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Extreme tensile strain states in La0.7Ca0.3MnO3 membranes

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Science  03 Apr 2020:
Vol. 368, Issue 6486, pp. 71-76
DOI: 10.1126/science.aax9753

Straining an oxide membrane

Perovskite manganites, such as La0.7Ca0.3MnO3, have complex phase diagrams with many competing states. Among the knobs that can be used to control their properties are magnetic field and strain. Hong et al. placed membranes of La0.7Ca0.3MnO3 on a flexible polymer layer (see the Perspective by Beekman). Stretching the flexible layer resulted in large strains of up to 8% on the membrane. By varying the magnitude and direction of the strain, the researchers were able to explore the phase diagram of the system and influence its magnetic and transport properties.

Science, this issue p. 71; see also p. 32

Abstract

A defining feature of emergent phenomena in complex oxides is the competition and cooperation between ground states. In manganites, the balance between metallic and insulating phases can be tuned by the lattice; extending the range of lattice control would enhance the ability to access other phases. We stabilized uniform extreme tensile strain in nanoscale La0.7Ca0.3MnO3 membranes, exceeding 8% uniaxially and 5% biaxially. Uniaxial and biaxial strain suppresses the ferromagnetic metal at distinctly different strain values, inducing an insulator that can be extinguished by a magnetic field. Electronic structure calculations indicate that the insulator consists of charge-ordered Mn4+ and Mn3+ with staggered strain-enhanced Jahn-Teller distortions within the plane. This highly tunable strained membrane approach provides a broad opportunity to design and manipulate correlated electron states.

Externally driven changes in atomic spacing offer access to distinct phases and functionalities of materials. In complex oxides (13), strain can be used to manipulate quantum states of matter (48) because the electrons in these materials and their correlated interactions are tightly coupled to the lattice. However, bulk oxide crystals are typically brittle and crack under relatively small tensile strain; larger strain states are usually only accessible under compression (9). Although epitaxial strain imparted by lattice mismatch between a thin film and the underlying substrate can modulate the properties of thin films (5, 6, 10, 11), the discrete lattice parameters of available substrates (10), combined with strain-driven defect formation during high-temperature synthesis (12, 13), present fundamental limitations to exploring how extreme and coherent strain fields affect correlated states in oxides. The recent development of free-standing complex oxide membranes (14) both circumvents these challenges and provides unique opportunities to realize previously unobserved strain-induced responses. Oxide membranes can be mechanically coupled to an external platform without an epitaxial relationship, for which strain states of different symmetries can be freely chosen by design. Moreover, the critical fracture strain is often greatly enhanced for small materials length scales (15, 16), enabling a viable route to impart large tensile strain states well beyond the typical values that ceramics can withstand.

Rare-earth perovskite manganites are correlated electron systems with multiple phases coupled to the lattice (17). A number of stable electronic and magnetic ground states arise at different carrier concentrations, as structural Jahn-Teller distortions to the MnO6 octahedra generate different bond network configurations, which therefore change the magnetic exchange interactions between 3d electrons on neighboring sites. Here, we focused on La0.7Ca0.3MnO3 (LCMO), a representative colossal magnetoresistance (CMR) material (17) with a transition between a low-temperature ferromagnetic metal (FM-M) and a high-temperature paramagnetic insulator (PM-I) at a Curie temperature TC ~ 250 K. The metallic ground state of LCMO is closely adjacent to many other phases, such as charge/orbital ordering (COO), a ferromagnetic insulating state, and antiferromagnetic states, thereby offering an ideal testbed to understand electronic correlations controlled by elastic lattice strain.

