Orientation control of the orbital ordering plane in epitaxial LaMnO₃ thin films by misfit strain

The orbital degree of freedom has played a significant role in determining the electronic and magnetic properties by means of double or super-exchange interactions in manganites [1–7]. In particular, LaMnO₃ (LMO) has attracted attention as the parent compound of colossal magnetoresistance materials [1,3] and as an oxide catalyst recently [8]. It also exemplifies the orbital-ordered system accompanying the cooperative Jahn-Teller (JT) distortion below ∼750 K with an orthorhombic crystal structure (space group Pbnm) [9]. The JT distortion of a MnO₆ octahedron lifts up the twofold degeneracy of $e_{g}$ orbitals in $\text{Mn}^{3+}(t_{2g}^{3}e_{g}^{1})$ and $d_{{3x}^{2}-r^{2}}/d_{{3y}^{2}-r^{2}}$ orbitals are alternatingly occupied within the orthorhombic ab-plane harmonizing with the cooperative JT distortion leading to the $(\pi \pi 0)$ order [9,10]. At low temperatures below $T_{\mathrm{N}}$ ∼140 K [11], there exists A-type antiferromagnetic spin order, i.e., two neighboring Mn spins within the OOP have ferromagnetic alignment and the inter-plane interaction is antiferromagnetic in bulk.

Because of the fruitful physics regarding the orbital order inherent in LMO, a variety of phenomena associated with conducting JT domain walls [12], topological magnetic phase in (111) bilayer [13], and uniaxial strain effects on competing spin/orbital orders [14–17] have been theoretically proposed requiring delicate manipulation of the orbital order by heteroepitaxial strains. Despite continual advances such as (110)-oriented orbital order [18] ultra-short laser pulse-induced transient orbital state [19], magnetic/orbital phase competition in LMO heterostructures [20,21] as well as hydrostatic pressure effect on a single crystal [22], experimental understanding of the orbital order in strained LMO is not entirely satisfactory.

It is a major difficulty to synthesize stoichiometric LMO films because of the notorious cation vacancy issue [11,23–27]; previous studies for LMO films have shown that cation vacancies are spontaneously created in as-grown films and they influence physical properties leading to the emergence of a rhombohedral crystal structure rather than the orthorhombic one and a large magnetoresistance alongside with weak ferromagnetism similar to those observed in hole-doped ones [11]. In the circumstance of hole doping, the orbital order is easily degraded because the electronic energy gain attributed to the JT distortion is reduced. Moreover, resonant X-ray scattering (RXS) [10,18,28,29], i.e., a probing technique for the cooperative JT distortion which is strongly tied to the orbital order, has been challenging for very thin films (∼15 nm in our study) that are free from strain relaxation, unless the crystallinity is good enough to ensure a measurable intensity of the resonant peak.

In this paper, we report that on high-crystalline LMO epitaxial strained films can be grown at a high temperature with sequential vacuum annealing to minimize the possible non-stoichiometry. The films exhibit clear RXS peaks of which the intensities are up to 0.36% as compared to that of the primary (002)_pc diffraction peak indicating well-defined orbital orders at room temperature. We discuss the orbital order in the strained epitaxial films in terms of the orientation of OOP and strain state.

