supplemental material forAsymmetric orbital-lattice interactions in ultra-thin correlated oxide films

J. Chakhalian,1, ∗ J.M. Rondinelli,2, 3 Jian Liu,1, 4 B.A. Gray,1 M. Kareev,1 E.J.

Moon,1 N. Prasai,5 J.L. Cohn,5 M. Varela,6 I.C. Tung,7 M.J. Bedzyk,7 S.G.

Altendorf,8 F. Strigari,8 B. Dabrowski,9 L.H. Tjeng,10 P.J. Ryan,3 and J.W. Freeland3

1Department of Physics, University of Arkansas, Fayetteville, Arkansas 70701, USA2Department of Materials Science & Engineering,

Drexel University, Philadelphia, Pennsylvania 19104, USA3Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

4Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA5Department of Physics, University of Miami, Coral Gables, Florida, 33124, USA

6Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA7Materials Science and Engineering, Northwestern University, Evanston, Illinois, 60208, USA

8II. Physikalisches Institut, Universitat zu Koln, Zulpicher Str. 77, 50937 Koln, Germany9Department of Physics, Northern Illinois University, Dekalb, Illinois 60115, USA

10Max Planck Institute for Chemical Physics of Solids, Nothnitzerstr. 40, 01187 Dresden, Germany(Dated: September 3, 2011)

PACS numbers: 73.20.-r

2

SAMPLE GROWTH AND STRUCTURAL CHARACTERIZATION

We show in Figure 1a a representative time-dependent RHEED specular intensity (RSI) plot for LaNiO3 growthon a SrTiO3 substrate prepared by our recently developed chemical wet-etch procedure [1]. The full recovery of RSIis characteristic of high precision LBL growth and found after deposition of each unit-cell layer. Smooth surfacemorphology is also evident from the well-defined spots of the (00) specular and (01) and (01) off-specular reflectionswith characteristic streaks in the resulting RHEED pattern [Fig. 1a(inset)]. Atomic force microscopy (AFM) scansover a 2×2 µm2 area (Figure 1b) indicate the sample surface is atomically flat with well-preserved vicinal steps andan rms surface roughness of < 75 pm. Reciprocal space maps Figure 1c-d show that the films are coherent and fullystrained to the substrate.

All the films are oriented along the (001) direction of pseudocube with respect to the substrates with the latticeparameters as follows: LAO - 3.79 A; SLGO - 3.84 A; STO - 3.91 A; and GSO - 3.97 A.

SrTiO3 (001)

LaNiO3

interface

1.0E4

1.3E5

103104105106107108109

1010

Inte

nsity

(arb

. uni

ts)

2.22.12.01.91.8L (STO r.l.u.)

SrTiO3 (002)

Film (002)

SL -1

SL -2

N = 5 u.c.

50

4540

3530

2520

15

RHEE

D In

tens

ity (a

.u.)

900800700600Time (s)

LNO1

LNO1

0

LAO1

LAO3

0.0

2.4nm

2µm2µm

Ra=75pm(A)

(B)

(C) (D)

Figure 4: Morphology and general characterization

14

(a) (b)

(c)(d)

4000

3500

3000

2500

2000

1500

1000

RHEE

D In

tens

ity (a

.u.)

550500450400350Time (sec)

SrTiO3 (001)

LaNiO3

interface

1.0E4

1.3E5

103104105106107108109

1010

Inte

nsity

(arb

. uni

ts)

2.22.12.01.91.8L (STO r.l.u.)

SrTiO3 (002)

Film (002)

SL -1

SL -2

N = 5 u.c.

50

4540

3530

2520

15

RHEE

D In

tens

ity (

a.u.

)

900800700600Time (s)

LNO1

LNO1

0

LAO1

LAO3

0.0

2.4nm

2µm2µm

Ra=75pm(A)

(B)

(C) (D)

Figure 4: Morphology and general characterization

14

(a) (b)

(c)(d)

4000

3500

3000

2500

2000

1500

1000

RHEE

D In

tens

ity (a

.u.)

