# Non-destructive characterisation of dopant spatial distribution in cuprate
superconductors

A.-E. Ţuţueanu  Institute Max von Laue Paul Langevin, 38042 Grenoble, France
M. Sales  K. L. Eliasen  Glass and Time, IMFUFA, Department of Science and
Environment, Roskilde University, DK-4000 Roskilde, Denmark  Nanoscience
Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen Ø,
Denmark  M.-E. Lǎcǎtuşu  Department of Energy Conversion and Storage,
Technical University of Denmark, 2800 Kgs. Lyngby, Denmark  Nanoscience
Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen Ø,
Denmark  J.-C. Grivel  Department of Energy Conversion and Storage, Technical
University of Denmark, 2800 Kgs. Lyngby, Denmark  N. Kardjilov  Institute of
Applied Materials, Helmholtz-Zentrum Berlin, 14109 Berlin, Germany  I. Manke
Institute of Applied Materials, Helmholtz-Zentrum Berlin, 14109 Berlin,
Germany  M. Krzyzagorski  Institute of Applied Materials, Helmholtz-Zentrum
Berlin, 14109 Berlin, Germany  Y. Sassa  Department of Physics, Chalmers
University of Technology, SE-412 96 Göteborg, Sweden  M. S. Andersson
Department of Engineering Sciences, Uppsala University, 751 21 Uppsala, Sweden
Department of Chemistry and Chemical Engineering, Chalmers University of
Technology, 412 96 Göteborg, Sweden  S. Schmidt  Department of Physics,
Technical University of Denmark, 2800 Kgs. Lyngby, Denmark  K. Lefmann
Nanoscience Center, Niels Bohr Institute, University of Copenhagen, 2100
Copenhagen Ø, Denmark

###### Abstract

Proper characterisation of investigated samples is vital when studying
superconductivity as impurities and doping inhomogeneities can affect the
physical properties of the measured system. We present a method where a
polarised neutron imaging setup utilises the precession of spin-polarised
neutrons in the presence of a trapped field in the superconducting sample to
spatially map out the critical temperature for the phase transition between
superconducting and non-superconducting states. We demonstrate this method on
a superconducting crystal of the prototypical high-temperature superconductor
(La,Sr)2CuO4. The results, which are backed up by complementary magnetic
susceptibility measurements, show that the method is able to resolve minor
variations in the transition temperature across the length of the LSCO
crystal, caused by inhomogeneities in strontium doping.

##  1 Introduction

More than 30 years after Bednorz and Müller’s discovery of superconductivity
(SC) at temperatures above 30 K [1], the nature of these unconventional or
high-temperature superconductors (HTSC) is still to be understood. Unlike
conventional superconductors, where the electron pairing mechanism is well
described through the theory put forward by Bardeen, Cooper and Schrieffer
(BCS) [2], the pairing mechanism in the unconventional HTSC remains an
unresolved question to this day. In recent years, increasing amounts of
evidence points to the interplay between magnetism and superconductivity as a
key factor in the emergence of the latter [3]. One of the most widely used
methods of studying highly correlated electron systems, and in particular
intertwined electronic orders, is neutron scattering. Especially when
investigating spin density wave order and the related fluctuations in cuprate
superconductors, neutron scattering has played a major part in revealing the
nature of their relationship with SC [4, 5, 6].

One of the many advantages of using neutrons as a probe is their charge
neutrality, which makes them interact rather weakly with most matter [7], in
contrast with, for example, X-rays. This allows the probing of the entire bulk
of the sample in different environments such as magnets, pressure cells,
cryostats or furnaces. However, the drawback is that, in order to measure weak
signals, samples of large masses are needed during experiments. When it comes
to cuprate superconductors, the growth of large single crystals is not a
trivial task. On top of that, due to the fact that the intrinsic properties of
these materials are under scrutiny, the use of high quality and purity samples
is a prerequisite as the analysed physical properties can be drastically
affected by defects, impurities or inhomogeneities. This has increased the
need for non-destructive characterisation methods which are able to accurately
determine the physical properties of the entire bulk of the sample. One such
property is the doping concentration, a parameter extremely important in
defining the phase diagram of the compound, since it has direct impact on the
superconducting properties [8].