Using pulsed laser deposition (PLD), we synthesized multilayer heterostructures consisting of SrCa2Al2O6 (used as a sacrificial layer), SrTiO3, and LCMO (fig. S1) to release free-standing LCMO nanomembranes. The solid-solution family of (Ba,Sr,Ca)3Al2O6 enables the continuous tuning of the sacrificial layer lattice constant from 0.382 nm (Ca 100%) to 0.413 nm (Ba 100%), covering the lattice constant range of the vast majority of perovskite and related oxides (18, 19). SrCa2Al2O6, a particular composition for the sacrificial layer developed for this experiment instead of Sr3Al2O6 used previously (14), is nearly perfectly lattice-matched (<0.1%) to the LCMO lattice constant (a = 0.386 nm). We found that minimizing lattice mismatch is a critical factor to avoid crack formation in the released membranes (fig. S2) and is therefore essential to achieve homogeneous tensile strain states over large areas. The LCMO layer was kept at a minimum of 10 unit cells to avoid the Berezinskii-Kosterlitz-Thouless crystalline melting transition previously observed in the ultrathin limit (20). All heterostructures were grown epitaxially and monitored by in situ reflection high-energy electron diffraction (RHEED). By selectively dissolving the sacrificial layer in water, the top oxide film was detached from the substrate and transferred onto a polyimide sheet, which we used as a stretchable substrate (21).

The strain state of the oxide membrane can be controlled by external forces (Fig. 1A). The four sides of the polymer layer were clamped and stretched by micromanipulators with ~0.1% precision. The strong adhesion between the oxide membrane and the polymer layer provides efficient strain transfer to the oxide membrane without any observable slippage. The macroscopic size of the membrane (area > 10 mm2) provides a uniform interior distribution of strain ε upon stretching and minimizes the edge effects observed in microflakes of exfoliated crystals (22). Finite-element analysis of the strained membrane/polyimide bilayer (Fig. 1A) indicated that the membrane area experiences a strain gradient near the membrane edges, whereas the majority of the membrane area at the center is homogeneously strained (Δε < 0.2%). The strained oxide/polymer bilayer was then glued onto a solid substrate such that the strain field was fixed even after the external force was removed (fig. S3) (21). The adhesive (polycaprolactone) used here can be reversibly melted by gentle heating (T < 100°C) on the sample assembly stage. Thus, it is possible to set and probe multiple strain states of the same membrane sample. Smaller strains less than 3% could be reset to the zero strain state by melting and releasing the adhesive, whereas higher strain states could only be stretched further in an irreversible manner thanks to the plastic deformation of the outer polymer layer (Fig. 1A). We found that the strain remains fixed for at least a week, down to cryogenic temperatures (T = 2 K) and under x-ray exposure, providing a versatile platform for multiple experiments.

Fig. 1 Designer strain in 2D oxide membranes.

(A) Schematic platform for straining oxide membranes. The lower maps plot finite-element analysis strain profiles of the polyimide/oxide bilayer under uniaxial and biaxial stress (21). The gray square in the strain maps indicates the boundary of the oxide membrane, beyond which only the polyimide remains. Inset: Lifting off a membrane from the substrate by etching a water-soluble layer in oxide heterostructures. (B) Optical microscope images of a 6-nm-thick LCMO membrane before (top) and after (bottom) stretching uniaxially. The ceramic chip carrier is used as a reference frame to optically characterize the strain state. (C) GIXRD strain as a function of the nominal strain observed optically. Error bars denote SD. Inset: GIXRD data of the LCMO (200) peak shifted by strain. (D and E) In-plane lattice changes and corresponding 2θ peaks of LCMO membranes characterized by GIXRD, for uniaxial (D) and biaxial (E) strain.

We first optically characterized the strained membrane and found that the membrane reaches extreme macroscopic strain states. Two optical images, taken before and after establishing uniaxial tensile strain, are compared in Fig. 1B to estimate the strain. (Note here that a small tensile stress is also applied in the perpendicular direction to prevent compression by the finite Poisson ratio.) Because the oxide membrane is nearly transparent on the polyimide layer, we measured the strain by tracking the spacing of evaporated metal (Au) markers. By stretching oxide membranes of different thickness d, we found that thicker membranes (d > 20 nm) undergo mechanical fracture under relatively small uniaxial tensile strains (<2%), as seen in optical images showing periodic crack formation (fig. S4). In contrast, ultrathin oxide membranes (d < 10 nm) could be stretched much more (>2%) without fracture.