550500450400350Time (sec)

LNO

STO

a

b

c

e

d

c

FIG. 1. Surface morphology and structural characterization of the LNO films. a, Time-dependent RHEED specular intensity(RSI) shows the full recovery of RSI and is characteristic of the high-quality layer-by-layer (LBL) growth of each unit-cell layer[indicated by the shaded (grey) area]. Smooth surface morphology is evident from the well-defined spots of the specular andoff-specular reflections (inset) with a characteristic of the quality of the surface streaks. b, AFM imaging confirms that thesample surface is atomically flat with well-preserved vicinal steps. c-d, Reciprocal space maps of the (222)LNO film reflectionson both the LAO(001) and STO(001) substrate surfaces. The measurements are with respect to the substrate lattice parametersand thus in-plane alignment of the reflections at the integer positions indicates fully lattice matched growth with completelateral strain of the LNO films.

3

X-ray Diffraction

Figure 2 shows x-ray diffraction measurements of LaNiO3 thin films grown on SrTiO3 (001)- and LaAlO3 (001)-oriented substrates. X-ray diffraction measurements are performed with a high-resolution Rigaku ATX-G diffrac-tometer using the Cu Kα1 radiation. Figures 2a-b show the θ-2θ scans through the (002) symmetric reflections offilms and substrates. The x-ray diffraction measurements indicate that the LaNiO3 films have crystallinity and (001)oriented on both substrates. The out-of-plan lattice spacing of the film are found by fitting to the curves and yields3.838 A on SrTiO3 and 3.899 A on LaAlO3 substrates. The R3c bulk value is 3.84 A; The primitive cell of bulkLaNiO3 is rhombohedral, with the lattice parameter a=5.46 A, and rhombohedral angle α=60.49o. The presence ofPendellosung fringes seen in the SrTiO3 case near the Bragg peak attest to the atomically smooth interface/surface.

100

101

102

103

104

105

106

107

Inte

nsity

3.83.63.43.23.02.8

Q(Å-1)

LaNiO3 (002)

LaAlO3 (002)

100

101

102

103

104

105

106

107

Inte

nsity

3.83.63.43.23.02.8

Q (Å-1)

SrTiO3 (002)

LaNiO3 (002)

a

b

FIG. 2. X-ray diffraction measurements of LaNiO3 thin films grown on a, SrTiO3 (001) and b, LaAlO3 (001) substrates.

4

ELECTRON DIFFRACTION PATTERNS

We compare simulated electron diffraction patterns for bulk rhombohedral LaNiO3 with our preliminary experimen-tal convergent beam electron nano-diffraction pattern of LaNiO3 grown on SrTiO3. Our simulations were generatedwith the commercially available JEMS software[2] using the experimental R3c structure.[3] We perform electron nano-diffraction with an electron beam focused to ∼1 nm on a the LNO/STO sample prepared in a cross-sectional geometryusing conventional methods—grinding, dimpling, and Ar-ion milling. Electron nano-diffraction patterns and annulardark field (ADF) images are acquired using an aberration corrected Nion UltraSTEM microscope operated at 100 kV.We show the resulting diffraction pattern in Figure 3; it reveals the presence of strong half-order Bragg reflections(indicated by arrows) which are forbidden in bulk LNO (overlay). These additional reflections indicate that LaNiO3

under tensile strain has an altered atomic structure with lower symmetry than that found in the bulk rhombohedralmaterial. It also strongly suggests that epitaxial strain stabilizes an atomic configuration that is absent in the bulkequilibrium phase space. Further experiments along additional zone axes are planned to deterministically refine thefilm structure.

LNO on STO[010] zone-axis

Simulated bulk R3c structure

FIG. 3. Simulated and experimental convergent beam electron diffraction (CBED) patterns of bi-axial strained LaNiO3 films.Electron nano-diffraction pattern on a cross-sectional LNO film on SrTiO3 taken along (010) zone-axis and indexed accordingto R3c space group (overlay). The arrows indicate the additional Bragg reflections (diffues discs) absent in bulk LNO butpresent in the LNO film under tensile strain due to the lower symmetry structure.

