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[orcid=0000-0001-5848-5520] [suffix=Jr.]

# Synthesis of Eu(HCOO)3 and Eu(HCOO)${}_{3}\cdot$(HCONH2)2 crystals and
observation of their 5D0 $\rightarrow$ 7F0 transition for quantum information
systems

Zachary W. Riedel  Donny R. Pearson  Manohar H. Karigerasi  Elizabeth A.
Goldschmidt<EMAIL_ADDRESS>Daniel P. Shoemaker<EMAIL_ADDRESS>Department of Materials Science and Engineering, University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, United States  Materials Research
Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois
61801, United States  Department of Physics, University of Illinois at Urbana-
Champaign, Urbana, Illinois 61801, United States  US Army Research Laboratory,
Adelphi, Maryland 20783, United States

###### Abstract

Two stoichiometric metal-organic frameworks containing Eu3+ cations are probed
as candidates for photon-based quantum information storage. Synthesis
procedures for growing 0.2 mm, rod-shaped Eu(HCOO)3 and 1-3 mm, rhombohedral
Eu(HCOO)${}_{3}\cdot$(HCONH2)2 single crystals are presented with visible
precipitation as soon as 1 h into heating for Eu(HCOO)3 and 24 h for
Eu(HCOO)${}_{3}\cdot$(HCONH2)2. Room temperature and 1.4 K photoluminescence
measurements of the 5D0 $\rightarrow$ 7FJ transitions of Eu3+ are analyzed for
both compounds. Comparisons of peak width and intensity are discussed along
with the notable first report for both of the 5D0 $\rightarrow$ 7F0
transition, the hyperfine structure of which has potential use in quantum
memory applications. The air instability of Eu(HCOO)${}_{3}\cdot$(HCONH2)2 and
the transformation of its photoluminescence properties are discussed.

###### keywords:

Luminescence Lifetime Crystal growth Quantum memory

##  1 Introduction

Stoichiometric compounds with lanthanide cations in crystallographic sites can
increase optical density for photon-based quantum information systems (QIS)
while also reducing the optical transitions’ inhomogeneous linewidths by
avoiding local strain and disorder due to doping. Such a reduction is required
to optically resolve the extremely long-lived hyperfine structure in these
ions, such as the 5D${}_{0}\rightarrow^{7}$F0 transition in Eu3+ [1, 2, 3].
Achieving this limit of inhomogeneous linewidth smaller than the splitting
between hyperfine levels is necessary to optically prepare the system in a
particular state, which would enable long-lived and efficient quantum memory
[2], quantum information processing [4, 5], quantum transduction [6], etc. [7]
Currently, only EuCl${}_{3}\cdot$6H2O has been shown to achieve this
inhomogeneous linewidth limit. Without isotopic purification, the 5D0
$\rightarrow$ 7F0 transition of Eu3+ with its advantageous hyperfine levels
has an inhomogeneous linewidth of 100 MHz in EuCl${}_{3}\cdot$6H2O [1].
Because of the proposed linear dependence of isotopic broadening on isotopes’
relative mass difference, atomic concentration, and natural abundance [8],
isotopic purification of EuCl${}_{3}\cdot$6H2O was performed for the Cl- ion.
The resulting 99.67% 35Cl purification reduced the linewidth to 25 MHz,
smaller than the material’s nearest-neighbor Eu3+ interactions ($\sim$40 MHz)
[9] and small enough to resolve the hyperfine structure [8]. But
EuCl${}_{3}\cdot$6H2O crystals are highly hygroscopic and unstable under
vacuum [1]. Therefore, selecting additional materials with low inhomogeneous
linewidths and improved environmental stability is critical for advancing the
study of stoichiometric rare-earth crystals for QIS. We identify and
synthesize two candidate stoichiometric europium-containing crystals and
investigate their structural and optical properties at room and cryogenic
temperatures. We find that both candidates can be grown from moderately heated
aqueous solutions in air, and exhibit the desired 7F0 $\rightarrow$ 5D0
transition with typical optical lifetime values.