Although the macroscopic strain state was visibly evident, we next assessed whether such large strains in the oxide membrane induce elastic or plastic deformation. We used grazing incident x-ray diffraction (GIXRD) to measure the change of the in-plane lattice constants. In an unstretched LCMO membrane, the perovskite (200) peak in a 2θ-ω scan corresponded to that of the bulk LCMO crystal. With increasing tensile strain, the GIXRD peak shifted to lower angles (Fig. 1C, inset), tracking the increase of the in-plane lattice constant. The strain values measured by the GIXRD scans closely matched the macroscopic strain observed in the optical images (Fig. 1C). The maximum tensile strain in the uniaxial geometry was 8.2% (a = 0.417 nm), far beyond typical tensile strains accessible in crystalline oxides [such as typical piezoelectrically induced strains up to ~1% (7)] and epitaxial strains in canonical oxide thin films up to ~3% (23). [It is again worth noting that for high-temperature synthesis, defect densities in such ionic materials often vary with strain (12, 13).] In addition, the symmetry of the strain field can be directly controlled. In Fig. 1, D and E, we present two examples for which the strain is independently tuned along different directions: asymmetric uniaxial strain states and symmetric biaxial strain states, respectively. The ability to design both the magnitude and symmetry of the strain field—for example, through linear combinations of the two aforementioned states—opens up avenues for the manipulation of complex oxide membranes hosting electrons sensitive to orbital symmetry and filling.

We next leveraged access to these extreme strain states to both modulate the transport properties of LCMO and stabilize a nonequilibrium phase of the LCMO membranes under biaxial strain. First, we measured the membrane resistivity using van der Pauw (vdP) electrodes near the center of the membrane (Fig. 2A). In the central vdP configuration, the distribution of electric current is quite insensitive to the geometry and strain gradient of the membrane edge (fig. S5) (21). This requires that the membranes are large with respect to the vdP dimensions, which is easily achieved here with millimeter-scale membranes. Therefore, the electronic transport measurements accurately reflect the intrinsic response of the central area with homogeneous strain. The temperature-dependent resistivity ρ(T) in the zero strain state exhibited TC ~ 250 K, defined by the peak in d[log(ρ)]/d(T), consistent with prior studies. Next, by repeatedly stretching the membrane in a symmetric (biaxial) manner, we acquired the full evolution of ρ(T) from the same oxide membrane at different strain states (Fig. 2B). We found that 5% biaxial tensile strain led to an increase in ρ(300 K) by more than two orders of magnitude. Moreover, TC of the FM-M/PM-I phase transition shifted to lower temperatures. These observations are consistent with the reduction of the in-plane orbital overlap between Mn d orbitals and O p orbitals under tensile strain, which is supported by our electronic structure calculations. The marked resistivity increase at room temperature evidences the reduced bandwidth and smaller hopping integral for itinerant electrons. In double exchange, the hopping eg electron is forced to align with the other core t2g electrons by a large Hund’s-rule coupling (Fig. 2B, inset). Thus, the electronic bandwidth is modulated by the spin orientation between Mn sites and gives an effective ferromagnetic interaction mediated by the electronic conduction. The smaller electronic hopping integral directly suppresses the double-exchange interaction, moving the phase boundary to substantially lower temperatures (24).

Fig. 2 Magnetotransport and phase diagram of biaxially strained La0.7Ca0.3MnO3 membranes.