5

X-RAY PHOTOEMISSION MEASUREMENTS.

The photoemission spectra were recorded at room temperature in a spectrometer equipped with a VG-ScientaR3000 electron energy analyzer and a Vacuum Generators twin crystal monochromatized Al-Kα (hν = 1486.6 eV)source. The overall energy resolution was set to 0.35 eV, as determined using the Fermi cut-off of a Ag referencewhich was also taken as the zero of the binding energy scale. The pressure in the spectrometer chamber was in the low10−10 mbar range. All samples are cleaned in-situ to remove surface contaminants at 100◦C prior to data acquisitionusing an Oxford TC-50 oxygen radical source.

ΔE∼0.35eV2000

1500

1000

500

0

Inte

nsity

(a.u

.)

536 532 528Energy (eV)

O core level

on LAO on STO

FIG. 4. Core level O 1s XPS spectra of LNO on STO (dark, blue line) and LAO (light, red line); the relative energy positionshift of the O 1s data on the two films at 528.2 and 528.5 eV indicates a strain-induced change in the Madelung energy of thetwo films.

6

DENSITY FUNCTIONAL CALCULATION DETAILS

Effect of epitaxial strain and elastic boundary conditions

In our calculations we do not explicitly simulate the substrates, but the symmetry reduction imposed by the elasticconstraint of equal in-plane lattice parameters on the bulk R3c structure is included by optimizing the internal degreesof freedom within a monoclinic (20-atom) unit cell (space group C2/c). The epitaxial constraint is set by fixing theNi–Ni distances in the (001) plane to match those of the experimental substrate. We examined twelve symmetryallowed combinations of NiO6 octahedral structural distortions and rotational patterns to identify the lowest energyatomic configuration and obtained equilibrium ground state structures through full structural optimization. Theresults are given in Tables I and II for homoepitaxial thin films of LaNiO3 on LaAlO3 and SrTiO3, respectively.

Atom x y z

La 0 0.248 0.25

Ni 0.25 0.25 0

O(1) 0 0.774 0.25

O(2) 0.260 0.0383 0.298

TABLE I. First-principles calculated crystallographic data for the experimental nickelate film on LaAlO3. The space groupis C2/c (#15), with a = 9.415, b = c = 5.536 A, and a monoclinic angle of 124.7◦. We find the in-plane and out-of-planeNi–O–Ni bond angles to be 162.1◦ and 172.5◦, respectively, compared to the experimental 1.5 K bulk rhombohedral structurewith uniform 164.8◦ Ni–O–Ni bond angles.[3]

Atom x y z

La 0.255 0.473 0.25

Ni(1) 0.5 0 0.50

Ni(2) 0 0 0

O(1) 0.183 0.010 0.245

O(2) 0.254 0.731 0.0339

O(3) 0.302 0.221 0.0334

TABLE II. First-principles calculated crystallographic data for the experimental nickelate film on SrTiO3. The space group isP21/c (#14), with a = b = 5.515, and c = 9.439 A, and a monoclinic angle of 125.8◦. We find the in-plane and out-of-planeNi–O–Ni bond angles to be 161.6◦ and 159.2◦, respectively, compared to the experimental 1.5 K bulk rhombohedral structurewith uniform 164.8◦ Ni–O–Ni bond angles.[3]

7

Strain effect on the electronic structure

To isolate the effect of strain on the electronic structure, we carry out structural relaxations about the theoreticalLSDA+U volume for experimentally accessible bi-axial strain states by optimizing the out-of-plane lattice parameterc and the internal atomic coordinates at each strain value. We also restrict the crystallography symmetry such thatall Ni sites are forced to be equivalent to isolate the intrinsic contribution of strain on the atomic structure. We thencompute the ground state electronic band structure for intermediate strain values ranging from -1.6% to 2.2%.

0 0.5 1 1.5 2energy (eV)

DO

S (a

rb. u

nits

)

-171

-170

-169

E M (e

V / f

.u.)

