Strain-driven disproportionation at a correlated oxide metal-insulator transition

Metal-to-insulator phase transitions (MITs) in strongly correlated electronic systems are fascinating phenomena which have attracted significant attention for decades [1]. Among complex oxide materials which exhibit MITs are rare-earth nickelates having the generic formula RNiO 3 , where the rareearth element (R) is smaller than lanthanum, i.e., R = Pr, Nd, … [2]. The critical temperature of the MIT is dependent on the Ni-O-Ni bond angle: straightening the angle with a larger R cation stabilizes the metallic state over the insulating state and lowers the transition temperature [3][4][5]. For example, the MIT temperatures in bulk NdNiO 3 and SmNiO 3 (Ni-O-Ni bond angles of 157.1 and 153.4 • , respectively) have been reported to be approximately 200 and 400 K, respectively. It should be also emphasized that a breathing order by disproportionation of the Ni-O bond length plays a crucial role in the MIT [6][7][8][9][10].

In RNiO 3 thin films, misfit strain arising from a lattice mismatch between the film layer and the underlying substrate affects the lattice volume, electrical conductivity, and MIT temperature [11][12][13][14][15][16][17][18]. In particular, films under in-plane tensile strain are more insulating compared to those under in-plane * ceom@wisc.edu compressive strain. The origin of this interesting phenomenon remains unclear, although a number of mechanisms have been proposed [19][20][21][22][23][24]. We also note that the effect of oxygen nonstoichiometry on the MIT has been reported in bulk RNiO 3 [25,26].

It is widely accepted that epitaxial strain in transition-metal oxide films can be accommodated through the formation of oxygen vacancy defects, resulting in off-stoichiometry of the compound [27]. Thus, cation/oxygen stoichiometry is an important factor involved with physical and functional properties of complex oxide films [2,28]. A missing cation or oxygen at a given lattice site modifies the local charge/spin/orbital configuration, critically affecting material properties. There have been recent studies on how such vacancy defects inducing off-stoichiometry influence the structural, electronic, magnetic, and transport characteristics of complex oxide films [27][28][29][30][31][32][33][34]. It is therefore possible that the experimentally observed strain-driven changes in the lattice volume, electrical conductivity, and MIT temperature of RNiO 3 thin films [11][12][13][14][15][16][17][18] are mediated by off-stoichiometry resulting from the formation of oxygen vacancies. Answering this question is of great significance for the understanding of a broader range of phenomena occurring in complex oxide thin films subject to epitaxial strain. In this work, we present the strain-dependent formation of oxygen vacancies and their impact on the metal-to-insulator phase transition in RNiO 3 (R = Nd, Sm) (001) thin films. Theory predicts that oxygen vacancies can be created to accommodate biaxial tensile strain in RNiO 3 films. The oxygen vacancies drive long-ranged structural and electronic modifications, which enhance disproportionation of the NiO 6 octahedra stabilizing the insulating phase [35]. Experiment observes that the pseudocubic unit-cell volume and resistivity in epitaxial RNiO 3 films increase with biaxial tensile strain, which is consistent with our theoretical predictions. It is highly likely that the strain-induced oxygen vacancies produce a more ionic Ni 2+ state and enhance the local disproportionation. Our results reveal that oxygen stoichiometry susceptible to epitaxial strain can be a key factor to figure out the metal-to-insulator transition in complex oxide thin films.

In order to address the above issue, we performed densityfunctional theory (DFT) calculations. Our theoretical results show that oxygen stoichiometry in RNiO 3 is very sensitive to in-plane biaxial strain [Fig. 1(a)]. The maximum oxygen vacancy formation energy (calculated using chemical potential corresponding to O 2 molecule/RNiO 3 in the dilute limit) decreases as the in-plane strain increases (Supplemental Material Fig. S1) [36] (see also Refs. [37][38][39][40][41][42][43][44] therein). For in-plane tensile strain above 1.9% (2.2%), the formation energy of an oxygen vacancy in NdNiO 3 (SmNiO 3 ) becomes negative and therefore, the materials become largely oxygen deficient at large tensile strain [Fig. 1(a)], while they are stoichiometric for compressive strain.

Further, we find that an oxygen vacancy is more easily formed in the NiO 2 plane than in the RO (R = Nd, Sm) plane of the RNiO 3 unit cell (Supplemental Material Fig. S2) [36]. When the oxygen atom connecting two octahedra is removed in the NiO 2 plane, both in-plane octahedra tilt toward each other [Fig. 1(b)]. The oxygen octahedral structure of bulk NdNiO 3 is represented by the tilt angle θ with respect to the z axis and rotation angle φ in the xy in-plane [the inset of Fig. 1(b)]. As in-plane biaxial strain increases, θ clearly decreases, while φ remains nearly constant, indicating the predominant effect of strain on octahedral tilting [45]. In the presence of oxygen vacancies, NiO 6 octahedra in RNiO 3 are more tilted, as reflected in smaller θ values, whereas φ is approximately unchanged.