(A) Electric potential mapping of the central vdP geometry in membranes. The boundary conditions were current nonpermeability at the edges; I+ and I represent the current source and current sink. The voltage at V is held at V = 0, and Vmax is calculated at V+. (B) Evolution of the temperature-dependent resistivity of an 8-nm-thick LCMO membrane as a function of strain: 0% (black), 1% (blue), 2% (green), 4% (orange), and 5% (red) biaxial strain. No thickness dependence was observed between membranes of d = 4 nm and d = 8 nm (fig. S6). Inset: Double exchange interaction between two Mn sites. (C) Resistivity-temperature curves of a strained LCMO membrane (d = 4 nm, ε = 3.5%) under perpendicular magnetic field. Inset: Resistivity-temperature curves of a LCMO film (d = 4 nm) grown on an SrTiO3 (001) substrate under perpendicular magnetic field. (D) Magnetoresistance of the 4-nm-thick LCMO membrane shown in (C) at different temperatures. (E) Phase diagram of biaxially strained LCMO membranes. The phase boundaries are determined by resistive transitions during cooling curves (B = 0 T or B = 5 T with zero strain) and magnetoresistance data during increasing field sweeps (T = 5 K), acquired from membranes of two different thicknesses (circles, d = 4 nm; triangles, d = 8 nm).

In addition to the large shift in TC, we found an unexpected insulating phase emerging at high biaxial strain states (>3%) at low temperatures. The insulating state below T = 70 K can be quenched by magnetic fields with a large negative magnetoresistance (Fig. 2, C and D) and magnetic field hysteresis (fig. S7). This insulator-to-metal transition upon the application of magnetic field qualitatively resembles the field-induced melting of COO in competition with the FM-M. Similar behavior has been observed in low-bandwidth manganites (25). However, here the phase arises in a very different physical parameter space (temperature, strain, and resistivity) from prior reports of bulk crystals and epitaxially strained thin films of similar doping (see also Fig. 2C, inset) (26). On the basis of these structural and electrical studies, we constructed a phase diagram of LCMO as a function of biaxial strain and magnetic field (Fig. 2E).

In addition to the biaxial strain states, we investigated electronic transport of the LCMO membrane under different uniaxial strains from 1% to 8% (Fig. 3A and fig. S8). We first observed that the vdP resistances of two directions, parallel and perpendicular to the uniaxial strain direction, are substantially different with large resistance anisotropy up to 107 (Fig. 3B). Electrostatic simulations on the finite-size vdP geometry (fig. S9) can be used to convert the maximum resistance anisotropy to a resistivity anisotropy (~103). For such large anisotropies, the measurement is much more sensitive to the finite-size boundary conditions than the biaxial case. Therefore, we report the directly measured resistance, from which the resistivities can be deduced (21). The temperature-dependent resistances R(T) of the two different directions were measured for a series of uniaxial strain states (Fig. 3, C and D), showing the reduction of TC by increasing strain. Nonmetallic temperature dependence in resistance-temperature curves first appears in the resistance parallel to the strain (ε = 6 to 8%) and is observed in the perpendicular direction at larger strains (ε = 7 to 8%). The insulating states for high uniaxial strains (T < 150 K, ε = 7 to 8%) are largely suppressed upon the application of magnetic field and show very large magnetoresistance (Fig. 3, E and F), similar to the biaxial strain states above 3%. The phase diagram of uniaxially strained LCMO membranes based on these electrical studies (Fig. 3G) qualitatively resembles the biaxial phase diagram (Fig. 2E) with the addition of a bifurcation of the resistively measured transition along the two different directions with respect to the strain direction.

Fig. 3 Magnetotransport and phase diagram of uniaxially strained La0.7Ca0.3MnO3 membranes.