In this paper, we demonstrate the use of polarised neutron imaging [9, 10, 11]
as a non-destructive method for determining the distribution of the
superconducting critical temperature (T${}_{\text{C}}$) along the length of a
HTSC sample, which is in turn related to the doping concentration
distribution. Our sample is the prototypical cuprate HTSC La2-xSrxCuO4 (LSCO).
With this method we were able to detect an inhomogeneous distribution of the
dopant throughout the sample. In contrast, when performing standard magnetic
susceptibility measurements only small sample pieces are used, usually cut
from only one side of the crystal, thus the result cannot be considered
representative for the entire bulk. By measuring magnetic susceptibility on
pieces originating from both ends of the main single crystal we were able to
confirm the T${}_{\text{C}}$ difference, but the precise Sr concentration at
each position in the sample went undetected.

##  2 The superconducting sample and its inhomogeneity level

The sample used throughout this study is a cylindrically shaped (17.9 mm
height, 4.75 mm diameter and $\sim$5 g mass) non-annealed LSCO sample with
nominal Sr doping x = 0.08. The crystal has been grown using the Travelling
Solvent Floating Zone technique (TSFZ) [12] at Department of Energy Conversion
and Storage, Technical University of Denmark. In the field of cuprates
superconductors the TSFZ method is preferred to other procedures, such as the
flux method or the Czochralski method, for a number of reasons. Firstly, the
crystallisation takes place inside a mirror furnace thus preventing
contamination which might arise from the chemical reaction between crucibles
and the melt [13]. As shown in Figure 1, the polycrystalline feed rod together
with the solvent pill (which acts as a promoter of the molten zone) are
vertically melted by very powerful halogen lamps. After a stable molten zone
has been achieved, the lamps are being translated upwards (or the feed rod
downwards) allowing the material to solidify and, if the right thermodynamic
conditions are achieved, crystallise into a single crystal phase. At the same
time, TSFZ is the only of the three above-mentioned techniques which permits
the growth of centimeter-size single crystals of compounds that melt
incongruently [14]. One of the disadvantages that might arise from using this
method to synthesise LSCO samples in particular is the lack of compositional
homogeneity of the melt throughout the growth process. This combined with the
fact that the Sr atoms are fixed after crystallisation, unlike compounds with
mobile dopants such as oxygen doped La2CuO4+y, results in heterogeneous
samples [15]. Because it is impossible to monitor or control the dopant
concentration during the growth, it is important to characterise the entire
bulk of the sample before proceeding to draw conclusions on the fundamental
properties of this family of superconductors.

Figure 1: Images from inside the mirror furnace. Left: Initial configuration
showing the three main components, the feed and seed rods, the solvent pill,
and the bright light radiating from the halogen lamps. Right: Snapshot taken
during a successful growth picturing the molten zone and the solidified single
crystal material.

There are numerous ways to determine the doping concentration of a LSCO
sample, some of the most widely used ones being measurements of magnetic
susceptibility [16], electrical resistivity [17], heat capacity [18] and of
the structural phase transition between the high temperature tetragonal phase
and the low temperature orthorhombic one by means of elastic neutron
scattering [19]. In order to test the doping homogeneity of our crystal, we
have performed temperature dependent magnetic susceptibility measurements
using a Quantum Design MPMS SQUID magnetometer. The set-up was used in DC
magnetic measurements mode where the magnetic moment of the sample is
determined from the local changes, induced by the movement of the sample, in
the applied magnetic flux. Taking into account the sample volume, the
magnitude of the applied magnetic field as well as demagnetising effects, the
measured magnetic moment can be converted into units of susceptibility
($\chi$) [20]. From the susceptibility as a function of temperature so
obtained, it is possible to determine the critical superconducting temperature
(T${}_{\text{C}}$) at which the material abruptly transitions from a small
positive susceptibility, corresponding to the antiferromagnetic state, to a
diamagnetic phase characterised by negative susceptibility. T${}_{\text{C}}$
can be defined in various ways, the onset of the transition and the midpoint
being the most popular ones. Throughout this paper we define the magnetic
susceptibility critical temperature ($T_{\text{C}}^{\chi}$) as the diamagnetic
saturation temperature obtained by fitting the data to a logistic function and
following the slope at the inflection point down to the lower asymptote as it
can be seen in Figure 2. This corresponds to the temperature at which a fully
coherent superconducting state is established in the sample.

