Association

76 4. Results I: Single-crystalline epitaxial EuO thin films on cubic oxides
Figure 4.17.: EuO/LAO (100) in-plane and out-of-plane crystal structure determined by reciprocal
space maps. The pseudocubic lattice parameter of LAO (100) is confirmed by the asymmetric
(2 0 4) reflex both in-plane and out-of-plane (a). Close to the LAO reflex, the asymmetric EuO
(3 0 4) diffraction peak allows one to determine the lattice parameters of the EuO film (b): inplane,
EuO adapts the LAO (100) lattice spacing. The broadening (highlighted grey in c) of
the LAO (2 0 3) and EuO (3 0 4) diffraction features in reciprocal space allow to identify a small
structural inhomogeneity for LAO and an in-plane mosaicity for EuO.
(h 00) diffraction pattern. The EuO diffraction peaks are located at 2θ = f (q ⊥ ) positions
which correspond to the perpendicular lattice parameter of d ⊥ = 5.14 Å, in agreement with
the literature value of bulk EuO. A simulation to fit X-ray reflectivity of the EuO/LAO multilayer
structure (Fig. 4.16b) reveals a thickness of 16 nm, a mean roughness of the EuO surface
of only 1 Å, and a density of EuO of 8.8 g/cm 3 . This result underlines the high-quality MBE
growth of EuO yielding smooth interfaces. However, the slightly increased density of the
EuO layer (+6%) can be explained by excess Eu clusters in the film arising from the Eu-rich
distillation growth condition.
Further information regarding the crystal structure of the strained EuO thin film is obtained
from a reciprocal space mapping, a two-dimensional X-ray diffraction technique. In Fig. 4.17,
we scanned the reciprocal space around the asymmetric EuO (3 0 4) and the LAO (2 0 3)
diffraction peaks. This provides information about in-plane and out-of-plane lattice parameters
and the crystal quality in these dimensions. A sharp diffraction peak confirming the LAO
pseudo cubic lattice parameter can be identified in Fig. 4.17a, here the two features with comparable
intensity distribution originate from the two lines of the Cu Kα 1, 2 radiation of the X-
ray anode. A conversion of the reciprocal vectors to real space distances reveals the in-plane
lattice parameter of EuO as 5.39 ± 0.02 Å, in agreement with the LAO (100) lattice parameter.
The perpendicular lattice parameter of EuO is almost unchanged (d z =5.140 ± 0.010 Å).
A specific material parameter describing volume elasticity under an axial strain is the Poisson
ratio, defined as
ν = − dε trans.
dε axial
1st order
approx.
= − Δl trans.
Δl axial
= dRSM z
dxy
RSM
− d ref.
z
− d ref. xy
. (4.2)
For epitaxial EuO/LAO (100) which reveals lateral tensile strain, we evaluate a Poisson ratio
The conversion between reciprocal coordinates and the real space is shown in Ch. 3.4.2. A well-explained
example of RSM to analyze effects of strain and relaxation is published in Liu and Canonico (2004). 165