(A) Electric potential mapping of the central vdP geometry in membranes under a uniaxial strain, with 1:100 resistivity anisotropy. The boundary conditions were current nonpermeability at the edges; I+ and I represent the current source and current sink. The voltage at V is held at V = 0, and Vmax is calculated at V+. (B) Room-temperature resistances RRT (T = 290 K) in the central vdP geometry with different uniaxial strains. Open circles are resistances parallel to the strain direction; solid circles are resistances perpendicular to the strain direction. (C and D) Evolution of the temperature-dependent resistance of an 8-nm-thick LCMO membrane, parallel (C) and perpendicular (D) to the uniaxial strain of 0% (black), 1% (purple), 3% (blue), 5% (green), 7% (orange), and 8% (red). Each resistance-temperature curve is normalized by RRT and is shifted vertically for visual clarity. (E) Resistance-temperature curves of the strained LCMO membrane (vdP resistance perpendicular to the strain ε = 8%) under perpendicular magnetic field. (F) Magnetoresistance of the LCMO membrane under perpendicular magnetic field at different temperatures. (G) Phase diagram of uniaxially strained LCMO membranes. The phase boundaries are determined by resistive transitions during cooling curves (B = 0 T or B = 5 T with zero strain) and magnetoresistance data during increasing field sweeps (T = 10 K), acquired from vdP resistances parallel (open circles) and perpendicular (solid circles) to the strain direction.

We next performed density functional theory (DFT) calculations to consider the microscopic origin of the strain-induced insulating state. We first modeled LCMO using a model with ordered La3+ and Ca2+ cations (rather than a solid-solution configuration) in a ratio of 2:1 on the perovskite A-cation site to find the ground state (27). We applied both uniaxial and biaxial tensile strain up to 8%. A strain condition was not imposed for the out-of-plane lattice direction, and it was allowed to computationally relax. We then compared the ground-state energies of two phases—the FM-M phase and an antiferromagnetic insulator (AFM-I) phase with A-type ordering—at different strain states (Fig. 4A). The bulk DFT-relaxed FM-M phase was ~45 meV per formula unit (f.u.) lower in energy than the AFM-I phase, consistent with the experimental bulk phase diagram. The half-metallic behavior held for the FM-M phase throughout the examined strain level, as seen from the electronic density of states (Fig. 4B). We found that the energy difference between the two states decreases with increasing tensile strain until reaching a critical value ε* ≈ 7% (uniaxial), 3% (biaxial), at which point a FM-M to AFM-I transition occurs, in good agreement with the experimental results. Beyond this point, the AFM-I phase is stabilized and characterized by a COO insulating state (Fig. 4C) for both uniaxial and biaxial strain configurations. In the AFM-I state, ordering of Mn4+O6 and Jahn-Teller–distorted Mn3+O6 octahedra is found (Fig. 4D). By modeling various configurations for the A-site to simulate solid solutions with random La/Ca site occupancy, we found that the stripe-type COO (fig. S10) is robust to the A-site chemical distribution (21) (fig. S11). The DFT calculations confirm that the experimentally observed insulating phase under high strain is the A-type AFM-I phase with a stripe COO. For the one-third–doped LCMO, such a stripe COO was predicted with a two-dimensional model Hamiltonian that includes double-exchange and Jahn-Teller phonons (28), but different ground states were observed in epitaxial films (29, 30). Although the detailed microscopic structure remains to be investigated, it is striking that such an anisotropic state is stabilized for both uniaxial and biaxial strain.

Fig. 4 Strain stabilization of insulating LCMO.

(A) DFT total energy difference between the ferromagnetic metallic (FM-M) and antiferromagnetic insulating (AFM-I) phases with respect to uniaxial and biaxial strain in La2/3Ca1/3MnO3. Schematic (top left) shows that Q3 Jahn-Teller distortion of the MnO6 octahedra active in the AFM-I phase drives the FM-M to AFM-I transition at the critical strain value ε* indicated by the bold vertical arrows. Increasing biaxial strain increases the bandgap of the insulating phase. (B and C) Electronic density of states for LCMO at 4% biaxial strain in the FM-M (B) and AFM-I (C) phases. (D) The AFM-I state displays charge-ordered Jahn-Teller–distorted Mn3+O6 (purple) and Mn4+O6 (orange) octahedra (see also fig. S10).