Previous experimental studies have revealed a strong critical temperature
anisotropy in LSCO superconductors. Measurements performed with applied
magnetic field parallel to the a-b plane show a higher critical temperature as
well as an unexpected paramagnetic Meissner effect, recorded in the field
cooled process under low applied magnetic fields [21]. To avoid this
complication and in order to be able to directly compare our results with the
ones from the literature [22] we chose to measure the magnetic susceptibility
in the c-direction by using an applied magnetic field, H $=800$ A/m ($10$ Oe),
parallel to the c-axis (H$\|$c). For this the sample was aligned by hard X-ray
diffraction, and small cubic pieces ($\sim$ 1 mm length) were cut from the two
ends of the large single crystal, such that the c-axis was parallel to one of
facets. The $\chi(T)$ measurements were performed using the field cooling (FC)
protocol, where the sample is cooled from a temperature above T${}_{\text{C}}$
in a small static magnetic field (H = $800$ A/m ), while continuously
recording data. Around the predicted critical temperature, from 24 K to 15 K,
measurements have been taken every 0.5 K, while outside this range, larger
temperature steps have been employed, 2 K steps from 40 K to 24 K and 1 K
steps from 15 K down to 2 K. The measurement has revealed a mismatch in
transition temperature between the two samples originating from the two ends
of the main single crystal. One piece had a transition temperature,
$T_{\text{C}}^{\chi}$, of $14.43\pm 0.09$ K and the other a
$T_{\text{C}}^{\chi}$ of $15.54\pm 0.18$ K (See Figure 2). This mismatch in
critical temperature motivated the search for a non-destructive method that
would be able to reveal doping variations in the entire bulk of the sample.

Figure 2: Magnetic susceptibility data of the two the cubes cut from each of
the ends (A and B) of the single crystal sample. The deviation from $\chi=-1$
at low temperatures is due to magnetic flux trapping, which occurs when
cooling the sample through the phase transition in an applied magnetic field H
$=800$ A/m ($10$ Oe). See Figure 5 and eq. 5 for fitting procedure.

##  3 Polarised neutron imaging

In order to probe the doping distribution along the entire length of the
crystal in a non-destructive manner, we have performed polarised neutron
imaging experiments at the PONTO-III (V21) instrument at the BER II nuclear
reactor in Helmholtz-Zentrum Berlin. The instrumental set-up is shown in
Figure 3. The instrument makes use of a cold neutron beam which, for this
experiment, was monochromatized to 3.4 Å.

Figure 3: Sketch of the polarised neutron set-up used for the present
measurements. Adapted from [23].

The control of the initial spin state of the neutrons as well as the analysis
of their final spin state was done with the help of two super-mirror
polarisers placed before and after the sample. A guide field was used to keep
the neutron spin vertically aligned from the polariser up to the sample region
and mu-metal shielding was used just before the sample as well as between the
sample and the analyser. A single spin-flipper was used to select between
spin-up and spin-down measurements.

In a polarised neutron imaging experiment there are two main methods of
determining the superconducting critical temperature: by probing the Meissner
transition or by imaging the trapped magnetic flux inside the superconductor
as a function of temperature [23, 24]. In this study we employed the latter
method. This requires cooling the superconductor through its critical
temperature inside an applied magnetic field and performing the measurements
while heating up the sample without applied field. This way, one is able to
trap magnetic flux inside the superconductor and probe its release as the
sample returns to the normal, non-superconducting state.

The single crystal used in this study was aligned in the $(b-c)$ plane and
mounted on an aluminium sample holder inside a closed cycle refrigerator which
was able to reach temperatures as low as 4.5 K. During the cooling procedure,
a pair of Helmholtz coils were used to apply a horizontal magnetic field
parallel to the c-axis of the sample and perpendicular to the neutron beam
direction. The sample was slowly cooled from room temperature down to 100 K
with a rate of 2 K/min followed by a higher cooling rate of 5 K/min down to 40
K. An external magnetic field was applied and the sample was further cooled
below its superconducting critical temperature down to the base temperature of
the closed cycle refrigerator, thus trapping the magnetic flux inside the
sample. The external magnetic field was then switched off and radiographs were
recorded, by a scintillator - CCD camera detection ensemble (camera: Andor DV
$434$-BV, effective pixel size: $77$ $\upmu$m, 6LiFZnS scintillator thickness:
$400$ $\upmu$m [25]), at various temperatures during the heating process. The
horizontal divergence of the neutron beam was $0.34^{\circ}$ and the vertical
divergence was $1.28^{\circ}$.

