk, by strain control28.

The CD in RNiO3, except for La, is ascribed to very small or negative charge-transfer energy Δ from O 2p to Ni 3d orbitals29,30. In LNO films, the misfit strain will induce a change of Madelung potential, resulting in a different Δ28, which would be an origin of CD in LNO films28,30. Chakhalian et al. predicted that the CD may occur under tensile strain28, but Lau and Millis proposed a phase diagram in which a charge ordering can occur at all strain conditions30. Meanwhile, recent theoretical calculations predicted that a spin-density-wave (SDW) order can emerge in metallic LNO thin films30,31,32. Especially, Lee et al. claimed that the SDW order should appear due to Fermi-surface (FS) nesting by tuning effective hopping parameters between Ni 3d orbitals31,32. In spite of these intriguing theoretical predictions, there have been few experimental evidences for them.

In this Letter, to investigate the systematic changes of electronic structures of LNO films under various misfit strains, we employed in situ angle-resolved photoemission spectroscopy (ARPES) and the dynamical mean-field theory (DMFT). As the strain states change from compressive to tensile, we observed that the eg-band rearrangement systematically changes the fermiology of LNO films. Additionally, all the LNO films show a FS superstructure with Q1 ≡ (1/2,1/2,1/2), implying an existence of CD fluctuations. A tensile-strained LNO film shows another FS superstructure with Q2 ≡ (1/4,1/4,1/4), suggesting an existence of a SDW instabilities due to significant FS nesting in the quasi-two-dimensional (2D) FS. Our results demonstrate how such latent instabilities are affected by misfit strain in LNO films. Thus, misfit strain can be used as a tuning parameter to search for latent orders in TMO films.

Results

Orbital-dependent electronic-structure changes induced by misfit strain

High-quality LNO films were epitaxially grown using pulsed laser deposition (PLD) on (001)-oriented LaAlO3 (LAO), NdGaO3 (NGO) and SrTiO3 (STO) substrates. Due to lattice mismatches, the LNO films on LAO, NGO and STO substrates should be under compressive strain (−1.3%, hereafter denoted by c-LNO), nearly free strain, i.e. bulk-like (+0.3%, b-LNO) and tensile strain (+1.7%, t-LNO), respectively. Since the LNO films have tetragonal distortions due to biaxial strain, we will use, in this paper, Brillouin zone (BZ) notation of the tetragonal structure for the symmetric points, as shown in Fig. 1a. Bulk LNO has a simple three-dimensional (3D) electronic structure composed of a small electron pocket centered at the Γ point and a large hole pocket at the A point33,34.

Figure 1
figure 1

Strain control of the electronic band dispersions in LNO films.

(a) BZ of tetragonal LNO. ARPES spectra along the MΓXM and the AZRA lines of (b,f) c-LNO, (c,g) b-LNO and (d,h) t-LNO, respectively. Quasiparticle-peak positions from MDCs and EDCs are represented by empty circles and triangles, respectively. Overlay of quasiparticle-peak positions under the different strain states along (e) the MΓXM and (i) the AZRA lines.

Full size image

Figures 1b–d show ARPES spectra of c-LNO, b-LNO and t-LNO along the MΓXM line. Quasiparticle-peak positions from intensity maxima in momentum or energy distribution curves (MDCs or EDCs) are also plotted by empty circles and triangles, respectively. Figure 1e shows an overlay of the quasiparticle-peak positions of the three LNO films, which clearly shows an upward shift of the bands as the misfit strain changes from compressive to tensile. Similar plots are presented in Figs. 1f–i along the AZRA line. As seen in Fig. 1i, in contrast to the MΓXM line, the band makes a downward shift.

To understand the strain-dependent band shifts, we compared our ARPES data (blue triangles) with the results of generalized gradient approximation (GGA, solid lines) and GGA + DMFT (orange-scale images) calculations in Figs. 2a–d (see Supplementary Information (SI) for calculation methods). Note that misfit-strain values in the calculations are a little different from experimental ones, since we chose the values at which converged solutions were obtained. See the Fig. 2 caption. On the other hand, the experimental kz resolution due to short photoelectron escape depth is about 0.13 Å−1 (full width at half maximum), so the GGA + DMFT results were presented after averaging over the kz resolution in the whole figures (see SI for a detail). As clearly seen in the figure, the GGA + DMFT describes the band dispersions much better than the GGA, which implies strong electron-electron correlations in all LNO films35,36. According to the calculations, the hole band along the MΓXM line is mostly composed of a d3z2–r2 orbital (SI Fig. S6). Under tensile strain, the smaller the distance between the d3z2–r2 orbital and apical oxygen ions becomes, the stronger the hybridization. Thus, it pushes the anti-bonding d3z2–r2 band toward higher energy as in Figs. 2a and 2c. On the other hand, the hole band along the AZRA line is mostly composed of a dx2–y2 orbital, thus we can expect opposite behavior as seen in Figs. 2b and 2d.

