Supplementary Information
Spatially and momentum resolved energy electron loss spectra from an ultra-thin
PrNiO3 layer.
M. K. Kinyanjui 1a,, G Benner 2, G. Pavia 2, F. Boucher 3, H. –U. Habermeier 4, B.
Keimer 4, U. Kaiser 1
1
University of Ulm, Central Facility of Electron Microscopy, Albert-Einstein Allee 11,
89081, Ulm, Germany
2
a
Carl Zeiss Microscopy GmbH, Carl-Zeiss-Str. 22, 73447 Oberkochen, Germany
3
Institut des Matériaux Jean Rouxel, UMR6502, CNRS - Université de Nantes, 2 rue de
la Houssinière, B.P.32229, 44322 Nantes cedex France
4
Max Planck Institute for Solid State Research, Heisenbergstrasse 1, D-70579 Stuttgart,
Germany
Corresponding author, michael.kinyanjui@uni-ulm.de
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1. Experimental Details
1.1. Determination of momentum resolution
With the nano beam electron diffraction (NBED) approach presented in this paper
momentum resolutions in the range 0.1- 0.5 Å-1 could be achieved. In the experiment, the
momentum resolution was determining by fitting the full width at half maximum
(FWHM) of Bragg diffraction spots in the ω-q map.
FIG. S1 (a) ω-q map for LaNiO3 layer obtained using the 200, -200 spots
(b)Momentum resolution determination using a 200 pseudocubic reflection of the
LaNiO3 layer The FWHM is determined to be ~ 0.23 Å-1.
Figures S1, S2, S3 show the (a) ω-q map (b) momentum resolution fitting using the 200
spot, 002 spot, and 110 spots for the LaNiO3 film, PrNiO3 film and LaSrAlO4 substrate
respectively. The momentum resolutions presented in Figs. S1, S2, and S3 are 0.23 Å-1,
0.35 Å-1, and 0.33 Å-1. These resolution values were obtained from different experiments
and are used to show that a range of momentum resolutions can be obtained.
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FIG. S2 (a) ω-q map for PrNiO3 layer obtained using the 002, 00-2 spots (b)
Momentum resolution determination using a 002 reflection of the PrNiO3 layer The
FWHM is determined to be ~ 0.35 Å-1.
FIG. S3 (a) ω-q map for LaSrAlO4 substrate obtained using the 011, 0-1-1 spots (b)
Momentum resolution determination using a 011 reflection of the LaSrAlO4
substrate The FWHM is determined to be ~ 0.33 Å-1.
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2. Momentum resolved EELS from a 70 nm thick LaNiO3
In Figure S4 we demonstrate that using the NBED approach, momentum resolved spectra
obtained can be obtained at different positions on a thin film. This is done on a 70 nm
thick LaNiO3 film grown on LaSrAlO4. Figure S4 (a) displays a Z-contrast image of the
LaNiO3 layer where 1, 2, and 3 represent respectively, the positions in LaSrAlO4
substrate, LaSrAlO4-LaNiO3 interface and LaNiO3 bulk where MREELS spectra were
acquired.
FIG. S4 (a) A Z-contrast TEM image of the LaNiO3 layer and the LaSrAlO4
substrate (b) A nano-beam electron diffraction pattern of the LaNiO3 layer in the
[100] orientation. The central spot (000) is marked with a dotted circle. Diffraction
spots marked (i) and (ii) are the (002) and (022) diffraction spots in the LaNiO3
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pseudo-cubic orientation. Momentum resolved EELS spectra showing energy loss
(horizontal axis) as a function of momentum transfer q (vertical axis) for (c)
LaSrAlO4 substrate bulk // [002] direction (d) LaSrAlO4 - LaNiO3 interface // [002]
direction (e) LaNiO3 bulk // [002] direction (f) LaNiO3 bulk // [022] direction
A representative nano-beam electron diffraction pattern obtained from the LaNiO3 film
(acquired at position 3 in Fig. S4(a)) is shown in Fig. S4 (b). The diffraction spots
marked with solid circle and dotted circle correspond to the (002) and (022) diffraction
spots respectively. The momentum resolved EELS spectra (ω-q map) parallel to [002] are
displayed in Figs. S4 (c) - (e) for the LaSrAlO4 substrate, LaSrAlO4-LaNiO3 interface
and LaNiO3 bulk respectively. The intensity map for LaNiO3 bulk parallel to [022] is
displayed in Fig. S4(f).