Europium formate Eu(HCOO)3 [“EF”] and europium formate formamide
Eu(HCOO)${}_{3}\cdot$(HCONH2)2 [“EF$\cdot$FA”] are two promising candidates
for QIS applications. Both compounds can be obtained by solution precipitation
[10, 11] and have published crystal structures, shown in Figures 1 and 2 (EF:
CSD Entry ZZZVME01 [12], EF$\cdot$FA: ICSD Entry 251671 [13]). A procedure for
reliably producing mm-scale crystals that are environmentally stable is
necessary for practical use in a quantum memory device and for the possibility
of future photonic integration.

Figure 1: Crystal structure of Eu(HCOO)3 ($R3m$, $a$ = $b$ = 10.4972 Å, $c$ =
4.0011 Å, $\alpha$ = $\beta$ = 90∘, $\gamma$ = 120∘) [Eu: teal, H: white, C:
gray, O: red] Figure 2: Crystal structure of Eu(HCOO)${}_{3}\cdot$(HCONH2)2
($C2$, $a$ = 11.4164 Å, $b$ = 7.1985 Å, $c$ = 6.6405 Å, $\beta$ = 109.829∘)
[Eu: teal, H: white, C: gray, O: red, N: blue]

EF consists of Eu3+ cations nine-fold coordinated to formate groups that
bridge them. EF$\cdot$FA on the other hand has eight-fold coordinated Eu3+
cations with six Eu3+-bridging formate groups and two terminal formamide
groups. The compounds’ non-europium elements have a dominant naturally
abundant isotope (1H: 99.99%, 12C: 98.89%, 16O: 99.76%, 14N: 99.64%), reducing
the need for isotopic purification to promote a narrow optical linewidth.
Still, deuteration of the compounds would be expected to improve quantum
efficiency and transition coherence time [14]. Both have relatively large Eu3+
separation within the material ($\geq$4.001 Å in EF and $\geq$6.640 Å in
EF$\cdot$FA), which is desirable to prevent interactions between the Eu3+
optical centers.

##  2 Experimental Procedures

###  2.1 Synthesis

Numerous clear, faceted EF and EF$\cdot$FA crystals were produced from a
solution of formamide and de-ionized water. For both, Eu(NO3)${}_{3}\cdot$5H2O
(Sigma-Aldrich, 99.9% REO) was added to a 7 mL glass vial along with a 3.5 mL
solution of 98% formamide HCONH2 (Alfa Aesar, 99%) and 2% de-ionized H2O, by
volume. The Eu(NO3)${}_{3}\cdot$5H2O concentration was 0.05 M for EF and 0.075
M for EF$\cdot$FA. The solutions were gently swirled and inverted until the
powder was dissolved. The uncovered vials were heated for 48 h on a hot plate
with the solution temperature at 125∘C for EF and 65∘C for EF$\cdot$FA. A
camera periodically captured images of the crystal precipitation
(Supplementary Material). Gravity filtration was used to separate the crystals
from the reaction solution, followed by rinsing with ethanol and drying at
80∘C for 20 min.

###  2.2 Characterization

Scanning electron microscopy images were collected with a JEOL 6060LV SEM. A
Bruker D8 diffractometer equipped with a capillary mount was used for powder
X-ray diffraction. Confocal room temperature photoluminescence measurements on
individual crystals were obtained with 532 nm excitation on a Nanophoton Raman
11 microscope. A 405 nm laser and a SpectraPro 300i spectrograph were used to
collect 1.4 K and 298 K photoluminescence spectra. Samples were mounted
vertically with Cu tape on a Cu plate in a Janis 10DT liquid He bath cryostat.
Data were collected for a single EF$\cdot$FA crystal and for a cluster of EF
ones. For lifetime measurements, the fluorescent emission was collected with a
single-photon avalanche diode and accumulated into a histogram of 1500 time
bins with a bin width of 10 $\mu$s. The cryogenic EF$\cdot$FA data was
collected using 66.3 $\mu$W of excitation power with a 300 $\mu$s pulse
duration and was integrated for 6 min. The cryogenic EF data was collected
using 6.58 $\mu$W excitation power with a 100 $\mu$s pulse duration and was
integrated for 2.5 min. Inductively coupled plasma mass spectrometry (ICP-MS)
was performed with a PerkinElmer NexION 350D using standards with
concentrations as low as 0.5 ppm.