In addition to octahedral rotations and tilts, we also observe disproportionation of the NiO 6 octahedra. There are two inequivalent octahedra [inset in Fig. 1 This change in disproportionation with oxygen vacancy dramatically affects the overall electronic properties. The cyan background in Fig. 1(d) shows the zero strain, stoichiometric, total density of states (DOS). It indicates an overall metallicity, with near band-edge states that are dominated by mixed O-2p and Ni-3d bands. The solid red line in the same panel shows the opening of a band gap when oxygen vacancies are included, driving a metal-insulator transition. The DOS (the dark-yellow line) shows that occupied defect states lie in the valence band of the host material and, hence, the defect-induced effects are long ranged. This is in contrast to wide band gap semiconductors where defect states lie in the band gap and their effect is short ranged. The long-ranged effect of oxygen vacancies promotes the octahedral tilting and produces additional disproportionation and drives the system into the insulating state. The metallicity of the defect-free system suggests that the DFT does not completely capture the electronic properties, but the calculation clearly indicates that vacancy-induced disproportionation drives the system toward the insulating state, which would result in a higher MIT temperature. For SmNiO 3 , the DFT calculations show qualitatively analogous behavior.

To study the effect of in-plane biaxial strain on oxygen stoichiometry, lattice structures, and electronic properties, we grew epitaxial RNiO 3 (R = Nd, Sm) (001) films using pulsed laser deposition (PLD) with in situ monitoring by reflection high-energy electron-diffraction (RHEED). During the PLD growth of RNiO 3 (001) films, RHEED oscillations were used to estimate the film thickness (Supplemental Material Fig. S3) [36]. In Fig. 2(a), atomic force microscopy (AFM) topography and RHEED pattern images show that the as-grown NdNiO 3 (14 nm) films have atomically flat surfaces with a clear stepterrace structure and high-crystalline qualities, respectively. As depicted in Fig. 2(b), LaAlO 3 (LAO) (001), NdGaO 3 (NGO) (110), and SrTiO 3 (STO) (001) substrates were used to investigate epitaxial films in a wide range of strain states. Note that the pseudocubic lattice constants of bulk NdNiO 3 and SmNiO 3 are 3.808 and 3.801 Å, respectively [5]. Thus, the lattice mismatch of an NdNiO 3 (SmNiO 3 ) film is -0.5% (-0.3%), 1.3% (1.5%), and 2.5% (2.7%) with respect to pseudocubic LAO, NGO, and STO substrates, respectively; that is, under in-plane compressive strain for the LAO substrate and under in-plane tensile strain for the NGO and STO substrates. To identify the coherency and actual strain states, reciprocal space mappings (RSMs) around the pseudocubic (-103) Bragg peaks were performed, as shown in Fig. 2(c) [for SmNiO 3 (001) films, see Supplemental Material Fig. S4(a)] [36]. These show that the films are coherent with respect to the underlying substrate and strained with the same in-plane lattice constant as that of the substrate in pseudocubic notation. By deriving a pseudocubic unit-cell volume from the measured lattice constants, we also examined the relation between structural properties and oxygen off-stoichiometry in RNiO 3 films.

As evident from Fig. 2(d), the pseudocubic unit-cell volume of RNiO 3 films increases with in-plane tensile strain, whereas it is identical to the bulk value for in-plane compressive strain (Supplemental Material Table S1) [36]. We found that the measured out-of-plane lattice constants deviate from those calculated assuming the volume conservation of RNiO 3 unit cells. This difference between the measured and calculated lattice constants gets larger with inplane tensile strain, indicative of a volume expansion (Supplemental Material Fig. S5) [36]. The volume expansion of RNiO 3 unit cells by in-plane tensile strain is also confirmed in atomic-scale scanning transmission electron microscopy (STEM) measurements (Supplemental Material Fig. S6) [36]. It is further interesting that an NdNiO 3 film on a STO substrate (a lattice mismatch of +2.5%) is coherent with a volume expansion, whereas an NdNiO 3 film on a YAlO 3 substrate (a lattice mismatch of -2.7%) is relaxed, preserving the unit-cell volume (Supplemental Material Fig. S7) [36]. For NdNiO 3 and SmNiO 3 films grown on STO (001) substrates, their unit-cell volumes increase up to 4.4% and 6.1%, respectively. Albeit the strain dependence of the Poisson's ratio is considered, this volume change in RNiO 3 films is too large. Note that the Poisson's ratio in complex oxides is usually in the range of 0.2-0.3 [46,47]. This is suggestive of a change in oxidation state under tensile strain, but not compressive strain. Similar volume expansion by in-plane tensile strain has been previously reported in other transition-metal oxide films where multiple oxidation states of the transition-metal element are allowed [48,49].