FIG. S5 (a) EELS spectra at q~ 0 Å-1obtained from (a) bulk PrNiO3 (12 nm) (b))
surface PrNiO3 film (c) LaNiO3 (70 nm) and (d) LaSrAlO4 substrate.
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Figure S5 displays EELS spectra at q~ 0 Å-1 obtained from (a) bulk PrNiO3 (12 nm) (b)
surface of a PrNiO3 film (c) bulk LaNiO3 (70 nm) and (d) LaSrAlO4 substrate. For
spectra from the PrNiO3 surface, the intensity of peaks A, B and E is increased compared
to bulk PrNiO3. In LaNiO3 peak feature A* (see Fig. S5 (c)) is shifted ~ 1 eV from the
peak position A (Fig. S5 (a)). In the spectra from the LaSrAlO4 substrate peak A is
missing and that the peak shoulder B is more prominent than in PrNiO3 and LaNiO3. The
spectra at ΔE ≥ 10 eV are very similar for LaNiO3, and PrNiO3 films as well as LaSrAlO4
substrate
3. Regarding the splitting of plasmon peak peak F in the spectra along q// 001 at
high momentum
From the diffraction pattern obtained from the [110] oriented domain we placed the slit
along the 002 diffraction spot. We observed the forbidden 001 type reflection in the
diffraction pattern. The interplanar distance for 002 is 3.81 Å the calculated q is therefore
(2*pi/3.81) which gives 1.649 Å-1, the interplanar distance for the forbidden 001 is 7.61
Å the calculated q is therefore 0.82 Å-1. For a domain oriented parallel to the [010]
direction we placed the slit along the 200 spots. The interplanar distance for the 200 spots
is 2.7073 Å the calculated q is therefore (2*pi/2.7073) which gives 2.31 Å-1. Since we
probed MREELS between 0 <q<0.8Å-1 We probed the whole BZ along q// 001 direction
and ~ 60% along q//100 therefore multiple scattering is more likely for spectra obtained
along q//001.
4. Electronic structure calculations
To assist in the interpretation of the experiemental results, electronic structure and
theoretical spectra for |q| → 0 were calculated using the full potential linearized
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augmented plane wave (FLAPW) approximation as implemented in the WIEN2k code.
We used muffin tin radii of 2.45 au, 1.96 au, and 1.68 au, for Pr, Ni and O atoms
respectively. The parameter RMT∗Kmax was set to 8.5, where RMT is the smallest atomic
sphere radius in the unit cell and Kmax is the magnitude of the largest K vector. For the
self consistency procedure, the number of k-points in the irreducible part of the Brillouin
zone (IBZ) was 1152 with a (23×16×23) full k-point mesh. In order to treat the effects of
local Coulomb interactions due to Pr 4f and Ni 3d electrons, the GGA + U method was
used. The value of the effective Coulomb parameter was set to Ueff = 4 eV for Ni 3d and
7 eV for Pr 4f electrons.1, 2, 3 The dielectric tensor was calculated using the Optic package
included in the WIEN2k code.4 To calculate the optical spectra a denser (32×23×32) kpoint mesh was used, leading to 3072 k-points in the IBZ
Frequency dependent dielectric calculations included local field effect have been
carried out with the ab initio total energy and molecular dynamics program VASP5
(Vienna
ab
initio
simulation
package).