Figure 2
figure 2

Calculated band dispersions with respect to misfit strain.

LNO band dispersions from GGA (solid lines) and GGA + DMFT (orange-scale images) calculations along the MΓXM and the AZRA lines calculated with (a,b) −1.7% compressive (c-LNO) and (c,d) +2.0% tensile strain (t-LNO), respectively. The experimental band dispersions are displayed by empty blue triangles.

Full size image

Strain control of Fermi-surface topology

Comparing the hole-band dispersions in Figs. 1b–d, we can find a hint that the FSs of the LNO films can be changed significantly due to misfit strain. While the bands of the c- and the b-LNO's are located below the Fermi level (EF), for t-LNO, the bands cross the EF to modify a FS shape. Because of the kz resolution, we can suspect that the bands may not cross the EF in a real situation. However, as seen in Fig. 3b, the hole pocket size in the ΓXM plane is larger than that from the GGA + DMFT. Thus, if the fermiology changes smoothly, we can expect that the hole pocket is more open along the kz-axis than the calculated one in Fig. 3f. Such a change in t-LNO cannot be explained simply by the GGA, in which the upward level shift of the hole band by the misfit strain is only about 0.2 eV (Figs. 2a and 2c). On the other hand, the GGA + DMFT results indicate that strong electron correlations push the hole band further in t-LNO. As a result, the bands make contact with the EF along the MΓ and the XM lines. This result suggests that both misfit strain and strong correlations should play an important role in the fermiology change in LNO films.

Figure 3
figure 3

Fermiology change of LNO films in response to misfit strain.

FS maps in the ΓXM and the ZRA planes of (a,c) c-LNO and (b,d) t-LNO, respectively. Left (Right) panels are for ARPES (GGA + DMFT). The red dashed lines in (c) and (d) are guidelines for better comparison of the FS shapes. FS maps in the XRAM plane of c-LNO and t-LNO are presented in (e) and (f) from GGA + DMFT, respectively.

Full size image

Figures 3a and 3b show this FS change (left panel: ARPES; right panel: GGA + DMFT) in the ΓXM plane. In c-LNO, there is only the electron pocket at the Γ point, whereas in t-LNO we can see a hole pocket centered at the M point. The intense feature at the M point in c-LNO does not originate from EF-crossing bands but from the kz resolution and the broadening of the hole band near the EF. This fermiology change in the ΓXM plane is well described by the GGA + DMFT, though the size of the hole pocket in t-LNO is smaller than the experimental one. FS maps in the ZRA plane also reveal another interesting FS change, as shown in Figs. 3c and 3d. As the strain state goes from compressive to tensile, the hole-pocket shape becomes a nearly perfect square with a large flat region, thus enhancing FS nesting. The details of the FS nesting and its possible relationship to density waves will be discussed later.

To figure out the whole FS shape, FS maps in the XRAM plane from the GGA + DMFT calculations are presented in Figs. 3e and 3f. For c-LNO, two hole pockets centered at the A points are well separated. On the other hand, for t-LNO, the two hole pockets merge together around the M point, resulting in an open FS along the kz-axis. Thus, the misfit strain can drive a Lifshitz transition, i.e. the hole FS topology evolves from 3D to quasi-2D as the strain state changes from compressive to tensile.

Two kinds of Fermi-surface superstructures depending on misfit strain

A careful examination of the FS maps in Figs. 3c and 3d reveals faint circles and lines in the ZRA plane, implying the existence of FS superstructures. Such superstructures are often related with FS instabilities, which can cause various intriguing emergent phenomena such as charge or spin density waves37,38 and superconductivity39. Thus, proper understanding of the FS superstructures will provide us valuable insights on possible emergent phenomena.