We deposited ∼15 nm thick epitaxial LMO thin films using pulsed-laser deposition equipped with a KrF excimer laser $(\lambda = 248\ \text{nm})$ on (001)_c-oriented cubic LSAT and (110)_o-oriented orthorhombic GSO substrates; herein we define the relation among pseudocubic ("pc" in subscript), cubic ("c") and orthorhombic ("o") notations as $[100]_{\mathrm{pc}} = [100]_{\mathrm{c}} = [\bar{1}10]_{\mathrm{o}}$, $[010]_{\mathrm{pc}} = [010]_{\mathrm{c}} = [001]_{\mathrm{o}}$ and $[001]_{\mathrm{pc}} = [001]_{\mathrm{c}} = [110]_{\mathrm{o}}$. Growths were made at a temperature of 950 °C in an oxygen gas environment of 0.01 torr. The laser fluence was 0.24 J/cm² with a repetition rate of 10 Hz. After the deposition, films were cooled down to room temperature at a rate of 10 °C min⁻¹ in vacuum environments (∼10⁻⁶ torr) to relieve the cation vacancy issue by reduction of oxygen excess. Surface topography was characterized by using atomic force microscope (Bruker Multimode V equipped with a Nanoscope controller V) and Pt-coated Si tips (HQ:NSC35/Pt, MikroMasch). X-ray diffraction measurements including conventional $\theta\text{-}2\theta$ scans and reciprocal space maps (RSMs) were carried out by using an X-ray diffractometer (PANalytical X'pert-PRO MRD) with Cu $K\alpha_{\mathrm{1}}$ radiation $(\lambda = 1.5406\ \unicode{8491})$. Transport measurements were performed in a physical property measurement system (Quantum Design, Inc.) using a conventional four-point-probe method.

Figures 1(a) and (b) show the surface topographic images of the as-grown LMO thin films on LSAT and GSO substrates. For the LMO/LSAT case, an atomically flat surface with a step-terrace structure is observed indicating the step-flow growth mode during the high-temperature LMO deposition. However, for the LMO/GSO case, anisotropic rectangular pits elongated along $[\bar{1}10]_{\mathrm{o}}$ are noticed between the atomically flat surfaces indicating an occurrence of step-bunching. Figure 1(c) displays X-ray $\theta\text{-}2\theta$ scans for the films on LSAT (blue) and GSO (red) substrates. No noticeable impurity peaks were detected except for the film and substrate peaks in the wide range of scan angles. A zoomed-in graph around (002)_pc peaks on the right-hand side enables the recognition of Kiessig fringes as well as the clear location of the film peaks. The oscillation period of the fringes around the film peak enables us to estimate film thickness to be ∼15 nm for both films. The $c_{\mathrm{pc}}$-axis lattice parameter of LMO is 3.98(8) Å for the LMO/LSAT and 3.86(4) Å for the LMO/GSO.

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In order to further investigate the crystal structure and strain state of the films, we measured RSMs for two asymmetric peaks; (103)_pc/(113)_pc Bragg reflections for the LMO film on cubic LSAT substrate and (103)_pc/(013)_pc reflections for the LMO film on orthorhombic GSO, respectively (fig. 2). The exact matches of the in-plane reciprocal positions of film peaks with those of substrate peaks in all the RSMs indicated that the two films were coherently grown and fully strained to each substrate. The in-plane lattice parameters were determined to be $a_{\mathrm{pc}}= b_{\mathrm{pc}}= 3.87(1)\ \unicode{8491}$ for the LMO on cubic LSAT and $a_{\mathrm{pc}}= 3.97(0)\ \unicode{8491}$, $b_{\mathrm{pc}}= 3.96(6)\ \unicode{8491}$ for the LMO/GSO. Besides, the monoclinic distortion of the pseudocubic unit cell can be evaluated by the vertical (along L) deviation of the asymmetric peaks from the pseudotetragonal position (represented by the dashed horizontal line in each RSM) which is deduced by the $(00L)_{\mathrm{pc}}$ peak position. If there were a significant monoclinic distortion in the pseudocubic unit cell, a clear split in each asymmetric peak should have been observed. For both the strained films, the monoclinic distortion angle of the pseudocubic unit cell is estimated to be nearly 90°(±0.4°), which is distinct from 92.14° in the bulk LMO [9].

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To get hints on the oxygen stoichiometry, we investigated the temperature dependence of resistivity and magnetoresistance at 300 K (fig. 3). The relation between electronic conduction and the non-stoichiometry has been carefully characterized and quantified; a high resistivity as much as ∼10⁵ Ωcm without a noticeable bump at 150 K is indicative of the stoichiometric LMO [24,27]. Our observed result is similar to the criterion and a small negative magnetoresistance is also detected to the extent that it is less than 3% at 9 T, suggesting that the non-stoichiometric issue is minimal in our films.