Each image registers the polarisation of the neutron spin, in modulo 360∘,
analysed by the second super-mirror polariser placed between the sample and
the scintillator. As the neutron passes through the magnetic field trapped
inside the superconducting material, the spin will undergo a so-called Larmor
precession. The precession angle ($\phi$) is dependent on the strength of the
applied magnetic field and the time spent by the neutron inside it, which in
turn is dependent on the neutron velocity (and thereby on its wavelength) as
well as the length of the path through the magnetic field [23]:

$\displaystyle\phi=\frac{\gamma_{L}m}{h}BL\lambda.$ (1)

Here, $\gamma_{L}={-1.83247179(43)}\times 10^{8}$ rad s-1 T-1 is the neutron’s
gyromagnetic ratio, $h=6.62607015\times 10^{-34}$ J s is Plank’s constant,
$m=1.674927471(21)\times 10^{-27}$ kg is the mass of a neutron and $B,L$ and
$\lambda$ are the strength of the applied magnetic field, the length of the
neutron trajectory inside the field and the neutron wavelength respectively.

The magnitude of the applied magnetic field was of the order of a few milli-
tesla, and was tuned to provide the most contrast while keeping the maximum
precession angle below 180∘ in order to avoid ambiguity, as the measured
polarisation is the cosine of the (ensemble average of the) neutron spin
precession angle:

$\displaystyle P=\langle\cos(\phi)\rangle$ (2)

In our experiment the maximum measured precession angle was $\sim
105^{\circ}$.

Radiographs were recorded in two spin configurations: spin up and spin down,
with the spin of the neutron in both being perpendicular to the beam
direction. Spin down was selected by using an additional magnetic field to add
a neutron spin precession angle of 180∘ before the analyser. For normalisation
purposes, dark frame images (DF) without neutrons and in zero applied magnetic
field were recorded at room temperature (which means no trapped field in the
sample) so that noise in the detector systems could be corrected for. Open
beam images (OB) were recorded as well at room temperature, in the absence of
both the sample and the applied magnetic field, so that imperfections in the
polarisation setup could be corrected for.

The dark frame radiographs were subtracted from all the corresponding images,
including the open beam ones. The measuring time was 10 minutes per image
(composed of 4 exposures of 150 s combined after DF subtraction). The open
beam polarisation was calculated as:

$\displaystyle
P_{OB}=\frac{\uparrow_{OB}-\downarrow_{OB}}{\uparrow_{OB}+\downarrow_{OB}}$
(3)

where $\uparrow$ and $\downarrow$ indicate the radiographs taken with spin up
and down configuration, respectively. The uncorrected polarisation signal with
sample, $P_{UC}$, was measured and calculated in the same way, whereafter the
open beam corrected polarisation, $P$, was calculated as:

$\displaystyle P=\frac{P_{UC}}{P_{OB}}.$ (4)

Figure 4: Polarisation transmission images as a function of temperature in the
range 5 K to 20 K. The sample position (blue spot) can be seen in 5 K plot
where neutrons passing through the trapped magnetic field in the sample
undergo precession thereby moving the spin directions away from their initial
polarisation along $y$. Neutrons were travelling along $z$ and probing the
trapped magnetic field, which was along $x$. As the temperature is raised the
trapped field dissipates and no precession signal is observed. At 20 K the
trapped field is completely gone. Notice how different ends of the sample lose
their trapped field at different temperatures.

##  4 Results and discussion

###  4.1 The polarised imaging data

Figure 4 shows an image of the polarisation of the beam transmitted through
the sample, collected at six temperatures between 5 K and 20 K. In total, we
collected data in temperature steps of 1 K between 5 K and 34 K. The direction
of the field was along $x$, the neutrons were initially polarised along $y$,
and the polarisation analysis was also performed along $y$. To improve
counting statistics, the data was rebinned spatially by a factor of 6 along
$x$ and $y$ to an effective pixel size of $0.462\times 0.462$ mm2. At the
lowest temperature it can be seen that the entire LSCO sample causes a large
deviation of the neutron beam polarisation vector with respect to the initial
imposed direction (blue colour). In the sample centre, the polarisation even
reaches negative values, indicating a coherent rotation of the neutron
polarisation inside the sample. This we interpret as the result of a trapped
magnetic field. When the temperature is increased, the release of the trapped
magnetic field is found to take place at different temperatures for different
parts of the sample, as is evident from Figure 4. In particular, at 14 K only
the left part of the sample depolarises the beam (i.e. is still in the
superconducting state).