##  3 Results and Discussion

###  3.1 Crystal Growth

Many clusters of EF crystals formed with a Eu content yield of 71.1% after 48
h. Time lapse video showed visible precipitation from the solution beginning
after only 1 h of heating without the presence of a seed crystal. For
EF$\cdot$FA, rhombohedral crystals formed with a Eu content yield of 53.0%
after 48 h. Visible precipitation began around 24 h without a seed crystal. EF
and EF$\cdot$FA crystals appeared to form throughout the solution, with some
dropping to the bottom of the vial and some being stuck on the side of the
vial at the liquid-air interface. SEM images showed that the EF crystals had
nice facets but were frequently fused together and had smaller crystals
sitting on their surface; imaging of EF$\cdot$FA crystals consistently
revealed surface defects (Figure 3). The lengthier growth process of the
EF$\cdot$FA crystals at a lower temperature promoted the formation of larger
crystals with sides around 1 mm long (Figure 7). Moreover, introducing a seed
crystal to the same initial solution led to the formation of a EF$\cdot$FA
crystal with 3 mm sides along with additional 1 mm scale crystals. Seeding did
not lead to any obvious differences for EF.

Figure 3: (a) EF rod crystal with smaller EF crystals dotting the surface (b)
Cluster of EF crystals that have grown off each other (c,d) EF$\cdot$FA
rhombohedral crystals with surface defects

The faster growth of smaller EF crystals can be explained kinetically. The
hydrolysis of formamide produces ammonia and formic acid, thus providing the
formate ions incorporated in the two structures [10]. Three pathways for the
hydrolysis of formamide have been proposed, acid catalyzed, base catalyzed,
and neutral water catalyzed. The neutral catalyzed pathway, although advocated
for by experimental fitting [15] and a computational study [16], has been
rejected by some on the basis of its high calculated activation energy [17].
Still, Miyakawa et al. studied the hydrolysis kinetics and provided an
experimental fit to the first-order rate constant for formamide hydrolysis
based on H+ and OH- concentration [18]. pH paper measurements at the beginning
and end of the crystal growths indicate that the reaction solutions remain
approximately neutral during the growth, and the water content of the two
solutions, based on added DI H2O and Eu(NO3)${}_{3}\cdot$5H2O concentration,
are similar (4.8 mmol H2O for EF and 5.2 mmol for EF$\cdot$FA). Utilizing the
Miyakawa equations, at pH 7, the rate of hydrolysis in the 125∘C EF solution
(2.4$\times$10-7 s-1) should be 38 times larger than in the 65∘C EF$\cdot$FA
solution (6.3$\times$10-9 s-1). This indicates that formate ions should form
much more quickly in the EF solution, leading to the observed faster growth.

###  3.2 Room Temperature Photoluminescence

The room temperature emission spectra of EF and EF$\cdot$FA are shown in
Figure 4. Both show peaks for the 5D0 $\rightarrow$ 7FJ set of transitions.
Comparing the spectra with literature values [10, 11, 19, 20], the EF
transitions centered at 579, 592, 616, 650, and 696 nm are assigned to $J$ =
0, 1, 2, 3, 4, respectively, and for EF$\cdot$FA, the same transitions are
centered at 579, 591, 612, 650, and 701 nm. This is the first observation of
the 5D0 $\rightarrow$ 7F0 transition for either material.