-19.6

-19.4

-19.2

-19.0

O 2s l

evel

(eV)

-1.6

-1.1

-0.54

0.00

0.50

0.77

1.03

1.30

1.57

1.83

2.10

a

c

b

0.16 eV / %

0.81 eV / %

-2 -1 0 1 2strain (%)

FIG. 5. Epitaxial strain evolution of the calculated electronic and atomic structure of thin film LaNiO3 with strain. a, Theunoccupied total densities of state from the Fermi level at 0 eV to the top of the hybridized oxygen and nickel eg band near2.5 eV with respect to the strain state (in % units). The curves are arbitrarily shifted along the y-axis, and the broken lineat ∼2 eV denotes the valence band edge for the unstrained film (0.00%). Evolution of the oxygen 2s state and the Madelungenergy EM with strain are shown in b, and c. The discontinuity on going from negative to positive strain at ∼0.50% is due toa transition of the predominate octahedral rotation axis from one normal to the epitaxial plane to one lying in the plane.

We find that compressive (tensile) strain leads to an enhancement (reduction) in the conduction bandwidth (Figure5a). This can be qualitatively understood as a result of the change in the out-of-plane Ni–O–Ni bond angles withstrain; it is also consistent with the previously reported structural studies on similar films [4] which find that withincreasing tensile strain the out-of-plane bond angle deviates more away from 180◦. We also show in Figure 5bthe change in Madelung stabilization energy with respect to strain and find a ∼0.81 eV per percent strain (performula unit). This order of magnitude change in the Madelung energy suggests that strain-induced modificationsof the Madelung energy should be experimentally detectable with core-level photoemission. Figure 5c also shows theevolution of covalency as a function of the change in the O 2s level position with applied strain. While this datacannot be directly compared to core-level photoemission, they strongly corroborate the strain-induced modification inthe Ni–O covalency. This calculation yields the value of 160 meV/% in agreement with the experimental data, albeitreduced from that determined using solely the Madelung potentials.

Madelung energy calculations

The Madelung energies are computed using the atomic positions from first-principles structural relaxations usinga primitive “monoclinic” 20 atom unit cell (as in Table I) for each given strain state. The site potentials φi were

8

calculated as sums over all of the ions j as

φi =∑j

qi4πε0rij

,

where we have assumed the charges qi to be the formal ionic ones for each atom: La (3+), Ni (3+) and O (2−). Thesummation is carried out over all ions (i 6= j) for distances rij using both direct and reciprocal space methods.

We use the site potentials to calculate the Madelung energy as

Em =1

2

∑i

φiqiwi ,

where wi is a normalization factor that depends on the number of symmetry equivalent atomic positions at site i inthe unit cell.

We carried out the calculations using the Fourier method implemented in the madel program available in thevesta software package [5]. The direct sums are computed using an ionic sphere with radius s set to 1.2 A for thecharge-density distributions ρ(r) given by

ρ(r) = ρ0[1− 6(r/s)2 + 8(r/s)3 − 3(r/s)4] .

The reciprocal space summations are calculated with Fourier coefficients taken up to 4 A−1; we also verified conver-gence of the Madelung energies by variation of these parameters.

∗ jchakhal@uark.edu[1] M. Kareev, S. Prosandeev, J. Liu, C. Gan, A. Kareev, J. W. Freeland, M. Xiao, and J. Chakhalian, Appl. Phys. Lett. 93,

061909 (2008).[2] JEMS is available from P. Stadelmann, CIME-EPFL, Lausanne, Switzerland at http://cime.epfl.ch.[3] J. L. Garcıa-Munoz, J. Rodrıguez-Carvajal, P. Lacorre, and J. B. Torrance, Phys. Rev. B 46, 4414 (1992).[4] S. J. May, J.-W. Kim, J. M. Rondinelli, E. Karapetrova, N. A. Spaldin, A. Bhattacharya, and P. J. Ryan, Phys. Rev. B

82, 014110 (2010).[5] K. Momma and F. Izumi, Journal of Applied Crystallography 41, 653 (2008).