###  4.2 Determining the distribution of $T_{\text{C}}$

Figure 5: Example showing the fitting procedure for the central pixel of the
sample using equation 5 to find the transition temperature, $T_{\text{C}}$,
indicated by the shaded area.

In order to quantitatively assess the superconducting transition temperature,
$T_{\text{C}}$, for each pixel within the sample region, we first convert the
polarization data to spin precession angle through $\phi=\arccos{(P)}$, for
each temperature, $T$. Values for pixel polarisations that due to noise were
(slightly) larger than 1 were set to 1. Next, a logistic curve was fitted to
the precession angle data, as the logistic function describes the sigmoidal
nature of the phase transition between superconducting and non-superconducting
states, such that values for the critical transition temperature can be
extracted:

$\displaystyle\phi=\phi_{\textrm{min}}+\frac{\phi_{\textrm{max}}-\phi_{\textrm{min}}}{1+\textrm{e}^{-n_{H}\left(T-T_{\textrm{mid}}\right)}}.$
(5)

$\phi_{\textrm{min}}$ and $\phi_{\textrm{max}}$ are the low and high
asymptotes, respectively, $T_{\textrm{mid}}$ is the temperature at the
inflection point of the slope, and $n_{H}$ is Hill’s coefficient, giving the
steepness of the curve.

A fitting example for the centre-most pixel of the sample is shown in Figure
5. We define the critical temperature, $T_{\text{C}}^{\phi}$, as the
temperature where the trapped field is fully released. Within the logistics
model, we approximate this by following the slope at the inflection point down
to the lower asymptote as indicated by the dotted lines in the figure. The
shaded area indicates the uncertainty interval of the estimated
$T_{\text{C}}^{\phi}$, where the error estimate was obtained from error
propagation of the errors from the least square fit of the data, which was
weighed using the error from the counting statistics of the measurement. Note
that the low asymptote is non-zero, since a background magnetic field from the
experimental set-up was present for the experiments at the given temperatures.

Figure 6: Top left: The transition temperature mapped out across the sample.
Found using the method presented in Figure 5. The regions of interest (ROIs)
indicated are used for comparing to susceptibility measurements on sample
pieces that were adjacent to the ROIs (See Figure 7). Bottom: Transition
temperature along the length of the sample, with data averaged over the width
of the sample. Top right: Transition temperature along the width of the
sample, with data averaged over the length of the sample. Note that, due to
the vertical divergence, quantitative conclusions on the radial variation are
limited.

The same fitting procedure was used to find $T_{\text{C}}^{\phi}$ for every
pixel covered by the sample. The result is shown in Figure 6. A clear
variation of $T_{\text{C}}^{\phi}$ is observed along the length of the sample,
with a maximum $T_{\text{C}}^{\phi}$ of about 19 K at approximately 4 mm from
one sample end. $T_{\text{C}}^{\phi}$ then drops to about 16 K at the end
closest to the maximum and to 14 K at the opposite end. This corresponds to a
doping range $x\simeq 0.075-0.082$ [16, 8]. The doping range is in agreement
with the nominal doping of the crystal, its average value being exactly the
intended doping value ($x=0.080$) of the initial powder mixture. The variation
across the length of the crystal can be explained as a slight accumulation of
strontium atoms during one stage of the growth which in turn caused a
deficiency of dopant at other stages. Furthermore, our results suggest that
there is a radial variation of Sr distribution with more Sr at the sample
surface, however, due to limited vertical resolution this result warrants
further investigation. The required resolution is available at other neutron
imaging instruments such as RADEN at J-PARC MLF [26].

In order to rule out a possible temperature gradient, the polarised imaging
data was analysed to confirm that the temperature had stabilised before
exposures and that no fluctuations were seen afterwards. Previous studies,
with the same cryogenic setup, mention temperature variations of maximum 0.01
K [24].