The noticeably sharper transitions for EF indicate phonon broadening effects
associated with the differing ligands. Although many other Eu3+-containing
systems have demonstrated large broadening effects due to a higher degree of
crystallinity or a lower number of defects within the sample [21, 22, 23, 24,
25], those explanations do not hold here as even the EF$\cdot$FA crystals that
decompose into EF experience drastic transition sharpening (Supplementary
Material). Accompanying this sharpening is the appearance of additional peaks
around the 5D0 $\rightarrow$ 7F1 transition of EF. These peaks, presumably,
arise from rare-earth impurities in the precursor. Although Nd3+ has
absorption spectrum 4I9/2 $\rightarrow$ 4G5/2 \+ 2G7/2 peaks that overlap with
the 5D0 $\rightarrow$ 7F1 transition of Eu3+ [26, 27, 28] and Gd3+ has
emission peaks for 6GJ $\rightarrow$ 6PJ transitions in the same region [29],
neither cation was detected using ICP-MS. The extra peaks also appear in
samples decomposing from EF$\cdot$FA to EF, but in that case, they are lower
in intensity than the $J$ = 0 peak (Supplementary Material).

Figure 4: Photoluminescence emission spectra of EF (left column) and
EF$\cdot$FA (right column) recorded with an excitation wavelength of 532 nm.

The 5D0 $\rightarrow$ 7F1 and 5D0 $\rightarrow$ 7F2 transitions are frequently
used to compare local coordination environments of Eu3+. The intensity of the
induced electric dipole transition 5D0 $\rightarrow$ 7F2 is strongly dependent
on the environment of Eu3+ while the magnetic dipole transition 5D0
$\rightarrow$ 7F1 is mostly independent of it [19]. As a result, an increase
in the ratio of integrated intensities, I(5D0 $\rightarrow$ 7F2)/I(5D0
$\rightarrow$ 7F1), can indicate distortions from centrosymmetric geometry for
Eu3+ [30]. Both experimental EF and EF$\cdot$FA structures contain Eu3+ ions
in non-centrosymmetric sites ($C_{3v}$ symmetry in EF and $C_{2}$ in
EF$\cdot$FA), so large values ($\sim$2-4 [31, 32, 33]) of the parameter are
expected. These values are shown in the $J$ = 2 column of Table 1. The site in
EF, with its higher symmetry, shows a larger ratio than that of the ion in
EF$\cdot$FA. The EF$\cdot$FA value of 2.0 exceeds that reported previously of
1.75 [10]. Although these values were obtained at different excitation
wavelengths, they can be compared since the ratio’s excitation wavelength
dependence is associated with site selective excitation arising from multiple
Eu3+ sites in the material [34, 35, 36], and EF$\cdot$FA only has one Eu3+
crystallographic site.

Table 1:  Room temperature integrated intensities of 5D0 $\rightarrow$ 7FJ
peaks normalized to the magnetic dipole $J$ = 1 transition with sample
standard deviations in parentheses

Compound | $J=0$ | $J=1$ | $J=2$ | $J=3$ | $J=4$
---|---|---|---|---|---
EF | 0.0011 | 1.0 | 3.2 | 0.019 | 2.0
| (0.00026) | (-) | (0.14) | (0.0012) | (0.19)
EF$\cdot$FA | 0.0010 | 1.0 | 2.0 | 0.066 | 1.6
| (0.00018) | (-) | (0.17) | (0.028) | (0.48)

The appearance of the 5D0 $\rightarrow$ 7F3 transition for the two compounds
is also notable. This transition is forbidden by the Judd-Ofelt rules for
magnetic and electric dipole transitions, but crystal field induced J-mixing
can lead to the transition’s presence in the spectrum [19, 37, 38]. For
several compounds, the 7F3 state has been shown to mix with the 7F2 and 7F4
states [23, 38].

The hypersensitive 5D0 $\rightarrow$ 7F0 transition, although also forbidden,
is allowed for Eu3+ ions with non-cubic, non-centrosymmetric site symmetries
[30, 39]. Therefore, it can, by point symmetry, appear for EF and EF$\cdot$FA,
but it has not been reported previously for either. In the spectra normalized
to the maximum 5D0 $\rightarrow$ 7F2 peak height (Figure 4), the EF$\cdot$FA
5D0 $\rightarrow$ 7F0 peak appears approximately an order of magnitude larger
than the one in EF. However, when more appropriately compared through a
normalization to the integrated intensity of the environment independent 5D0
$\rightarrow$ 7F1 transition, the intensities of the 5D0 $\rightarrow$ 7F0
transitions in the two compounds are remarkably similar (Table 1).

