Association

46 3. Experimental details
is moved through the ring (Fig. 3.10a), which induces a ring current. At the same time, the
magnetic flux through the ring has to result in an integer multiple of Φ 0 . To fulfill this condition,
the Josephson contact generates voltage oscillations with the time period of one ΔΦ 0
(Fig. 3.10b, c). These voltage oscillations are detected by an RF coil and further processed (see
Fig. 3.10).
In practice, when ˜m(T ) denotes a measured magnetization, ˜m off the magnetization offset from
zero when only a vanishing signal is expected (i. e. at T ≫ T C ), ˜m 0 = m(T →0) the measured
saturation magnetization, and m theo the theoretically expected magnetization, then the magnetic
moment m in μ B per magnetic formula unit can be expressed as
m( ˜m(T )) = ˜m(T ) − ˜m off
fμ B
d = ˜m 0 − ˜m off
fμ B m theo
· Vcell
A .
· Vcell
, or (3.6a)
Ad
(3.6b)
Here, μ B denotes Bohr’s magneton, V cell = a 3 the volume of the cubic unit cell of the magnetic
oxide, f the number of magnetic units per cubic cell, A the area and d the thickness of the
magnetic thin film. Application of eq. (3.6a) with known geometry of the magnetic thin film
reveals the specific magnetic moment m. Alternatively, by assuming an optimum sample
with reference magnetization ˜m 0 = m theo , the thin film thickness d can be obtained from eq.
(3.6b).
In this work, a Quantum Design MPMS XL SQUID magnetometer is used to determine the
magnetic properties of magnetic oxide thin films. The magnetization m(T ) is recorded as
field warm curve at a minimum saturation field (usually ∼100 Oe), which we determined by
hysteresis measurements for every thin film sample.
3.4.2. X-ray diffraction methods (XRD, XRR, RSM)
Based on the Bragg equation nλ =2d sinθ, X-ray diffraction (XRD) is a versatile technique
which allows for the determination of structural properties such as the distance between
crystal lattice planes, the thickness of layers, interface and surface roughness, texturing, and
mosaicity, to mention the most common properties.
In a simple Bragg-Brentano setup, in which one axis (2θ) is moved in order that the sample
surface is always at ω = θ, a standard 2θ–ω diffractogram is obtained (Fig. 3.11). Here, only
crystallites oriented parallel to the surface contribute to the diffraction peak. The observable
peaks directly arise from the diffraction after Bragg’s law, and the exact peak position on the
2θ scale allows to calculate the distance between diffracting planes (c: out-of-plane lattice
parameter). The width of those peaks provides information about the orientation distribution
of the crystallites, i. e. the mosaicity. Thus, already simple XRD diffractograms provide
information about orientation and quality of thin films with good crystallinity. 135
Using small angle scattering in the 2θ–ω setup, also known as X-ray reflectivity (XRR), a
simulation of Kiessig fringes using the Parratt model 136 allows for the determination of the
thickness of several layers from roughly two up to hundreds of nanometers. Moreover, from
the damping of these fringes, the interface and surface roughness can be modeled.