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To verify the existence of orbital order and determine the orientation of OOP in our films, we carried out RXS under ambient conditions at the beamline 3A of Pohang Accelerator Laboratory. A Si (111) double-crystal monochromator was used to generate the incident light with σ-polarization, i.e., the linear light polarization perpendicular to the scattering plane, and the photon energy was calibrated using a Mn foil at its K-absorption edge (6.539 keV) within an energy resolution of 0.5 eV. The scattered light from the sample was detected via a highly oriented pyrolytic graphite (002) analyzer at a scattering angle of 32.6° in a $\sigma\text{-}\pi'$ mode. The $\pi'$ stands for a scattered light's polarization that is in the scattering plane and thus perpendicular to the incident σ polarization. This polarization rotation from σ to $\pi'$ is anomalous in terms of the fact that it is not allowed in the conventional Thomson scattering [10,28–30].

The $(\frac{1}{2}\frac{1}{2}0)_{\mathrm{pc}}$ reflection corresponding to $(100)_{\mathrm{o}}$ is forbidden for the LMO, but the intensity of the reflection can be enhanced under a resonant condition due to the anisotropic tensor susceptibility of the Mn³⁺ ion containing the anisotropic charge of the $e_{g}$ orbital in an environment of the anisotropic ligand field due to the local JT distortion [10,28]. The scattering amplitude can be different depending on whether the incident light polarization is more parallel to the charge elongation axis of the $e_{g}$ orbital or not. The difference is usually negligible in non-resonant conditions, however, this can be obvious leading to the noticeable ordering peak when the photon energy is tuned to the Mn K-edge. Although a cooperative antiferro-distortive rotation of regular oxygen octahedrons can generate resonant peaks at the La-edge below ∼1000 K where the bulk LMO undergoes the GdFeO₃-type octahedral rotation [31], the emergence of resonant peaks at the Mn-edge is involved in the anisotropic local environment of the Mn³⁺ ion, i.e., the JT distortion.

In examining the photon energy dependence of the integrated intensity of the forbidden peak at a reciprocal position specified by the orbital order, we were able to observe the enhancement of the peak intensity at the Mn K-absorption edge. For the purpose of determining the orientation of OOPs in our films, we performed the experiment at the representative $(\frac{1}{2}\frac{1}{2}2)_{\mathrm{pc}}$, $(\frac{1}{2}0\frac{1}{2})_{\mathrm{pc}}$ and $(0\frac{1}{2}\frac{1}{2})_{\mathrm{pc}}$ reflections; the $(\frac{1}{2}\frac{1}{2}2)_{\mathrm{pc}}$ reflection was selected instead of the fundamental $(\frac{1}{2}\frac{1}{2}0)_{\mathrm{pc}}$ reflection to avoid the grazing-incident geometry. Figure 4 shows the results of energy-dependent integrated intensities (of the θ-rocking curves) at the aforementioned reflections. Here, all the data were normalized by the integrated intensity of the LMO (002)_pc peak at a non-resonant condition of 6.5 keV. The photon energy at the maximum slope of the fluorescence data defines the absorption edge (doted vertical lines). In the LMO/LSAT (fig. 4(a)), the intensities of the $(\frac{1}{2} 0 \frac{1}{2})_{\mathrm{pc}}$ and $(0\frac{1}{2}\frac{1}{2})_{\mathrm{pc}}$ reflections enhance at 6.555 keV, which is ∼2 eV above the absorption edge indicating that the resonance originates from the 1s-to-4p electric dipole transition as described in ref. [28]. The additional resonant peak at 6.568 keV is due to the splitting of 4p levels as a result of the anisotropic ligand field [32]. Interestingly, the $(\frac{1}{2}\frac{1}{2}2)_{\mathrm{pc}}$ reflection does not exhibit the resonance, indicating fully vertical OOPs in the LMO/LSAT. On the contrary, the LMO/GSO mainly has the $(\frac{1}{2}\frac{1}{2}2)_{\mathrm{pc}}$ reflection with forbidding the vertical $(0\frac{1}{2}\frac{1}{2})_{\mathrm{pc}}$ reflection, although a tiny peak is observed at $(\frac{1}{2}0\frac{1}{2})_{\mathrm{pc}}$ indicating that the vertical OOP parallel to $[\bar{1}10]_{\mathrm{o}}$ is also existent in a small area. Schematics in the insets of figs. 4(a) and (b) depict the resultant OOPs on each substrate.