We also found that electronic transport properties strongly depend on epitaxial strain. Figure 2(e) shows the temperature dependence of resistivity in the 14-nm-thick NdNiO 3 (001) films. NdNiO 3 samples undergo an explicit MIT as the temperature decreases. It is evident that NdNiO 3 films under in-plane tensile strain (grown on NGO and STO substrates) exhibit larger resistivity than those under in-plane compressive strain (grown on a LAO substrate) at all temperatures. In SmNiO 3 films, similar transport behaviors are observed [Supplemental Material Fig. S4(b)] [36]. In particular, the MIT in the tensile-strained NdNiO 3 films occurs at a higher temperature, whereas it is suppressed in the compressive-strained NdNiO 3 films with a lower MIT temperature (Supplemental Material Fig. S8) [36]. And, the NdNiO 3 /LAO film with better electrical conductivity gave higher carrier concentrations of mobile charges than the NdNiO 3 /STO film (Supplemental Material Fig. S9) [36]. These strain-dependent transport properties are consistent with previous reports [11][12][13][14]17,18]. Strain-induced oxygen vacancies increase a pseudocubic unit-cell volume and resistivity in RNiO 3 films. By carrying out cathodoluminescence (CL) measurements of our as-grown NdNiO 3 (001) films (Supplemental Material Fig. S10) [36], we first found that the formation of oxygen vacancies in RNiO 3 films is quite dependent on the in-plane biaxial strain. In the tensile-strained NdNiO 3 films (i.e., NdNiO 3 /NdGaO 3 and NdNiO 3 /SrTiO 3 films) unlike the compressive-strained NdNiO 3 /LaAlO 3 film, we only observed distinct CL signals at the low photon energies of 1.8 eV which are directly related with oxygen-vacancy-mediated optical transitions [50,51]. By visualizing oxygen atoms in annular bright field-STEM images of NdNiO 3 /STO and NdNiO 3 /LAO films, we also verified that the tensile-strained NdNiO 3 film is more oxygen deficient than the compressivestrained NdNiO 3 film (Supplemental Material Fig. S11) [36]. Then, by performing in situ annealing experiments of as-deposited NdNiO 3 films in different oxygen-ambient environments, it was further identified that more oxygendeficient NdNiO 3 films exhibit a larger unit-cell volume in pseudocubic notation and higher resistivity (Supplemental Material Fig. S12) [36]. A possibility of cation vacancies in this volume expansion could be excluded by examining the cation stoichiometry of as-grown NdNiO 3 films using Rutherford backscattering spectrometry (Supplemental Material Fig. S13) [36]. For two NdNiO 3 films, one with in-plane compressive strain and the other with in-plane tensile strain, the ratio of chemical composition between Nd and Ni atoms is 1:1 within measurement errors. It is highly likely that the oxygen vacancy concentration in tensile-strained RNiO 3 films is higher than that in compressive-strained RNiO 3 films. Then, the greater amount of oxygen vacancy defects in the tensile-strained RNiO 3 films leads to further enlarged volume and further enhanced resistivity.

We observe a reduction of Ni valence state in 10-unit-cellthick NdNiO 3 (3.8 nm) films under in-plane tensile strain 3+ , respectively. For Ni 2+ , two distinct peaks (870.8 and 871.9 eV) were calculated with the estimated crystal-field splitting parameter, 10Dq, 1.1 eV, while three peaks (870.1, 871.9, and 873.8 eV) with higher 10Dq, 1.8 eV were found in the Ni 3+ state. using the atomic-resolved STEM and electron-energy-loss spectroscopy (EELS) techniques. For two epitaxial NdNiO 3 thin films with atomically sharp interfaces grown on STO (2.5% in-plane tensile strain) and LAO (0.5% in-plane compressive strain) (001) substrates, as shown in Figs. 3(a 3(e)] makes sure that the valence states of Ni cations are strongly correlated with the in-plane biaxial strain. Further confirmation with EELS calculation of Ni 2+ and Ni 3+ valence states reveals that the oxidation states of Ni cations in the NdNiO 3 /STO and NdNiO 3 /LAO films are more toward ionic Ni 2+ and covalent Ni 3+ , respectively [36] (see also Refs. [52,53]