###  3.3 Cryogenic Photoluminescence

Photoluminescence emission spectra for both compounds were collected at 1.4 K
in order to increase the intensity of the 5D0 $\rightarrow$ 7FJ transitions
and to eliminate phonon broadening. Figure 5 shows these spectra along with
room temperature spectra collected with the same mounting setup for
comparison. Even at low laser power, the $J$ = 0 transition is clearly seen
for both compounds. The integrated intensity of the transition’s peak relative
to those of $J$ = 1 is now 0.11 for EF and EF$\cdot$FA, 100x larger than in
the room temperature data in Table 1.

The EF$\cdot$FA peaks are noticeably less broad than at room temperature and
have comparable widths to those of EF. This further confirms that
EF$\cdot$FA’s broad room temperature spectrum is a product of phonon effects,
which are mitigated at 1.4 K. Moreover, the improved resolution allows for the
observation of additional splittings in the EF$\cdot$FA $J$ = 1 and $J$ = 2
peaks. The splitting of the $J$ = 1 peak is indicative of the site symmetry of
the Eu3+ ion. The transition in EF has two components, as could be seen at
room temperature, and the expected three components of the transition for
EF$\cdot$FA [40] are now resolved at 1.4 K.

Both compounds experience peak shifts to longer wavelengths at 1.4 K. In other
Eu3+ systems, as temperatures lower, 5D0 $\rightarrow$ 7FJ transition red-
shifts are typically noted [41, 42, 43]. Here, for the most prominent $J$ = 2
peak for each compound in the 405 nm data (Figure 5), the shifts are +0.09 nm
for EF and +0.04 nm for EF$\cdot$FA, quite small for both. To compare the $J$
= 0 peak positions, observed in the 532 nm room temperature and the 405 nm 1.4
K spectra, it must be noted that the 405 nm room temperature spectrum has a
peak shift of +0.30 nm compared to the 532 nm room temperature data. This is
likely due to a difference in the calibration techniques for the two
instrument setups and needs to be accounted for when comparing the $J$ = 0
peak positions. Since the maxima of the $J$ = 0 peaks in the 532 nm room
temperature data are at 579.19 nm for EF and 579.13 nm for EF$\cdot$FA and are
at 580.20 nm (+1.01 nm) for EF and 580.11 nm (+0.98 nm) for EF$\cdot$FA in the
405 nm 1.4 K data, the corrected shifts are roughly +0.71 nm for EF and +0.68
nm for EF$\cdot$FA. The peak shifts, therefore, vary between the Eu3+
transitions but are fairly consistent between the two compounds.

Figure 5: Photoluminescence data collected at 1.4 K using an excitation
wavelength of 405 nm with the 5D0 $\rightarrow$ 7FJ transitions labelled. The
$J$ = 0 peak appears for both while it is not visible at the same collection
times at room temperature.

Figure 6: (left) Room temperature photoluminescence decay and (right) 1.4 K
photoluminescence decay using an excitation wavelength of 405 nm.

###  3.4 Photoluminescence Lifetime

While a room temperature photoluminescence lifetime for EF’s 5D0 level has
previously been reported as 1.06 ms [11], the cryogenic value has not been
reported, and no lifetime measurements have been reported for EF$\cdot$FA. The
room temperature lifetime of EuCl${}_{3}\cdot$6H2O, the other stoichoimetric
rare-earth crystal studied for QIS, is 0.130 ms [44]. Lifetime plots are shown
in Figure 6.

Photoluminescence decay was observed using 405 nm excitation pulses where the
pulse duration, $t_{exc}$, is short compared to the observed lifetime, $\tau$.
The excitation pulses were transmitted to the samples through a short-pass
dichroic mirror. Photoluminescence emission from the materials was then
collected from the dichroic mirror reflection, passed through a pair of 550 nm
long-pass filters, and sent to a single-photon avalanche diode (SPAD) via
coupling into a multi-mode fiber. The collected emission was then averaged
over many cycles. Further details can be found in the Supplementary Material.
The decay for both materials was fitted to a single-exponential with a
vertical offset to account for background and dark counts.