The FM-M phase is stable at low-strain states because the smaller in-plane lattice constants favor reduced Q3 Jahn-Teller distortions of the MnO6 octahedra (four short and two long Mn-O bonds, shown schematically in Fig. 4A) and more uniform Mn-O-Mn bond angles (31). In contrast, the COO AFM-I exhibits inequivalent Mn4+/Mn3+ sites, forming an ordered structure controlled by the long Mn-O bond from the Q3 Jahn-Teller distortion (fig. S10). The long Mn-O bond network is staggered in an alternating manner along 〈110〉 with respect to the orthorhombic lattice vectors, in which the longer Mn-O bond is elastically favored by larger in-plane lattice constants achieved through large tensile strains in the LCMO membranes. Furthermore, under extreme strain, superexchange interactions and electron localization (from weakened orbital overlap) dominate over metallic double exchange and stabilize the AFM-I ground state, which is consistent with the observed magnetic field–induced insulator-to-metal transitions (Figs. 2C and 3E).

The ability to achieve tensile strains in a continuous manner, complementing compressive strain states set by hydrostatic pressure (9), offers a vast unexplored phase space to control atomic spacing in correlated electron systems. The example of LCMO membranes demonstrates that a macroscopic, crack-free oxide membrane can be synthesized using a lattice tunable sacrificial layer, and is applicable to a large set of complex oxide materials to which large and uniform tensile strains can be applied. The access to such extreme tensile strain states, available in nanoscale oxide membranes, offers great opportunities to vary fundamental parameters and energy scales wherever competing orders exist, which may enable theory-based design and experimental exploration of phases beyond those in bulk equilibrium materials. Beyond complex oxides, the strain approach demonstrated here can be broadly applied to strain engineering of free-standing 2D layers, including 2D van der Waals materials (32) and compound semiconductor membranes (33).

Supplementary Materials

science.sciencemag.org/content/368/6486/71/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S11

References (3744)

References and Notes

  1. See supplementary materials.
  2. Data and computational codes are available at Zenodo (doi:10.5281/zenodo.3653340).
  3. Computational codes are available at Zenodo (doi:10.5281/zenodo.3647659).
  4. Computational codes are available at Zenodo (doi:10.5281/zenodo.3648630).
Acknowledgments: We thank A. P. Mackenzie, A. Millis, and A. Pasupathy for helpful discussions. Funding: Supported by the U.S. Department of Energy, Office of Basic Energy Sciences (DOE-BES), Division of Materials Sciences and Engineering, under contract DE-AC02-76SF00515 (synthesis and measurements) and the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems Initiative through grant GBMF4415 (development of strain platform). Also supported by the Air Force Office of Scientific Research (AFOSR) Hybrid Materials MURI under award FA9550-18-1-0480 (V.H.); DOE grant DE-SC0012375 (M.G.); Army Research Office (ARO) grant W911NF-15-1-0017 (J.M.R.); and the German Science Foundation (DFG) within CRC TRR80 (project G03 and G08) (M.V. and R.P.). Calculations were performed using the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant ACI-1548562 and the CARBON Cluster at Argonne National Laboratory (DOE-BES, contract DE-AC02-06CH11357), and the MagnitUDE supercomputer at the University of Duisburg-Essen (DFG grants INST 20876/209-1 FUGG, INST20876/243-1 FUGG). Part of this work was performed at the Stanford Nano Shared Facilities (SNSF), supported by NSF award ECCS-1542152. Author contributions: S.S.H., Y.H., and H.Y.H. designed the experiment. S.S.H., B.Y.W., and D.L. synthesized materials and fabricated the devices. S.S.H. and A.V. carried out GIXRD measurements. V.H. and S.S.H. carried out mechanical and electrical simulations. M.G., M.V., R.P., and J.M.R. performed the DFT calculations and analysis of the electronic structure. S.S.H. wrote the paper with input from all co-authors. Competing interests: The authors declare no competing interests. Data and materials availability: All data presented in this paper and a finite-element calculation code are deposited at Zenodo (34). Atomic structure models used for the electronic structure calculations are available at Github and Zenodo (35, 36); additional output files are available upon request. The Vienna Ab Initio Simulation Package (VASP) is proprietary software available for purchase at www.vasp.at/.

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