Projector
augmented-wave
(PAW)
pseudopotentials were used. Standard PAW was chosen for O (PAW PBE O: 2s22p4)
and semicore states were included for Ni (PAW PBENi_pv: 3p64s23d8) and Pr
(PAW_PBE: 5s25p66s24f3). The self-consistency on electronic density was obtained with
a 600-eV plane-wave energy cutoff and a (6×4×6) Monkhorst-Pack k-point mesh [144 k
points in the irreducible part of the Brillouin zone (IBZ)]. The frequency-dependent
dielectric function (DF) including LFE were obtained by using the GW routines
implemented in the VASP. The microscopic DF was calculated at the RPA level by
evaluating the microscopic polarizability matrices at q→0. The frequency dependence
was evaluated up to 65 eV, Kohn-Sham wave functions being evaluated for many
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additional empty bands
(306 bands above the Fermi level). The macroscopic DF
including LFE at the RPA level was obtained from the inversion of the full microscopic
dielectric tensors, taking into account the range dependencies with respect to reciprocallattice G vectors. Converged LFE were obtained with a set of G vectors defined by a
plane-wave energy cutoff of 50 eV, i.e., 95 G vectors.
To determine the effects of sample geometry, thickness, surface and accelerating
voltage of the TEM instrument on the EELS spectra; relativistic EELS calculations based
on Kroeger formalism were used where the required dielectrical constants were obtained
from our DFT calculations.
4.1. Density of states
Fig. S6 presents the calculated density of states for orthorhombic PrNiO3. The energy
states at the Fermi level are dominated by hybridized Ni-3d and O-2p states. Pr-f states
are located above between 3 eV-8 eV. The deeper lying states at 15-20 eV below the
Fermi level are dominated by O-2s states and Pr-5s states. Ni-sp states are found around
10 eV from the Fermi level. The lowest interband transitions are from the bands at/near
the Fermi level to the bands with mainly 3d character at the bottom of the valence band.
Based on density of states calculations for PrNiO3, the energy states at the Fermi level are
dominated by hybridized Ni-3d and O-2p states. Pr-f states are located between 3 eV-8
eV. The deeper lying states at 15-20 eV below the Fermi level are dominated by O-2s
states and Pr-5s states. Ni-sp states are found around 10 eV from the Fermi level.
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FIG. S6. Density of states for orthorhombic PrNiO3
5. Bandstructure and nature and origin of observed interband transitions
Fig. S7 presents the calculated band structure for orthorhombic PrNiO3. The size
of the circle symbols shows the Ni 3d character of each band. The band structure can be
divided into four energy regions each comprised of a group of bands. The first energy
region around -15 eV below the Fermi level, the second energy region is found between 5 eV and Fermi level, the third region is found between the Fermi level and 3 eV, and the
fourth energy region above 3 eV.
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FIG. S7 Band structure for orthorhombic PrNiO3 along different symmetry
directions where bands 40, 68, 72, 92, 93, 97, 132 and 138 are indicated. The size of
the solid spheres shows the Ni 3d character of each band.
We have highlighted several bands as representative of each energy region. These
are band 40 in the first energy region, bands 68, 72, 83 in the second energy region,
bands 92 and 93 in the third energy region, and bands 132 and 138 in the fourth energy
region. Based on this analysis bands 40 has mainly a O 2s, bands 68/72 have mainly a O
2p character, and band 83, 92, 93 show mainly Ni 3d character. In Figs. S8(a) - (d) we
display the calculated calculated ε2zz, energy loss function, and various partial ε2zz
calculated for interband transitions from bands 40, 68, 72, 83 to bands 92, 93, 97, 132 and
138 respectively. This is possible since we can decompose the calculated ε2 function back
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into the components from which it was calculated. In this case we can decompose the ε2
function into contribution from a pair of valence and conduction bands.
FIG. S8 Comparison of calculated energy loss function (dotted curve), ε2(solid
curve) and partial ε2 curves for interband transitions from (a) band 83 (b) band 72
(c) band 68 (d) band 40 to bands 92, 93, 97, 132 and 138
The lowest interband transitions are from the bands at/near the Fermi level (bands 83 to
93 and 92 for example) to the bands with mainly 3d character at the bottom of the
valence band. These transitions make contributions to peaks found at positions A and B
in the experimental spectra. Transitions from the lower bands with mainly O 2p character
are responsible for the peak features observed at higher energy losses.This is observed for
example by the contribution of the interband transition 72 to 132 to the peak feature D.
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Interband transitions from the deep lying states such as from Band 40 which are mainly O
s states contribute to the peak E.
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