To investigate the FS superstructures more clearly, we constructed constant-energy-surface (CES) maps in the ZRA plane at a binding energy of 30 meV using a log scale, as displayed in Figs. 4a and 4b for c- and t-LNO, respectively. In c-LNO, we can observe a circular-shape superstructure at the A point, which is similar to that observed at the Γ point, as shown in Fig. 3a. Thus, this superstructure can be considered as a replica of the electron pocket. To reproduce this superstructure, we folded the whole BZ with Q1 and plotted a resulting CES map in Fig. 4c. This schematic CES map represents the experimental map quite well, suggesting that a Q1 modulation should exist in c-LNO. Note that the FS superstructure in the ΓXM plane is also consistent with the Q1 modulation and that b-LNO also shows a similar superstructure (SI Figs. S9 and S10).

Figure 4
figure 4

Strain-dependent FS superstructures.

Experimental CES maps in the ZRA plane at 30 meV of (a) c-LNO and (b) t-LNO on a log scale. Schematic CES maps for (c) c-LNO after folding the BZ with Q1 = (1/2,1/2,1/2) and (d) t-LNO after an additional folding of the hole pocket with Q2 = (1/4,1/4,1/4).

Full size image

On the other hand, the CES map for t-LNO displays more complicated superstructures, as shown in Fig. 4b. In addition to the superstructure at the A point, it shows additional one centered at the Z point with a rounded-square shape. To reproduce this superstructure, we folded the hole pocket in the BZ with Q2 in addition to the folding of the whole BZ with Q1, which results in a CES map shown in Fig. 4d. This schematic CES map matches well the complicated superstructure in Fig. 4b. This result suggests that t-LNO should have another periodic modulation with Q2 for the hole pockets. Note that the periodic modulation with Q = (1/4,1/4,0) will give a similar superstructure in Fig. 4b, but it cannot reproduce a FS superstructure in the ΓXM plane (SI Fig. S11).

Discussion

Now, let us elucidate the origin of the Q1 modulation. First possibility is a √2×√2 surface reconstruction40. Such surface reconstruction will make an electron pocket at the Γ point reappear at the M point not at the A point, thus the surface reconstruction cannot be the origin of the Q1 modulation. Second possibility is the coupling between the misfit strain and metal-oxygen octahedral rotations41. Under misfit strain, NiO6 octahedra can be rotated cooperatively, which produces a FS superstructure with a Q1 modulation. If it occurs, the superstructure intensity in c- or t-LNO films should be stronger than that in b-LNO. However, the superstructure intensity of b-LNO is similar to that of c-LNO (SI Fig. S10). And we could not observe any significant difference in RHEED patterns during the film growth (SI Fig. S1). Therefore, the observed FS superstructure with the Q1 modulation in our LNO films should have an electronic origin.

It is well known that 3D RNiO3, except R = La, has CD with a rocksalt-pattern lattice distortion42,43. Such charge ordering will result in a BZ folding with Q1. In contrast, a bulk LNO remains as a metal at all temperatures14, so it is rather difficult to expect such charge ordering in LNO at a first glance. However, recently, a slight CD was predicted to exist even in a metallic bulk RNiO329,30. Our observation of the Q1 modulation supports such theoretical predictions. Note also that ARPES is an ultrafast probe in the femtosecond regime, so it is quite sensitive to short- as well as long-range orders44,45. Therefore, the superstructure with the Q1 modulation could be originated from either short- or long-range CD in the metallic LNO films.

Let us look into the Q2 modulation. The RNiO3, except R = La, has an AFM ordering with an ‘up-up-down-down’ spin configuration14,46. Such magnetic ordering could result in a band folding with Q2. Since bulk LNO has a paramagnetic ground state14, such magnetic ordering is not likely to occur. However, Lee et al. recently proposed that if FS nesting in a nickelate becomes strong at Q2, a SDW order appears even in the metallic regime31,32. As we demonstrated earlier with Fig. 3d, the FS of t-LNO exhibits a large parallel flat region in the quasi-2D hole pocket. This flattened FS can induce large FS nesting at Q2. To confirm this intriguing possibility, we calculated susceptibilities from the GGA band dispersions and obtained a sharp peak near Q2 (SI Fig. S12). This peak in t-LNO is sharper than those in other films. This result implies that it is highly plausible that the t-LNO film has SDW instabilities with Q2, consistent with earlier theoretical predictions31,32. Actually, recent muon spin rotation24 and resonant x-ray diffraction25 measurements showed an AFM ordering in two-unit cell-thick LNO superlattice, but no signature in thicker ones. These results and our observations imply that SDW fluctuations exist even in thicker LNO films. We should note that the nesting vector Q2 is 3D in the quasi-2D FS. This seems to be self-contradictory, but it could be explained by that the spin instability is strongly coupled to the 3D CD.