Using the polarised neutron imaging method we were able to identify the
precise pattern of the critical temperature gradient, and implicitly the
doping distribution, along the entire 17.9 mm length of the sample, in the
growth direction. Considering that, within the TSFZ method, the molten zone is
continually mixed and the material crystallises layer by layer, we do not
expect a significant doping gradient in the radial direction. This can however
be investigated using the tomography capabilities of a polarised imaging set-
up. One of the advantages of using highly underdoped LSCO samples for this
type of investigation is the fact that in this region of the phase diagram
T${}_{\text{C}}$ varies steeply with doping, meaning that a small variation in
Sr concentration corresponds to a significant critical temperature difference.
However, using a high accuracy temperature control one would be able to
determine the doping variation in sample across the entire superconducting
dome, except the range $x=0.14-0.18$, where $T_{\rm C}$ is essentially
constant.

###  4.3 Validation of the polarised imaging method

Figure 7: Blue: Fit of precession angle, $\phi$, obtained by measuring
polarised neutron spin precession in a trapped magnetic field as function of
temperature. Red: Fit of susceptibility, $\chi$, measured on cut off sample
pieces that were adjacent to the two ROIs as indicated in Figure 6, ROI A
(Top) and ROI B (Bottom).

We have also benchmarked our imaging results against magnetic susceptibility
($\chi(T)$) data. In Figure 7, we show, in comparison, the susceptibility data
and the measurement of polarised neutron spin precession in trapped magnetic
field for the two ends of the sample (shown as the two panels in the figure).
As seen, the results from the two measurements are in agreement, if we define
$T^{\chi}_{\text{C}}$, from the susceptibility data, to be the temperature
where the negative susceptibility is saturated. Within errorbars, we find the
same difference between the two sample ends for the two measurement methods.
Due to the fact that the two methods are mapping different phenomena (one
follows the diamagnetic response of the superconductor while the other images
the expulsion of the trapped magnetic field as a function of temperature) a
precise definition of T${}_{\text{C}}$, to be applied to both measurements, is
very hard, if not impossible, to formulate. However, the great agreement we
are able to obtain by using the same fitting routine on the two data sets
indicates that a fully developed superconducting state is a prerequisite for
the formation of a vortex lattice and it proves that polarised neutron imaging
is a reliable method of determining the spatial variation of the
superconducting critical temperature and thus the doping level of
superconducting crystals.

Where the susceptibility method is more accurate (uncertainty around 0.1 K)
than the polarised imaging method (uncertainty around 0.5 K), the latter
method yields a complete picture of the sample and is furthermore non-
destructive. For this reason, we can imagine polarised imaging to be an
interesting alternative to susceptibility measurements for investigating the
spatial variations in transition temperatures, and doping implicitly, in
samples of centimetre sizes. Furthermore, by upgrading the instrumental
components and extending the exposure time (and/or neutron flux) the precision
of the measured transition temperature can be improved as it is currently
limited by counting statistics. The spatial resolution can be improved as well
down to 100 $\mu m$ [27].

##  5 Conclusion

Homogeneity of a sample is important when investigating the superconducting
properties, especially when performing bulk measurements. We have shown that
through spin-polarised neutron imaging it is possible to directly map out the
spatial distribution of the critical temperature thereby providing a
characterisation method capable of eliminating uncertainties and sources of
error related to – in this case – variations of the distribution of Sr doping
in a La2-xSrxCuO4 high temperature superconductor. The results have been
substantiated by magnetic susceptibility measurements showing the same trend
for the $T_{\text{C}}$ variation between the two ends of the sample.

Furthermore, as we are simply measuring a scalar property, our presented
method for mapping the $T_{\text{C}}$ distribution, can easily be expanded to
three dimensional investigations using standard filtered backprojection
methods for tomographic reconstructions.

## Acknowledgements

We would like to thank the Helmholtz Zentrum Berlin for granting us beam time
to perform the polarised imaging studies. The neutron scattering experiments
were supported by the Danish Agency for Research and Innovation through
DANSCATT. A.-E. Ţuţueanu was supported through the Institute Max von Laue Paul
Langevin (ILL) Ph.D. program. Y. Sassa was fully supported by a VR neutron
project grant (BIFROST, Dnr. 2016-06955) as well as a VR starting grant (Dnr.
2017-05078). The authors would like to thank Dr. Pierre Courtois and Philipp
Gausmann, from the ILL, for their help in cutting and aligning the crystals in
preparation for the magnetic susceptibility measurements.

## Author Contributions

The two authors, A.-E. Ţuţueanu and M. Sales, contributed equally to this
work.

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