The room temperature lifetime of EF, 1.10$\pm$0.01 ms, is similar to that
reported previously, and the room temperature lifetime of EF$\cdot$FA is
1.24$\pm$0.01 ms. The cryogenic lifetimes for EF (1.57$\pm$0.01 ms) and for
EF$\cdot$FA (1.43$\pm$0.01 ms) exceed by an order of magnitude the lifetime
observed for EuCl${}_{3}\cdot$6H2O below 4 K (0.116$\pm$0.001 ms) but are
shorter than its deuterium analog (2.6 ms) [14]. Both compounds show an
increase in lifetime with decreasing temperature. An increase is common in
Eu3+ compounds [45, 46, 47, 48, 49, 50, 51], but this trend is occasionally
not consistent [52, 53], notably in the case of EuCl${}_{3}\cdot$6H2O [14,
44].

###  3.5 Phase Stability

Both synthesis procedures produce phase pure crystals as confirmed by powder
X-ray diffraction. Over time, however, with exposure to air, EF$\cdot$FA
crystals form a film of EF on their surface, giving them a cloudy appearance
before eventually appearing opaque (Figure 7). This transformation is also
confirmed by single crystal X-ray diffraction, showing diffraction spots
corresponding to EF$\cdot$FA and powder rings corresponding to EF
(Supplementary Material).

Figure 7: (left) EF$\cdot$FA crystal with $\sim$1 mm sides shown after growth
and (right) after a week in air. The crystals form a film of EF on the surface
before transforming further into an opaque crystal. Figure 8: Powder X-ray
diffraction data demonstrating the complete decomposition of EF$\cdot$FA
(right column) into EF and the stability of EF (left column) over time when
stored in air.

The complete structural transformation to EF is not immediate, but high
humidity will cause significant changes in the material’s optical properties
after only a day as the room temperature photoluminescence pattern shifts
quickly from that of EF$\cdot$FA to that of EF. The decomposition of five
crystals was monitored during storage in air at 50-55% relative humidity. In
particular, the distinguishing I(5D0 $\rightarrow$ 7F2)/I(5D0 $\rightarrow$
7F1) ratio, noted before for its sensitivity to crystal symmetry, was tracked
as a measure of spectrum transformation. Full transformation of the emission
spectrum occurred in a week. Plots and images detailing this transformation
are provided in the Supplementary Material. Powder X-ray diffraction of
crushed EF$\cdot$FA crystals stored in air showed a full phase transformation
into EF after a year (Figure 8). The storage of EF$\cdot$FA in a desiccator or
inert atmosphere prevents this decomposition into EF. On the other hand, EF
remains stable over the same period of time.

##  4 Conclusions

Quick synthesis procedures were developed for forming faceted 0.2 mm crystals
of EF and 1-3 mm crystals of EF$\cdot$FA. The first reported recording of the
5D0 $\rightarrow$ 7F0 transition was shown for EF and EF$\cdot$FA. Emission
spectra at 1.4 K revealed a one hundred fold increase in the relative
intensity of the transition and a reduction in phonon broadening effects for
EF$\cdot$FA. The 5D0 $\rightarrow$ 7F0 peak for both materials shifted by
roughly +0.7 nm upon cooling. The materials exhibit lifetimes of 1.57 ms and
1.43 ms at 1.4 K for EF and EF$\cdot$FA, respectively. The decomposition of
the EF$\cdot$FA crystals into EF due to air exposure was shown and eliminated
by storage in a desiccator or inert atmosphere. EF remains stable in air over
time. Photoluminescence excitation will be necessary to probe the materials’
5D0 $\rightarrow$ 7F0 hyperfine structures at cryogenic temperatures.

##  5 Acknowledgements

Research for this work was carried out in part in the Materials Research
Laboratory Central Research Facilities, University of Illinois. This work is
supported by the U.S. Department of Energy, Office of Science, National
Quantum Information Science Research Centers. Z.W.R. was supported by a DIGI-
MAT fellowship from the NSF DGE program, Award No. 1922758.

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