Appearance of the FS superstructures in our LNO films provides new insights into strain-induced changes of charge and spin orderings in RNiO3. Recently, Lau and Millis investigated charge and spin orderings in bulk RNiO3 and few-layered RNiO3 using the slave-rotor Hartree–Fock formalism30. In their proposed phase diagram, there is a 3D metallic region with a slight charge ordering, but no spin ordering in bulk RNiO3. Our c-LNO should belong to this 3D metallic region, because it has the 3D electronic structure as in Fig. 3e. And it shows a superstructure with the Q1 modulation only, consistent with a CD instability. On the other hand, in ultrathin RNiO3 films, they predicted a 2D metallic region with both charge and spin orderings. Our t-LNO film should belong to this 2D metallic region, because it has the quasi-2D electronic structure with strong FS nesting at Q2 as in Fig. 3f. In addition, its FS map shows superstructures with both the Q1 and Q2 modulations, suggesting coexistence of CD and SDW instabilities. Our study demonstrates that misfit strain can reveal latent instabilities in LNO films.

In conclusion, we systematically investigated how misfit strain can change the electronic structure of LNO films, combining APRES measurements and GGA + DMFT calculations. As the strain state goes from compressive to tensile, strongly renormalized Ni eg bands are rearranged and change FS topology, accompanied by flattening of the FS shape in a tensile-strained LNO film. Additionally, in all LNO films, we observed a FS superstructure, which reveals a signature of CD fluctuations. We observed an additional FS superstructure in the tensile-strain case, which can be attributed to SDW fluctuations. Our results suggested that misfit strain can be a useful tuning parameter to search for latent instabilities and have possibilities to induce latent orders in strongly correlated electron systems.

Methods

Sample preparation

High-quality 10 unit-cell-thick LNO films were epitaxially grown using pulsed laser deposition (PLD) on (001)-oriented single-crystalline substrates. To investigate the strain-dependent changes in electronic structures, we grew three kinds of LNO epitaxial films on (001)-oriented LaAlO3 (LAO), NdGaO3 (NGO) and SrTiO3 (STO) substrates. The lattice constants of bulk LNO, LAO and NGO are 3.84, 3.79 and 3.851 Å in pseudocubic notation, respectively. And the lattice constant of STO is 3.905 Å for the cubic structure. Due to the lattice mismatch, the LNO films on LAO, NGO and STO substrates should be under compressive strain, nearly strain-free and tensile strain, respectively. For PLD, we used a KrF excimer laser (λ = 248 nm) with a repetition rate of 2 Hz to ablate sintered stoichiometric targets. The laser energy density was in the range of 1–1.5 J cm−2 at the target position. The deposition temperature and the P(O2) were 600°C and 1 × 10−2 Torr, respectively. Then, we cooled down the samples below 100°C in P(O2), 1 × 10−2 Torr, to avoid the oxygen vacancy generation. We monitored the film thickness by using in situ reflection high-energy electron diffraction. We confirmed that all of the LNO films were fully and homogeneously strained by x-ray diffraction at the 9C beamline of Pohang Light Source (PLS). (For the details of film characterizations, see Supplementary Information, Fig. S1).

In situ ARPES measurements

ARPES measurements were performed at the Beamline 7.0.1 of ALS, of which end-station was equipped with PLD and ARPES. After deposition, the thin films were transferred to an analysis chamber at a pressure of 5 × 10−11 Torr without breaking a vacuum. The sample temperature was kept at 90 K during the measurements. The total energy resolution was 30 meV at hν = 150 eV. Since LNO films have three-dimensional electronic structures, appropriate photon energies for the high-symmetry planes of the each film were determined by scanning photon energies in the normal emission; the ΓXM (ZRA) plane was found to be located at slightly different energies of 150 eV (114 eV) for LNO/LAO, 154 eV (117 eV) for LNO/NGO and 157 eV (120 eV) for LNO/STO due to different lattice parameters. For the details of ARPES measurements, see Supplementary Information, Fig. S2.