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The strain states of the films will be evaluated in the following lines. The lattice parameters of the orthorhombic bulk LMO are $a_{\mathrm{o}}= 5.5367\ \unicode{8491}$, $b_{\mathrm{o}}= 5.7473\ \unicode{8491}$, $c_{\mathrm{o}}= 7.6929\ \unicode{8491}$ [9], and they can be expressed as $a_{\mathrm{pc}}= 3.990\ \unicode{8491}$, $b_{\mathrm{pc}}= 3.990\ \unicode{8491}$, $c_{\mathrm{pc}}= 3.846\ \unicode{8491}$, $\alpha_{\mathrm{pc}} = \beta_{\mathrm{pc}}= 90^{\circ}$, $\gamma_{\mathrm{pc}} = 92.14^{\circ}$ in the pseudocubic notation. The orthorhombic (or pseudocubic) ab-plane of LMO corresponds to the OOP and we found that it is perpendicular (parallel) to the film surface for the LMO/LSAT (LMO/GSO). With this in mind, we estimate the in-plane misfit strain on film to be −2.98% and 0.65% (−1.17% on average) on (001)_c LSAT $(a_{\mathrm{c}}= b_{\mathrm{c}}= c_{\mathrm{c}}= 3.871\ \unicode{8491})$. Besides, the OOP lying on surface underwent a misfit strain of −0.50% along $[\bar{1}10]_{\mathrm{o}}$ and −0.60% along [001]_o (−0.55% on average) on (110)_o GSO (a_pc = 3.970 Å, b_pc = 3.966 Å, c_pc = 3.965 Å).

Orbital orders have been observed in various compounds to lift up the electronic degeneracy via crystal structural anisotropy and they can be coupled to magnetic or/and charge orders [33]. Accordingly, strain engineering and octahedral tilt rotation control as well as low-dimensional effect through heteroepitaxial growths [34,35] will provide useful pathways to control the orientation of orbital orders, create a new state of order, and realize a domain structure of multiple competing ordering states. The domain structures of our films remain unexplored and further investigations are required to explore useful physics regarding domain wall conduction [12,36], magnetism [20], and ordering dynamics [19].

In summary, we successfully deposited epitaxial LMO thin films fully strained on LSAT and GSO substrates and detected the diffraction peak regarding the cooperative JT distortion by RXS at room temperature. The orientation of OOP could be controlled by selection of the substrates so that it pointed to either out-of-plane or in-plane directions. We found that the coherent growth on LSAT made OOPs be vertical to the film surface under a compressive misfit strain (−1.17%). In contrast, the GSO substrate resulted in the plane lying on the film surface and the misfit strain was still compressive (−0.55%) owing to the larger lattice parameters within the plane compared to the inter-plane spacing in the bulk. The rotational control of OOP with conserving its cooperative JT distortion provides a new pathway to orbital engineering for emergent phenomena and future multifunctional devices in oxides.

This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (Contract Nos. 2014R1A2A2A01005979, 2016R1A5A1008184 and 2013S1A2A2035418) and the Global Frontier R&D Program on Center for Hybrid Interface Materials (HIM) funded by the Ministry of Science, ICT & Future Planning (2013M3A6B1078872). The Pohang Accelerator Laboratory is supported by POSTECH and MSIP of Korea.